text:
Man (disambiguation)

A man is an adult male of the modern human species, its individuals, and nearest extinct relatives. See also man (word) for the etymology.

Man or MAN may also refer to:

Places

 * Isle of Man, located in the Irish Sea, part of the British Isles
 * Man Island (Andaman and Nicobar Islands), a small uninhabited island in the Bay of Bengal
 * Man (Vidhan Sabha constituency), political district in India
 * Man Department, Ivory Coast
 * Man, Ivory Coast, a town and capital of the department
 * Roman Catholic Diocese of Man, Ivory Coast
 * Man, West Virginia, a town in the United States
 * Man., abbreviation for Manitoba, a Canadian province
 * Man, Vikramgad, a village in Maharashtra, India
 * Manchester Airport's IATA airport code
 * Manchester Piccadilly station's National Rail station code MAN

Music

 * Man (band), a Welsh progressive rock group
 * Man (Man album), 1971
 * Man (Neneh Cherry album), the third solo album by Swedish singer Neneh Cherry, released in 1996
 * "Man" (Skepta song), 2016
 * "Man" (JoJo song), 2020
 * "Man", a 1989 song on the album Staring at the Sun by Level 42
 * "Man", a 2003 song on the album Fever to Tell by the Yeah Yeah Yeahs
 * "Man", a 2016 song on the album Air for Free by Relient K
 * "Man", a 2018 song on the album Blue Madonna by Børns
 * "Man", a song by the band The Worst featured in the 2020 Netflix crime documentary series, Unabomber: In His Own Words.

Businesses

 * MAN Truck & Bus, a German engineering company that manufactures (amongst other things) buses and trucks
 * Man Group plc, a British financial services company
 * The stock symbol of Manpower, Inc., an American employment agency

Political organizations

 * Marea Adunare Naţională, the Great National Assembly in Communist Romania
 * Mongolian People's Party, a political party in Mongolia (Монгол Ардын Нам)
 * Movement of Arab Nationalists
 * Movimento de Acção Nacional or the National Action Movement (Portugal)
 * Movimiento de Acción Nacional or the National Action Movement (Venezuela)
 * National Alternative Movement, a political party in Moldova (Mișcarea Alternativa Națională)
 * Partido MAN (Movementu Antia Nobo or New Antilles Movement), a political party in Curaçao

Computing

 * Metropolitan area network, large computer networks usually spanning a campus or a city
 * The "man" command, used to retrieve a man page, a software documentation page on Unix and Unix-like operating systems

People

 * Edward Man (1549–1622), English politician

Other uses

 * A chess piece or pawn; sometimes the word "piece" is defined to exclude pawns.
 * Man!, American anarchist periodical, 1933–1940
 * Man (name) (includes a list of people with the name)
 * The Man, derisive slang phrase for higher authority
 * Man or Nanman, ancient Chinese ethnic group
 * Standard romanization of the Manchu people
 * Man (Middle-earth), people in the writings of J. R. R. Tolkien
 * Man (journal) (1901–1994), continued by The Journal of the Royal Anthropological Institute
 * Man (unit), an ancient Arabic and Persian unit of mass
 * "Man", a statue by Virgil Cantini
 * Ultraman, a Japanese television series often referred to as "Man"
 * In neo-pagan Germanic mysticism, the alternative name of the Norse Algiz rune, where it is used as a purported life rune

title: Man (disambiguation)


text:
Sliding mode control

In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior. The state-feedback control law is not a continuous function of time. Instead, it can switch from one continuous structure to another based on the current position in the state space. Hence, sliding mode control is a variable structure control method. The multiple control structures are designed so that trajectories always move toward an adjacent region with a different control structure, and so the ultimate trajectory will not exist entirely within one control structure. Instead, it will slide along the boundaries of the control structures. The motion of the system as it slides along these boundaries is called a sliding mode and the geometrical locus consisting of the boundaries is called the sliding (hyper)surface. In the context of modern control theory, any variable structure system, like a system under SMC, may be viewed as a special case of a hybrid dynamical system as the system both flows through a continuous state space but also moves through different discrete control modes.

Introduction

Figure 1 shows an example trajectory of a system under sliding mode control. The sliding surface is described by $$s=0$$, and the sliding mode along the surface commences after the finite time when system trajectories have reached the surface. In the theoretical description of sliding modes, the system stays confined to the sliding surface and need only be viewed as sliding along the surface. However, real implementations of sliding mode control approximate this theoretical behavior with a high-frequency and generally non-deterministic switching control signal that causes the system to "chatter" in a tight neighborhood of the sliding surface. Chattering can be reduced through the use of deadbands or boundary layers around the sliding surface, or other compensatory methods. Although the system is nonlinear in general, the idealized (i.e., non-chattering) behavior of the system in Figure 1 when confined to the $$s=0$$ surface is an LTI system with an exponentially stable origin. One of the compensatory methods is the adaptive sliding mode control method proposed in which uses estimated uncertainty to construct continuous control law. In this method chattering is eliminated while preserving accuracy (for more details see references [2] and [3]). The three distinguished features of the proposed adaptive sliding mode controller are as follows: (i) The structured (or parametric) uncertainties and unstructured uncertainties (un-modeled dynamics, unknown external disturbances) are synthesized into a single type uncertainty term called lumped uncertainty. Therefore, a linearly parameterized dynamic model of the system is not required, and the simple structure and computationally efficient properties of this approach make it suitable for the real-time control applications. (ii) The adaptive sliding mode control scheme design relies on the online estimated uncertainty vector rather than relying on the worst-case scenario (i.e., bounds of uncertainties). Therefore, a-priory knowledge of the bounds of uncertainties is not required, and at each time instant, the control input compensates for the uncertainty that exists. (iii) The developed continuous control law using fundamentals of the sliding mode control theory eliminates the chattering phenomena without trade-off between performance and robustness, which is prevalent in boundary-layer approach.

Intuitively, sliding mode control uses practically infinite gain to force the trajectories of a dynamic system to slide along the restricted sliding mode subspace. Trajectories from this reduced-order sliding mode have desirable properties (e.g., the system naturally slides along it until it comes to rest at a desired equilibrium). The main strength of sliding mode control is its robustness. Because the control can be as simple as a switching between two states (e.g., "on"/"off" or "forward"/"reverse"), it need not be precise and will not be sensitive to parameter variations that enter into the control channel. Additionally, because the control law is not a continuous function, the sliding mode can be reached in finite time (i.e., better than asymptotic behavior). Under certain common conditions, optimality requires the use of bang–bang control; hence, sliding mode control describes the optimal controller for a broad set of dynamic systems.

One application of sliding mode controller is the control of electric drives operated by switching power converters. Because of the discontinuous operating mode of those converters, a discontinuous sliding mode controller is a natural implementation choice over continuous controllers that may need to be applied by means of pulse-width modulation or a similar technique of applying a continuous signal to an output that can only take discrete states. Sliding mode control has many applications in robotics. In particular, this control algorithm has been used for tracking control of unmanned surface vessels in simulated rough seas with high degree of success.

Sliding mode control must be applied with more care than other forms of nonlinear control that have more moderate control action. In particular, because actuators have delays and other imperfections, the hard sliding-mode-control action can lead to chatter, energy loss, plant damage, and excitation of unmodeled dynamics. Continuous control design methods are not as susceptible to these problems and can be made to mimic sliding-mode controllers.

Control scheme
Consider a nonlinear dynamical system described by

where
 * $$\mathbf{x}(t) \triangleq \begin{bmatrix}x_1(t)\\x_2(t)\\\vdots\\x_{n-1}(t)\\x_n(t)\end{bmatrix} \in \mathbb{R}^n$$

is an $$-dimensional state vector and
 * $$\mathbf{u}(t) \triangleq \begin{bmatrix}u_1(t)\\u_2(t)\\\vdots\\u_{m-1}(t)\\u_m(t)\end{bmatrix} \in \mathbb{R}^m$$

is an $n$-dimensional input vector that will be used for state feedback. The functions $$f: \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}^n$$ and $$B: \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}^{n \times m}$$ are assumed to be continuous and sufficiently smooth so that the Picard–Lindelöf theorem can be used to guarantee that solution $$\mathbf{x}(t)$$ to Equation ($m$) exists and is unique.

A common task is to design a state-feedback control law $$\mathbf{u}(\mathbf{x}(t))$$ (i.e., a mapping from current state $$\mathbf{x}(t)$$ at time $$ to the input $$\mathbf{u}$$) to stabilize the dynamical system in Equation ($t$) around the origin $$\mathbf{x} = [0, 0, \ldots, 0]^\intercal$$. That is, under the control law, whenever the system is started away from the origin, it will return to it. For example, the component $$x_1$$ of the state vector $$\mathbf{x}$$ may represent the difference some output is away from a known signal (e.g., a desirable sinusoidal signal); if the control $$\mathbf{u}$$ can ensure that $$x_1$$ quickly returns to $$x_1 = 0$$, then the output will track the desired sinusoid. In sliding-mode control, the designer knows that the system behaves desirably (e.g., it has a stable equilibrium) provided that it is constrained to a subspace of its configuration space. Sliding mode control forces the system trajectories into this subspace and then holds them there so that they slide along it. This reduced-order subspace is referred to as a sliding (hyper)surface, and when closed-loop feedback forces trajectories to slide along it, it is referred to as a sliding mode of the closed-loop system. Trajectories along this subspace can be likened to trajectories along eigenvectors (i.e., modes) of LTI systems; however, the sliding mode is enforced by creasing the vector field with high-gain feedback. Like a marble rolling along a crack, trajectories are confined to the sliding mode.

The sliding-mode control scheme involves Because sliding mode control laws are not continuous, it has the ability to drive trajectories to the sliding mode in finite time (i.e., stability of the sliding surface is better than asymptotic). However, once the trajectories reach the sliding surface, the system takes on the character of the sliding mode (e.g., the origin $$\mathbf{x}=\mathbf{0}$$ may only have asymptotic stability on this surface).
 * 1) Selection of a hypersurface or a manifold (i.e., the sliding surface) such that the system trajectory exhibits desirable behavior when confined to this manifold.
 * 2) Finding feedback gains so that the system trajectory intersects and stays on the manifold.

The sliding-mode designer picks a switching function $$\sigma: \mathbb{R}^n \to \mathbb{R}^m$$ that represents a kind of "distance" that the states $$\mathbf{x}$$ are away from a sliding surface. The sliding-mode-control law switches from one state to another based on the sign of this distance. So the sliding-mode control acts like a stiff pressure always pushing in the direction of the sliding mode where $$\sigma(\mathbf{x}) = 0$$. Desirable $$\mathbf{x}(t)$$ trajectories will approach the sliding surface, and because the control law is not continuous (i.e., it switches from one state to another as trajectories move across this surface), the surface is reached in finite time. Once a trajectory reaches the surface, it will slide along it and may, for example, move toward the $$\mathbf{x} = \mathbf{0}$$ origin. So the switching function is like a topographic map with a contour of constant height along which trajectories are forced to move.
 * A state $$\mathbf{x}$$ that is outside of this sliding surface has $$\sigma(\mathbf{x}) \neq 0$$.
 * A state that is on this sliding surface has $$\sigma(\mathbf{x}) = 0$$.

The sliding (hyper)surface/manifold is typically of dimension $$n-m $$ where $$ is the number of states in $$\mathbf{x}$$ and $n$ is the number of input signals (i.e., control signals) in $$\mathbf{u}$$. For each control index $$1 \leq k \leq m$$, there is an $$(n-1)$$-dimensional sliding surface given by

The vital part of SMC design is to choose a control law so that the sliding mode (i.e., this surface given by $$\sigma(\mathbf{x})=\mathbf{0}$$) exists and is reachable along system trajectories. The principle of sliding mode control is to forcibly constrain the system, by suitable control strategy, to stay on the sliding surface on which the system will exhibit desirable features. When the system is constrained by the sliding control to stay on the sliding surface, the system dynamics are governed by reduced-order system obtained from Equation ($m$).

To force the system states $$\mathbf{x}$$ to satisfy $$\sigma(\mathbf{x}) = \mathbf{0}$$, one must:
 * 1) Ensure that the system is capable of reaching $$\sigma(\mathbf{x}) = \mathbf{0}$$ from any initial condition
 * 2) Having reached $$\sigma(\mathbf{x})=\mathbf{0}$$, the control action is capable of maintaining the system at $$\sigma(\mathbf{x})=\mathbf{0}$$

Existence of closed-loop solutions
Note that because the control law is not continuous, it is certainly not locally Lipschitz continuous, and so existence and uniqueness of solutions to the closed-loop system is not guaranteed by the Picard–Lindelöf theorem. Thus the solutions are to be understood in the Filippov sense. Roughly speaking, the resulting closed-loop system moving along $$\sigma(\mathbf{x}) = \mathbf{0}$$ is approximated by the smooth dynamics $$\dot{\sigma}(\mathbf{x}) = \mathbf{0};$$ however, this smooth behavior may not be truly realizable. Similarly, high-speed pulse-width modulation or delta-sigma modulation produces outputs that only assume two states, but the effective output swings through a continuous range of motion. These complications can be avoided by using a different nonlinear control design method that produces a continuous controller. In some cases, sliding-mode control designs can be approximated by other continuous control designs.

Theoretical foundation
The following theorems form the foundation of variable structure control.

Theorem 1: Existence of sliding mode
Consider a Lyapunov function candidate where $$\|\mathord{\cdot}\|$$ is the Euclidean norm (i.e., $$\|\sigma(\mathbf{x})\|_2$$ is the distance away from the sliding manifold where $$\sigma(\mathbf{x})=\mathbf{0}$$). For the system given by Equation ($$) and the sliding surface given by Equation ($$), a sufficient condition for the existence of a sliding mode is that
 * $$ \underbrace{ \overbrace{\sigma^\intercal}^{\tfrac{\partial V}{\partial \sigma}} \overbrace{\dot{\sigma}}^{\tfrac{\operatorname{d} \sigma}{\operatorname{d} t}} }_{\tfrac{\operatorname{d}V}{\operatorname{d}t}} < 0 \qquad \text{(i.e., } \tfrac{\operatorname{d}V}{\operatorname{d}t} < 0 \text{)} $$

in a neighborhood of the surface given by $$\sigma(\mathbf{x})=0$$.

Roughly speaking (i.e., for the scalar control case when $$m=1$$), to achieve $$\sigma^\intercal \dot{\sigma} < 0$$, the feedback control law $$ u(\mathbf{x}) $$ is picked so that $$\sigma$$ and $$\dot{\sigma}$$ have opposite signs. That is, Note that
 * $$u(\mathbf{x})$$ makes $$\dot{\sigma}(\mathbf{x})$$ negative when $$\sigma(\mathbf{x})$$ is positive.
 * $$u(\mathbf{x})$$ makes $$\dot{\sigma}(\mathbf{x})$$ positive when $$\sigma(\mathbf{x})$$ is negative.
 * $$\dot{\sigma}

= \frac{\partial \sigma}{\partial \mathbf{x}} \overbrace{\dot{\mathbf{x}}}^{\tfrac{\operatorname{d} \mathbf{x}}{\operatorname{d} t}} = \frac{\partial \sigma}{\partial \mathbf{x}} \overbrace{\left( f(\mathbf{x},t) + B(\mathbf{x},t) \mathbf{u} \right)}^{\dot{\mathbf{x}}}$$ and so the feedback control law $$\mathbf{u}(\mathbf{x})$$ has a direct impact on $$\dot{\sigma}$$.

Reachability: Attaining sliding manifold in finite time
To ensure that the sliding mode $$\sigma(\mathbf{x})=\mathbf{0}$$ is attained in finite time, $$\operatorname{d}V/{\operatorname{d}t}$$ must be more strongly bounded away from zero. That is, if it vanishes too quickly, the attraction to the sliding mode will only be asymptotic. To ensure that the sliding mode is entered in finite time,
 * $$\frac{\operatorname{d}V}{\operatorname{d}t} \leq -\mu (\sqrt{V})^{\alpha}$$

where $$\mu > 0$$ and $$0 < \alpha \leq 1$$ are constants.

Explanation by comparison lemma
This condition ensures that for the neighborhood of the sliding mode $$V \in [0,1]$$,
 * $$\frac{\operatorname{d}V}{\operatorname{d}t} \leq -\mu (\sqrt{V})^{\alpha} \leq -\mu \sqrt{V}.$$

So, for $$V \in (0,1]$$,
 * $$\frac{ 1 }{ \sqrt{V} } \frac{\operatorname{d}V}{\operatorname{d}t} \leq -\mu,$$

which, by the chain rule (i.e., $$\operatorname{d}W/{\operatorname{d}t}$$ with $$W \triangleq 2 \sqrt{V}$$), means
 * $$\mathord{\underbrace{D^+ \Bigl( \mathord{\underbrace{2 \mathord{\overbrace{\sqrt{V}}^{ {} \propto \|\sigma\|_2}}}_{W}} \Bigr)}_{D^+ W \, \triangleq \, \mathord{\text{Upper right-hand } \dot{W}}}} = \frac{ 1 }{ \sqrt{V} } \frac{\operatorname{d}V}{\operatorname{d}t} \leq -\mu$$

where $$D^+$$ is the upper right-hand derivative of $$2 \sqrt{V}$$ and the symbol $$\propto$$ denotes proportionality. So, by comparison to the curve $$z(t) = z_0 - \mu t$$ which is represented by differential equation $$\dot{z} = -\mu$$ with initial condition $$z(0)=z_0$$, it must be the case that $$2 \sqrt{V(t)} \leq V_0 - \mu t$$ for all $$. Moreover, because $$\sqrt{V} \geq 0$$, $$\sqrt{V}$$ must reach $$\sqrt{V}=0$$ in finite time, which means that $$ must reach $$V=0$$ (i.e., the system enters the sliding mode) in finite time. Because $$\sqrt{V}$$ is proportional to the Euclidean norm $$\|\mathord{\cdot}\|_2$$ of the switching function $$\sigma$$, this result implies that the rate of approach to the sliding mode must be firmly bounded away from zero.

Consequences for sliding mode control
In the context of sliding mode control, this condition means that
 * $$ \underbrace{ \overbrace{\sigma^\intercal}^{\tfrac{\partial V}{\partial \sigma}} \overbrace{\dot{\sigma}}^{\tfrac{\operatorname{d} \sigma}{\operatorname{d} t}} }_{\tfrac{\operatorname{d}V}{\operatorname{d}t}} \leq -\mu ( \mathord{\overbrace{\| \sigma \|_2}^{\sqrt{V}}} )^{\alpha}$$

where $$\|\mathord{\cdot}\|$$ is the Euclidean norm. For the case when switching function $$\sigma$$ is scalar valued, the sufficient condition becomes
 * $$ \sigma \dot{\sigma} \leq -\mu |\sigma|^{\alpha} $$.

Taking $$\alpha =1$$, the scalar sufficient condition becomes
 * $$ \operatorname{sgn}(\sigma) \dot{\sigma} \leq -\mu $$

which is equivalent to the condition that
 * $$ \operatorname{sgn}(\sigma) \neq \operatorname{sgn}(\dot{\sigma})

\qquad \text{and} \qquad That is, the system should always be moving toward the switching surface $$\sigma = 0$$, and its speed $$|\dot{\sigma}|$$ toward the switching surface should have a non-zero lower bound. So, even though $$\sigma$$ may become vanishingly small as $$\mathbf{x}$$ approaches the $$\sigma(\mathbf{x})=\mathbf{0}$$ surface, $$\dot{\sigma}$$ must always be bounded firmly away from zero. To ensure this condition, sliding mode controllers are discontinuous across the $$\sigma = 0$$ manifold; they switch from one non-zero value to another as trajectories cross the manifold.
 * \dot{\sigma}| \geq \mu > 0$$.

Theorem 2: Region of attraction
For the system given by Equation ($$) and sliding surface given by Equation ($t$), the subspace for which the $$\{ \mathbf{x} \in \mathbb{R}^n : \sigma(\mathbf{x})=\mathbf{0} \}$$ surface is reachable is given by
 * $$\{ \mathbf{x} \in \mathbb{R}^n : \sigma^\intercal(\mathbf{x})\dot{\sigma}(\mathbf{x}) < 0 \}$$

That is, when initial conditions come entirely from this space, the Lyapunov function candidate $$V(\sigma)$$ is a Lyapunov function and $$\mathbf{x}$$ trajectories are sure to move toward the sliding mode surface where $$\sigma( \mathbf{x} ) = \mathbf{0}$$. Moreover, if the reachability conditions from Theorem 1 are satisfied, the sliding mode will enter the region where $$\dot{V}$$ is more strongly bounded away from zero in finite time. Hence, the sliding mode $$\sigma = 0$$ will be attained in finite time.

Theorem 3: Sliding motion
Let
 * $$ \frac{\partial \sigma}{\partial{\mathbf{x}}} B(\mathbf{x},t) $$

be nonsingular. That is, the system has a kind of controllability that ensures that there is always a control that can move a trajectory to move closer to the sliding mode. Then, once the sliding mode where $$ \sigma(\mathbf{x}) = \mathbf{0} $$ is achieved, the system will stay on that sliding mode. Along sliding mode trajectories, $$\sigma(\mathbf{x})$$ is constant, and so sliding mode trajectories are described by the differential equation
 * $$\dot{\sigma} = \mathbf{0}$$.

If an $$\mathbf{x}$$-equilibrium is stable with respect to this differential equation, then the system will slide along the sliding mode surface toward the equilibrium.

The equivalent control law on the sliding mode can be found by solving
 * $$ \dot\sigma(\mathbf{x})=0 $$

for the equivalent control law $$\mathbf{u}(\mathbf{x})$$. That is,

\frac{\partial \sigma}{\partial \mathbf{x}} \overbrace{\left( f(\mathbf{x},t) + B(\mathbf{x},t) \mathbf{u} \right)}^{\dot{\mathbf{x}}} = \mathbf{0}$$ and so the equivalent control
 * $$\mathbf{u} = -\left( \frac{\partial \sigma}{\partial \mathbf{x}} B(\mathbf{x},t) \right)^{-1} \frac{\partial \sigma}{\partial \mathbf{x}} f(\mathbf{x},t)$$

That is, even though the actual control $$\mathbf{u}$$ is not continuous, the rapid switching across the sliding mode where $$\sigma(\mathbf{x})=\mathbf{0}$$ forces the system to act as if it were driven by this continuous control.

Likewise, the system trajectories on the sliding mode behave as if
 * $$\dot{\mathbf{x}} = \overbrace{f(\mathbf{x},t) - B(\mathbf{x},t) \left( \frac{\partial \sigma}{\partial \mathbf{x}} B(\mathbf{x},t) \right)^{-1} \frac{\partial \sigma}{\partial \mathbf{x}} f(\mathbf{x},t)}^{f(\mathbf{x},t) + B(\mathbf{x},t) u} = f(\mathbf{x},t)\left( \mathbf{I} - B(\mathbf{x},t) \left( \frac{\partial \sigma}{\partial \mathbf{x}} B(\mathbf{x},t) \right)^{-1} \frac{\partial \sigma}{\partial \mathbf{x}} \right)$$

The resulting system matches the sliding mode differential equation
 * $$\dot{\sigma}(\mathbf{x}) = \mathbf{0}$$

, the sliding mode surface $$\sigma(\mathbf{x})=\mathbf{0}$$, and the trajectory conditions from the reaching phase now reduce to the above derived simpler condition. Hence, the system can be assumed to follow the simpler $$\dot{\sigma} = 0$$ condition after some initial transient during the period while the system finds the sliding mode. The same motion is approximately maintained when the equality $$ \sigma(\mathbf{x}) = \mathbf{0} $$ only approximately holds.

It follows from these theorems that the sliding motion is invariant (i.e., insensitive) to sufficiently small disturbances entering the system through the control channel. That is, as long as the control is large enough to ensure that $$\sigma^\intercal \dot{\sigma} < 0$$ and $$\dot{\sigma}$$ is uniformly bounded away from zero, the sliding mode will be maintained as if there was no disturbance. The invariance property of sliding mode control to certain disturbances and model uncertainties is its most attractive feature; it is strongly robust.

As discussed in an example below, a sliding mode control law can keep the constraint
 * $$ \dot{x} + x = 0 $$

in order to asymptotically stabilize any system of the form
 * $$ \ddot{x}=a(t,x,\dot{x}) + u$$

when $$a(\cdot)$$ has a finite upper bound. In this case, the sliding mode is where
 * $$\dot{x} = -x$$

(i.e., where $$\dot{x}+x=0$$). That is, when the system is constrained this way, it behaves like a simple stable linear system, and so it has a globally exponentially stable equilibrium at the $$(x,\dot{x})=(0,0)$$ origin.

Control design examples

 * Consider a plant described by Equation ($V$) with single input $$ (i.e., $$m = 1$$). The switching function is picked to be the linear combination
 * where the weight $$s_i > 0$$ for all $$1 \leq i \leq n$$. The sliding surface is the simplex where $$\sigma(\mathbf{x})=0$$. When trajectories are forced to slide along this surface,
 * $$\dot{\sigma}(\mathbf{x}) = 0$$
 * and so
 * $$s_1 \dot{x}_1 + s_2 \dot{x}_2 + \cdots + s_{n-1} \dot{x}_{n-1} + s_n \dot{x}_n = 0$$
 * which is a reduced-order system (i.e., the new system is of order $$n-1$$ because the system is constrained to this $$(n-1)$$-dimensional sliding mode simplex). This surface may have favorable properties (e.g., when the plant dynamics are forced to slide along this surface, they move toward the origin $$\mathbf{x}=\mathbf{0}$$). Taking the derivative of the Lyapunov function in Equation ($$), we have

\dot{V}(\sigma(\mathbf{x})) = \overbrace{\sigma(\mathbf{x})^{\text{T}}}^{\tfrac{\partial V}{\partial \mathbf{x}}} \overbrace{\dot{\sigma}(\mathbf{x})}^{\tfrac{\operatorname{d} \sigma}{\operatorname{d} t}}$$
 * To ensure $$\dot{V} < 0$$, the feedback control law $$u(\mathbf{x})$$ must be chosen so that
 * $$\begin{cases}

\dot{\sigma} < 0 &\text{if } \sigma > 0\\ \dot{\sigma} > 0 &\text{if } \sigma < 0 \end{cases}$$
 * Hence, the product $$\sigma \dot{\sigma} < 0$$ because it is the product of a negative and a positive number. Note that

 * The control law $$u(\mathbf{x})$$ is chosen so that
 * $$u(\mathbf{x})

= \begin{cases} u^+(\mathbf{x}) &\text{if } \sigma(\mathbf{x}) > 0 \\ u^-(\mathbf{x}) &\text{if } \sigma(\mathbf{x}) < 0 \end{cases}$$
 * where
 * $$u^+(\mathbf{x})$$ is some control (e.g., possibly extreme, like "on" or "forward") that ensures Equation ($$) (i.e., $$\dot{\sigma}$$) is negative at $$\mathbf{x}$$
 * $$u^-(\mathbf{x})$$ is some control (e.g., possibly extreme, like "off" or "reverse") that ensures Equation ($u$) (i.e., $$\dot{\sigma}$$) is positive at $$\mathbf{x}$$
 * The resulting trajectory should move toward the sliding surface where $$\sigma(\mathbf{x})=0$$. Because real systems have delay, sliding mode trajectories often chatter back and forth along this sliding surface (i.e., the true trajectory may not smoothly follow $$\sigma(\mathbf{x})=0$$, but it will always return to the sliding mode after leaving it).

 * Consider the dynamic system
 * $$\ddot{x}=a(t,x,\dot{x})+u$$
 * which can be expressed in a 2-dimensional state space (with $$x_1 = x$$ and $$x_2 = \dot{x}$$) as

\begin{cases} \dot{x}_1 = x_2\\ \dot{x}_2 = a(t,x_1,x_2) + u \end{cases}$$
 * Also assume that $$\sup\{ |a(\cdot)| \} \leq k$$ (i.e., $$|a|$$ has a finite upper bound $$ that is known). For this system, choose the switching function
 * $$\sigma(x_1,x_2)= x_1 + x_2 = x + \dot{x}$$
 * By the previous example, we must choose the feedback control law $$u(x,\dot{x})$$ so that $$\sigma \dot{\sigma} < 0$$. Here,
 * $$\dot{\sigma} = \dot{x}_1 + \dot{x}_2 = \dot{x} + \ddot{x} = \dot{x}\,+\,\overbrace{a(t,x,\dot{x})+ u}^{\ddot{x}}$$
 * When $$x + \dot{x} < 0$$ (i.e., when $$\sigma < 0$$), to make $$\dot{\sigma} > 0$$, the control law should be picked so that $$u > |\dot{x} + a(t,x,\dot{x})|$$
 * When $$x + \dot{x} > 0$$ (i.e., when $$\sigma > 0$$), to make $$\dot{\sigma} < 0$$, the control law should be picked so that $$u < -|\dot{x} + a(t,x,\dot{x})|$$
 * However, by the triangle inequality,
 * $$|\dot{x}| + |a(t,x,\dot{x})| \geq |\dot{x} + a(t,x,\dot{x})|$$
 * and by the assumption about $$|a|$$,
 * $$|\dot{x}| + k + 1 > |\dot{x}| + |a(t,x,\dot{x})|$$
 * So the system can be feedback stabilized (to return to the sliding mode) by means of the control law
 * $$u(x,\dot{x})

= \begin{cases} |\dot{x}| + k + 1 &\text{if } \underbrace{x + \dot{x}} < 0,\\ -\left(|\dot{x}| + k + 1\right) &\text{if } \overbrace{x + \dot{x}}^{\sigma} > 0 \end{cases}$$
 * which can be expressed in closed form as
 * $$u(x,\dot{x}) = -(|\dot{x}|+k+1) \underbrace{\operatorname{sgn}(\overbrace{\dot{x}+x}^{\sigma})}_{\text{(i.e., tests } \sigma > 0 \text{)}}$$
 * Assuming that the system trajectories are forced to move so that $$\sigma(\mathbf{x})=0$$, then
 * $$\dot{x} = -x \qquad \text{(i.e., } \sigma(x,\dot{x}) = x + \dot{x} = 0 \text{)}$$
 * So once the system reaches the sliding mode, the system's 2-dimensional dynamics behave like this 1-dimensional system, which has a globally exponentially stable equilibrium at $$(x,\dot{x})=(0,0)$$.

Automated design solutions
Although various theories exist for sliding mode control system design, there is a lack of a highly effective design methodology due to practical difficulties encountered in analytical and numerical methods. A reusable computing paradigm such as a genetic algorithm can, however, be utilized to transform a 'unsolvable problem' of optimal design into a practically solvable 'non-deterministic polynomial problem'. This results in computer-automated designs for sliding model control.

Sliding mode observer
Sliding mode control can be used in the design of state observers. These non-linear high-gain observers have the ability to bring coordinates of the estimator error dynamics to zero in finite time. Additionally, switched-mode observers have attractive measurement noise resilience that is similar to a Kalman filter. For simplicity, the example here uses a traditional sliding mode modification of a Luenberger observer for an LTI system. In these sliding mode observers, the order of the observer dynamics are reduced by one when the system enters the sliding mode. In this particular example, the estimator error for a single estimated state is brought to zero in finite time, and after that time the other estimator errors decay exponentially to zero. However, as first described by Drakunov, a sliding mode observer for non-linear systems can be built that brings the estimation error for all estimated states to zero in a finite (and arbitrarily small) time.

Here, consider the LTI system
 * $$\begin{cases}

\dot{\mathbf{x}} = A \mathbf{x} + B \mathbf{u}\\ y = \begin{bmatrix}1 & 0 & 0 & \cdots & \end{bmatrix} \mathbf{x} = x_1 \end{cases}$$ where state vector $$\mathbf{x} \triangleq (x_1, x_2, \dots, x_n) \in \mathbb{R}^n$$, $$\mathbf{u} \triangleq (u_1, u_2, \dots, u_r) \in \mathbb{R}^r$$ is a vector of inputs, and output $$ is a scalar equal to the first state of the $$\mathbf{x}$$ state vector. Let
 * $$A \triangleq \begin{bmatrix} a_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix}$$

where
 * $$a_{11}$$ is a scalar representing the influence of the first state $$x_1$$ on itself,
 * $$A_{21} \in \mathbb{R}^{(n-1)}$$ is a row vector corresponding to the influence of the first state on the other states,
 * $$A_{22} \in \mathbb{R}^{(n-1) \times (n-1)}$$ is a matrix representing the influence of the other states on themselves, and
 * $$A_{12} \in \mathbb{R}^{1\times(n-1)}$$ is a column vector representing the influence of the other states on the first state.

The goal is to design a high-gain state observer that estimates the state vector $$\mathbf{x}$$ using only information from the measurement $$y=x_1$$. Hence, let the vector $$\hat{\mathbf{x}} = (\hat{x}_1,\hat{x}_2,\dots,\hat{x}_n) \in \mathbb{R}^n$$ be the estimates of the $$ states. The observer takes the form
 * $$\dot{\hat{\mathbf{x}}} = A \hat{\mathbf{x}} + B \mathbf{u} + L v(\hat{x}_1 - x_1)$$

where $$v: \R \to \R$$ is a nonlinear function of the error between estimated state $$\hat{x}_1$$ and the output $$y=x_1$$, and $$L \in \mathbb{R}^n$$ is an observer gain vector that serves a similar purpose as in the typical linear Luenberger observer. Likewise, let
 * $$L = \begin{bmatrix} -1 \\ L_{2} \end{bmatrix}$$

where $$L_2 \in \mathbb{R}^{(n-1)}$$ is a column vector. Additionally, let $$\mathbf{e} = (e_1, e_2, \dots, e_n) \in \mathbb{R}^n$$ be the state estimator error. That is, $$\mathbf{e} = \hat{\mathbf{x}} - \mathbf{x}$$. The error dynamics are then
 * $$\begin{align}

\dot{\mathbf{e}} &= \dot{\hat{\mathbf{x}}} - \dot{\mathbf{x}}\\ &= A \hat{\mathbf{x}} + B \mathbf{u} + L v(\hat{x}_1 - x_1) - A \mathbf{x} - B \mathbf{u}\\ &= A (\hat{\mathbf{x}} - \mathbf{x}) + L v(\hat{x}_1 - x_1)\\ &= A \mathbf{e} + L v(e_1) \end{align}$$ where $$e_1 = \hat{x}_1 - x_1$$ is the estimator error for the first state estimate. The nonlinear control law $$ can be designed to enforce the sliding manifold
 * $$0 = \hat{x}_1 - x_1$$

so that estimate $$\hat{x}_1$$ tracks the real state $$x_1$$ after some finite time (i.e., $$\hat{x}_1 = x_1$$). Hence, the sliding mode control switching function
 * $$\sigma(\hat{x}_1,\hat{x}) \triangleq e_1 = \hat{x}_1 - x_1.$$

To attain the sliding manifold, $$\dot{\sigma}$$ and $$\sigma$$ must always have opposite signs (i.e., $$\sigma \dot{\sigma} < 0$$ for essentially all $$\mathbf{x}$$). However,

\dot{\sigma} = \dot{e}_1 = a_{11} e_1 + A_{12} \mathbf{e}_2 - v( e_1 ) = a_{11} e_1 + A_{12} \mathbf{e}_2 - v( \sigma ) $$ where $$\mathbf{e}_2 \triangleq (e_2, e_3, \ldots, e_n) \in \mathbb{R}^{(n-1)}$$ is the collection of the estimator errors for all of the unmeasured states. To ensure that $$\sigma \dot{\sigma} < 0$$, let
 * $$v( \sigma ) = M \operatorname{sgn}(\sigma)$$

where
 * $$M > \max\{ |a_{11} e_1 + A_{12} \mathbf{e}_2| \}.$$

That is, positive constant $$ must be greater than a scaled version of the maximum possible estimator errors for the system (i.e., the initial errors, which are assumed to be bounded so that $k$ can be picked large enough; al). If $y$ is sufficiently large, it can be assumed that the system achieves $$e_1 = 0$$ (i.e., $$\hat{x}_1 = x_1$$). Because $$e_1$$ is constant (i.e., 0) along this manifold, $$\dot{e}_1 = 0$$ as well. Hence, the discontinuous control $$v(\sigma)$$ may be replaced with the equivalent continuous control $$v_{\text{eq}}$$ where

0 = \dot{\sigma} = a_{11} \mathord{\overbrace{e_1}^{ {} = 0 }} + A_{12} \mathbf{e}_2 - \mathord{\overbrace{v_{\text{eq}}}^{v(\sigma)}} = A_{12} \mathbf{e}_2 - v_{\text{eq}}.$$ So

\mathord{\underbrace{v_{\text{eq}}}_{\text{scalar}}} = \mathord{\underbrace{A_{12}}_{1 \times (n-1) \atop \text{ vector}}} \mathord{\underbrace{\mathbf{e}_2}_{(n-1) \times 1 \atop \text{ vector}}}. $$ This equivalent control $$v_{\text{eq}}$$ represents the contribution from the other $$(n-1)$$ states to the trajectory of the output state $$x_1$$. In particular, the row $$A_{12}$$ acts like an output vector for the error subsystem

\mathord{\overbrace{ \begin{bmatrix} \dot{e}_2\\ \dot{e}_3\\ \vdots\\ \dot{e}_n \end{bmatrix} }^{\dot{\mathbf{e}}_2}} = A_2 \mathord{\overbrace{ \begin{bmatrix} e_2\\ e_3\\ \vdots\\ e_n \end{bmatrix} }^{\mathbf{e}_2}} + L_2 v(e_1) = A_2 \mathbf{e}_2 + L_2 v_{\text{eq}} = A_2 \mathbf{e}_2 + L_2 A_{12} \mathbf{e}_2 = ( A_2 + L_2 A_{12} ) \mathbf{e}_2. $$ So, to ensure the estimator error $$\mathbf{e}_2$$ for the unmeasured states converges to zero, the $$(n-1)\times 1$$ vector $$L_2$$ must be chosen so that the $$(n-1)\times (n-1)$$ matrix $$( A_2 + L_2 A_{12} )$$ is Hurwitz (i.e., the real part of each of its eigenvalues must be negative). Hence, provided that it is observable, this $$\mathbf{e}_2$$ system can be stabilized in exactly the same way as a typical linear state observer when $$A_{12}$$ is viewed as the output matrix (i.e., "$n$"). That is, the $$v_{\text{eq}}$$ equivalent control provides measurement information about the unmeasured states that can continually move their estimates asymptotically closer to them. Meanwhile, the discontinuous control $$v = M \operatorname{sgn}( \hat{x}_1 - x )$$ forces the estimate of the measured state to have zero error in finite time. Additionally, white zero-mean symmetric measurement noise (e.g., Gaussian noise) only affects the switching frequency of the control $v$, and hence the noise will have little effect on the equivalent sliding mode control $$v_{\text{eq}}$$. Hence, the sliding mode observer has Kalman filter–like features.

The final version of the observer is thus
 * $$\begin{align}

\dot{\hat{\mathbf{x}}} &= A \hat{\mathbf{x}} + B \mathbf{u} + L M \operatorname{sgn}(\hat{x}_1 - x_1)\\ &= A \hat{\mathbf{x}} + B \mathbf{u} + \begin{bmatrix} -1\\L_2 \end{bmatrix} M \operatorname{sgn}(\hat{x}_1 - x_1)\\ &= A \hat{\mathbf{x}} + B \mathbf{u} + \begin{bmatrix} -M\\L_2 M\end{bmatrix} \operatorname{sgn}(\hat{x}_1 - x_1)\\ &= A \hat{\mathbf{x}} + \begin{bmatrix} B & \begin{bmatrix} -M\\L_2 M\end{bmatrix} \end{bmatrix} \begin{bmatrix} \mathbf{u} \\ \operatorname{sgn}(\hat{x}_1 - x_1) \end{bmatrix}\\ &= A_{\text{obs}} \hat{\mathbf{x}} + B_{\text{obs}} \mathbf{u}_{\text{obs}} \end{align}$$ where That is, by augmenting the control vector $$\mathbf{u}$$ with the switching function $$\operatorname{sgn}(\hat{x}_1-x_1)$$, the sliding mode observer can be implemented as an LTI system. That is, the discontinuous signal $$\operatorname{sgn}(\hat{x}_1-x_1)$$ is viewed as a control input to the 2-input LTI system.
 * $$A_{\text{obs}} \triangleq A,$$
 * $$B_{\text{obs}} \triangleq \begin{bmatrix} B & \begin{bmatrix} -M\\L_2 M\end{bmatrix} \end{bmatrix},$$ and
 * $$u_{\text{obs}} \triangleq \begin{bmatrix} \mathbf{u} \\ \operatorname{sgn}(\hat{x}_1 - x_1) \end{bmatrix}.$$

For simplicity, this example assumes that the sliding mode observer has access to a measurement of a single state (i.e., output $$y=x_1$$). However, a similar procedure can be used to design a sliding mode observer for a vector of weighted combinations of states (i.e., when output $$\mathbf{y} = C \mathbf{x}$$ uses a generic matrix $M$). In each case, the sliding mode will be the manifold where the estimated output $$\hat{\mathbf{y}}$$ follows the measured output $$\mathbf{y}$$ with zero error (i.e., the manifold where $$\sigma(\mathbf{x}) \triangleq \hat{\mathbf{y}} - \mathbf{y} = \mathbf{0}$$).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Sliding mode control


text:
Khorasan province

Khorasan (also transcribed as Khurasan, Xorasan and Khorassan), also called Traxiane during Hellenistic and Parthian times, was a province in northeastern Iran until September 2004, when it was divided into three new provinces: North Khorasan, South Khorasan, and Razavi Khorasan.

Khorasan historically referred to a much larger area, comprising the east and the northeast of the Persian Empire. The name Khorāsān is Persian and means "where the sun arrives from". The name was first given to the eastern province of Persia during the Sasanian Empire and was used from the Late Middle Ages in distinction to neighbouring Transoxiana.

This province, whose people are mainly Shia Muslims, roughly encompassed the western portion of the historical Greater Khorasan. The modern boundaries of the Iranian province of Khorasan were formally defined in the late nineteenth century and the province was divided into three separate administrative divisions in 2004.

History
The name Khorāsān (lit. "sunrise"; "east"; or "land of the rising sun") was originally given to the eastern province of Persia during the Sassanian period. The old Iranian province of Khorasan roughly formed the western half of the historical Greater Khorasan, a region which included parts that are today in Iran, Afghanistan, Tajikistan, Turkmenistan and Uzbekistan. Some of the main historical cities of Persia are located in the older Khorasan: Nishapur and Tus (now in Iran); Merv and Sanjan (now in Turkmenistan); Samarkand and Bukhara (both now in Uzbekistan); Herat and Balkh (now in Afghanistan); and Khujand and Panjakent (now in Tajikistan). The term was also used from the Late Middle Ages–especially in post-Mongol (Chagatai and Timurid) times–to distinguish the region from neighbouring Transoxiana. The modern Iranian boundaries of the province of Khorasan were defined and formalised in the late nineteenth century.

In August 1968 and September 1978, the region was the scene of two major earthquakes that left 12,000 and 25,000 people dead, respectively. A third major earthquake, the 1997 Qayen earthquake, took place on 10 May 1997 and left 1,567 dead, 2,300 injured, and 50,000 homeless.

Modern divisions
Khorasan was the largest province of Iran until it was divided into three separate provinces in September 2004:

 * North Khorasan, center: Bojnourd, other counties: Shirvan, Esfarayen, Garmeh and Jajarm, and Maneh and Samalgan
 * South Khorasan, center: Birjand, other counties: Ferdows, Qaen, Nehbandan, Sarayan, Sarbisheh and Darmian.
 * Razavi Khorasan, center: Mashhad, other counties: Sabzevar, Neyshabour, Torbat-e-Heydariyeh, Quchan, Torbat-e Jam, Kashmar, Taybad, Gonabad, Dargaz, Sarakhs, Chenaran, Fariman, Khaf, Roshtkhar, Bardaskan, Kalat and Khalilabad.

Some parts of the province were added to
 * some southern parts to Sistan and Baluchestan Province
 * some western parts to Yazd Province

Demographics
The major ethnic groups in the region are Persians with Khorasani Kurds, Khorasani Turks and Turkmen as the minorities. Smaller minorities are Baloch(Khorasani Baloch), Jews, Mongols, and Roma. Most of the people in the region natively speak closely related modern day dialects of Persian. The region is home to a significant Sunni Muslim minority. The largest cluster of settlements and cultivation stretches around the city of Mashhad northwestward, containing the important towns of Quchan, Shirvan, and Bojnurd.

title: Khorasan province


text:
Wikipedia:Articles for deletion/Reptilian humanoid

This page is an archive of the discussion surrounding the proposed deletion of a page entitled Reptilian humanoid.

Further comments should be made on the talk page rather than here as this page is kept as an historic record.

The article was kept as there was no clear consensus to delete: approximately 6 votes to delete, 1 abstain, 1 unclear, 7 keep (though of those 2 were anon and one was later blocked)

 * Reptilian humanoid: This article is complete nonsense. It was put here by the loop Khranus, who has now been banned, but has left this, among other idiotic articles, behind. Various people have tried to "NPOV" it, but that just makes it even siller, because now it mostly consists of statements to the effect that "no-one has ever verified that reptilian humanoids exist." The article doesn't contain one single positive statement that anyone seriously believes they do exist, and in fact I think the article was nothing but a piece of trolling provocation by Khranus. I have tried to ridicule it out of existence (Arborealoids), but it is still hanging around making WP look silly. Can we get rid of it? Adam 14:40, 17 Nov 2003 (UTC)
 * At least as it exists, this article is borderline, to say the least. A lot of it is spent on animals that are not purported to be humanoid, and a lot of the rest is just a mass of statements going way beyond equivocation.  Radical, radical editing to restrict to real reptilian humanoids (if any exist, or exist in legend or myth), but I am leaning towards a vote for deletion.  --Daniel C. Boyer 18:38, 17 Nov 2003 (UTC)
 * Reptilian humanoids is also sumthing in Dungens And Dragons that is how much I no about it. 24.207.69.51 14:50, 17 Nov 2003 (UTC)
 * Absolute delete. This is the kind of article that will bring this place into disrepute. It just isn't possible trying to NPOV such a subjective load of half-baked nonsense. Bmills 14:53, 17 Nov 2003 (UTC)
 * I think it might be possible to make an interesting and useful article about the conspiracy theory and the theorists - David Icke is quite prominent, after all. So abstain. Morwen 14:58, 17 Nov 2003 (UTC)
 * Having read the David Icke article (I'd never heard of him before this discussion), my view is that "reptilian humanoids" are adequately discussed at that article and that this one should be deleted. Adam 01:08, 18 Nov 2003 (UTC)
 * Marginal - there may be an article in this somewhere, and some of the info in this article may be relevant to that, but this certainly isn't the article if Wikipedia is to be a reputable source of information. Delete, and if anyone wants to do a new article they should take a copy before it goes. Onebyone 15:05, 17 Nov 2003 (UTC)
 * Painful as it is, I think this should probably stay. There are enough nutters around who believe this stuff that they deserve an article. However we could also move the info into other articles. However to stay someone has to find out who actually really believes this stuff. Currently I don't even believe the list of people who believe in it. DJ Clayworth 19:21, 17 Nov 2003 (UTC)
 * Keep; copyedit it to include "conspiracy theory" and "fictional" accounts; I have heard of fringe discussion about this (not that it's true, but it is a widely known topic in "crank" circles). "The crackpot"
 * This is 1 kind uv article that I think you shud keep; evin if is nonsense -- 24.207.69.51 21:20, 17 Nov 2003 (UTC)
 * Now that is an inspiring testimonial - Marshman 23:22, 17 Nov 2003 (UTC)
 * Delete, makes Wikipedia look like a laughingstock. -- Fuzheado 23:33, 17 Nov 2003 (UTC)
 * Delete. -- BCorr ¤ Брайен 01:54, 18 Nov 2003 (UTC)
 * Keep. It's as legit as Klingons or Greys; that is, it's about a real fiction.  I've rewritten the intro to make it a bit more "respectable". -- VV 06:35, 18 Nov 2003 (UTC)
 * still a little problematic, but it's now dekhranised enough to begin looking like a real article. Keep. Kosebamse 13:08, 18 Nov 2003 (UTC)

end of archived debate
 * It now says that it is reporting on fringe and unproven ideas. It can't be worse than the List of fictional cats, surely?207.189.98.44 18:27, 19 Nov 2003 (UTC)
 * This now looks like one of many articles on mythology. It needs development, but there's no need to delete it. Keep. -- Miguel
 * Keep. This article gives a quality summary of the topic. It is entertaining and informative. Kingturtle 00:36, 23 Nov 2003 (UTC)


text:
Talk:Airport security

Is citation number 22 reliable?
Citation 22 links to an obscure blog post based on first person anecdotal experiences in an Israeli airport. How do you guys feel? Caitlin.swartz (talk) 08:33, 5 June 2013 (UTC)

Several issues
Most large airports have their own police force
 * Did the original writer mean that most airports have police on site all the time (undoubtedly true) or that most airports have a dedicated force e.g. the JFK airport police force. If the latter, is this true in the United States. It isn't true in, for example, the UK so should probably be changed. Pete 13:20, 18 Nov 2003 (UTC)
 * I don't believe that what the writer meant is important. What matters is what it appears to say.  In this case you could take either position.  I took it to be their own police and not a dedicated force from the local department.  After looking at the intro it seems to have several flaws including the one you mentioned.  Another being the use of military.  I believe that in some countries the military is the normal security force.  I'm going to redo the introduction to try and make this a bit more accurate.  Vegaswikian 18:42, 19 October 2005 (UTC)

The world's worst failure of airport security was the September 11th attack on the World Trade Center and The Pentagon using hijacked jetliners.
 * This is an awkward one. Didn't the hijackers have no weapons to speak of? If so, in what sense did airport security fail? One could easily argue that, for instance, the Lockerbie bombing was a greater failure. Pete 13:22, 18 Nov 2003 (UTC)
 * The author may be referring to the box cutters that were used as weapons to intimidate the passengers and crew. Box cutters were legal to carry onboard prior to 9/11.  So, I would agree that the article should be revised to reflect this fact. —Preceding unsigned comment added by 205.174.22.20 (talk • contribs) 2007-01-10

Content to merge or ignore

 * Removed from Airline Security (which needs review):

gay boy Currently, in the United States of America, airline security is largely handled by the Transportation Security Administration (TSA), which provides airport security at major airports (400 to 429 airports).

The terrorist attacks of September 11, 2001 spurred the adoption of heightened security measures. New technologies were developed prior to September 11, 2001, which would have provided airline security without requiring security screeners at airports. Prior to September 11, 2001, most airlines paid the salaries of the airport's security screeners. TSA is considering allowing the airlines and airports to rehire security screeners because the Federal Government and TSA believe too much money is being spent on security at airports.

 * Not sure how much is salvageable or not covered here, but airline security clearly should not duplicate airport security. zoney ♣ talk 15:38, 11 Oct 2004 (UTC)

New article?
The world's worst failure of airport security was the September 11th attack on the World Trade Center and The Pentagon using hijacked jetliners.

I think that was true if it is viewed as a failure of policy in that the airports carried out their instructions correctly, but the instructions were flawed. They didn't include a wide enough definition of what a weapon was. Airport and airline security are two sides of the same coin. Perhaps there should be a new article called something like Commercial air transport security which both redirect to. --Jll 16:21, 12 Oct 2004 (UTC)

 * indeed, the sept 11 terorrists didnt carry anything onboard that was banned from carrying at the time.. even today, we can carry bottles of wine, a sock full of coins, and fists and feet onboard a commercial aircraft. unbelievable! --Kvuo 02:25, 2 October 2005 (UTC)
 * Uh-uh...no more wine. Not even listerine.  DRosenbach  ( Talk 23:45, 18 November 2008 (UTC)

Airline vs. Airport security
I'm not sure what needs to be done with Airport security and Airline security. I think we need to really look at these two articles and move some of this stuff around, at least for the US operations. It is not clear from the articles where airport security ends and airline security begins. I don't believe that the TSA is responsible for security at the airport. They screen passengers and baggage. They also supply, at least at some airports, the bomb sniffing dogs. Airport security, I believe, is assigned by the FAA to the owner of the airport who then designates the responsible agency or department. The airlines are responsible for the security of their airplanes and must follow directives from the FAA and TSA and probably Customs. Access to secure areas of the airport are controlled by the owner of the airport with direction from some govermental agency. I think it is important to get this correct in the articles. Vegaswikian 07:05, 12 October 2005 (UTC)

Recent developments
I think it would be interesting to actually add a bit of how security messures and policy has developed as well as were we stand today. However, I consider most of the airport security nothing but a scam to keep the public calm and what I can come up with just sounds a bit too partial. So I challenge somebody to give a good overview, prefereably with references. P.S. 00:06, 27 December 2005 (UTC)

Need for history section?
Hi. It would be interesting to have a history section that outlines the development of the security process and the machinery itself. —Preceding unsigned comment added by 68.222.99.12 (talk • contribs) 2006-07-03

I think, this chapture is of great importance as this matter does not exist from the beginning of aviation and if there was no hijacking and terrorism, it would never got a matter. —Preceding unsigned comment added by 78.42.249.152 (talk) 10:57, 8 August 2008 (UTC)

Israel
There needs to be a section for Israel on here. Ben Gurion Airport has the tightest airport security in the world, with some very unique security measures. --Mrskippy 09:50, 13 August 2006 (UTC)
 * You read my mind, Skippy --- five months before I had the thought! :-) --Micahbrwn 17:21, 31 January 2007 (UTC)

History Section is Essential
My first experience with Airport Security would be surprising to most people under the age of 40 -- NONE. Zero. Nada.

In 1972, when I took my first airplane flight, you simply walked up to the ticket counter and then to the gate. No security line, no questions, no fence around the airport or the landing field.

Now the sheep (and I am, shamefully, baa-ing as loudly as anyone else) -- now we sheep meekly line up to be partially strip-searched, felt up, and otherwise man-and-woman-handled. Soon us cattle will be mass-x-rayed as well. The humiliation is now, the cancers will come later.

The day will come when the fences will be torn down, but not in my lifetime. —Preceding unsigned comment added by 84.228.129.126 (talk • contribs) 2007-05-24

What's with the resealable plastic bags?
I'm curious. What's the (alleged) reason for requiring passengers to put liquids and gels in a sealed plastic bag? I can see banning liquids and gels (in case they're explosives) but what good does it do to ask people to keep them in a plastic bag? (If there's an answer to this, I think it would be worth putting in the article -- surely I'm not the only one curious about this!)

 * News release about the plastic-bag requirement

 * Maybe this sort-of answers the question. Putting the various containers of liquids in a single, clear plastic bag makes it easier for airport security officials to conveniently glance at them.  Why it has to be sealed and resealable is not clear.  It's also not clear whether use of a twist-tie or a knot counts as sealing.  --Coppertwig 12:15, 15 July 2007 (UTC)

israel
what about ben gurion international airport? this airport is the most secur airport in teh world.... —Preceding unsigned comment added by 79.179.133.197 (talk) 14:00, 20 October 2007 (UTC)
 * Yeah -- funny how that one was missing. Took care of it.  DRosenbach  ( Talk 22:24, 13 November 2008 (UTC)

Clarification of Statistics
The statistics cited for bomb detection in carry-on luggage by the TSA are extremely misleading. I've clarified them. The source provided originally supports my edit, leading me to question the motives of whoever originally wrote that segment. 66.66.154.162 (talk) 23:53, 10 August 2008 (UTC)

Security flaws
Perhaps Bruce Shneier's tips on improving airport security can be mentioned. Eg its weird one may pack a gas lighter or a chainsaw in the hand luggage. Also, airport security is said to focus too much on arabic/light or darker-skinned persons. See http://www.schneier.com/blog/archives/2008/08/security_idiocy.html

Also, the site http://www.stupidsecurity.com/ was mentioned —Preceding unsigned comment added by 91.176.13.194 (talk) 09:27, 4 June 2009 (UTC)

Articles and references to criticism, tests, and failures would be good. Here is a great article http://www.theatlantic.com/doc/200811/airport-security Gampgamp (talk) 17:17, 18 June 2009 (UTC) I just added two examples in the security flaw section: A 9 year old boy managed to fly from Seattle to San Antonio before being found out he had no boarding pass after her mom told CNN his son gave out a fake name to a ticketing agent. In Manchester,England an 11 year old boy managed to slip away from his mother during a shopping trip and was able to board a flight all the way to Rome without a boarding pass or passport. His dreams were shattered because,he never left Rome and was sent back to his parents.

These recent examples clearly show the gaps in security at airports in the US and UK.Naakyea (talk) 00:53, 5 November 2013 (UTC)

Isn't the article completely biased?
The whole article contains no mention of any criticism of the airport security. I won't deny that it is also my personal view, but I think that we, meaning people with the opinion, that airport security is a worthless, artificially engineered waste of money, is not so negligible. I like to refrain from writing to wiki as my English is limited, but someone should look into this. As the article stands, it just supports this activity and gives a feeling that it is an unquestionable necessity.

The arguments that can be given are along several lines: 1. false sense of security, as the "terrorists" can always think one step ahead, make up new ways to bypass the checks that look only for things that already have been tried 2. promoting "terrorism", as by giving up our freedoms and convenience, we show them, that they have actually succeeded and encourage them to do more 3. irrational choice of aircraft as the main security concern, when the "terrorists" can strike whenever they wish (see Madrid trains, London buses) 4. possibility of artificially overestimating the "terrorist" threat to make more money for the security business and to invade people's privacy.

I believe, that there is plenty of relatively mainstream material to each of these points, that can be cited as an opinion of a sizeable group of pepole.

Jan Ebr —Preceding unsigned comment added by 168.96.148.2 (talk) 23:08, 6 October 2010 (UTC)

Completely valid point. You are correct this should be an article about propaganda and promoting false sense of security. This article needs to be examined and criticism put on the document. The US has spent over $40 Billion dollars on this single effort and it has had questionable value at best. —Preceding unsigned comment added by 63.249.91.225 (talk) 03:55, 24 November 2010 (UTC)

A few minor adjustments
I made a few minor edits, but thought I should explain.

1) the United States section under Airport Security was prefaced by a link to Airport Racial profiling (in the place one normally finds a link to an article for which the section is a summary. This is not a summary for airport racial profiling, it's the broader topic of all security in US airports. I moved the racial profiling link down to the "see also" section, where more specific, related links go. I don't think the link is necessarily inappropriate, it just was inappropriate where it was placed (not because of content, but because of the convention described above).

2) In the See Also section there was a link to "Flying While Muslim". There is no page for that, it redirects to "racial profiling" in general. Since I just added the airport racial profiling article and it is a redirect (that redirects to a MUCH more general article), it seemed redundant, so I deleted it. Essentially, it's better covered by the airport profiling article.

Thanks! 204.65.34.157 (talk) 17:01, 4 August 2011 (UTC)

Neutrality
This article reads like a promotion for airport security and it's benefits. Especially the summary. JMJimmy (talk) 22:06, 8 August 2011 (UTC)

The article contains none of the references to critical discussion of the United States TSA, particularly their recent institution of "Full body scanners" (also implemented in England). 96.232.207.14 (talk) 01:44, 31 August 2011 (UTC)

Vector version available for File:Security_layers.jpg
If you look on the description page, you'll note that I've made a vector graphic to replace the jpg. If you like it, please use it in its place. Morgan Phoenix (talk) 20:49, 14 September 2011 (UTC)

Proposed merge with Airport security repercussions due to the September 11 attacks
Other article is a stub and narrow in focus, would be better served merged into this article as a US subsection. Dea db  eef  03:54, 18 May 2013 (UTC)
 * Oppose Though the present sparsely sourced article doesn't show it, post 9/11 airport security in the United States is an extremely high profile, notable issue, involving allegations of political motivations for placement of people on the no-fly list, x-ray body scanners which allegedly amount to virtual strip searches, etc. DavidLeighEllis (talk) 20:45, 21 January 2014 (UTC)

Blacklisted Links Found on the Main Page
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✅ This issue has been resolved, and I have therefore removed the tag, if not already done. No further action is necessary.— cyberbot II NotifyOnline 19:28, 9 April 2014 (UTC)

Question re:Reference format
Recently I have seen references on Wikipedia start to contain more information that just the link, I have done this in the paragraph I have just added about passive monitoring & passenger flow systems. If anyone has any feedback about the format I have used (Or at least tried to user) please let me know. RoyalBlueStuey (talk) 14:14, 17 June 2014 (UTC)

Illustration
What is a "demonstrative image"? I thought Wikipedia was supposed to use the English language! Wouldn't "mock up" or "demonstration" be better English?Royalcourtier (talk) 22:24, 20 March 2015 (UTC)

GE Secure Registered Traveler paragraph removed
I removed the following paragraph from the United States section because the program has been shut down and is no longer noteworthy.

''Noticing the demand for new technology in airport security, General Electric (GE) started to develop the Secure Registered Traveler System. The new system would use newly developed technology such as automated carry-on scanning, automatic biological pathogen detection, millimeter-wave full body scanning and a quadrupole resonance carpet that would detect threats in shoes without having to take them off. The SRT program also works with smartcard technology along with fingerprint technology to help verify passengers. The fingerprint scanner also detects for explosive material traces on the person's fingers.''

It might be useful to make some mention of the one surviving element of the system, the full-body scanner, but I'll leave that to someone else. 71.197.166.72 (talk) 00:29, 26 May 2015 (UTC)

Article badly needs a "criticism" section
The merits of Airport security is commonly a subject of debate. Discussion of its merits and criticisms should certainly be added as a section of this article. For example, what arguments or evidence exist in favour or against its effectiveness? I am certain plenty of citable sources on both sides exist.Spudst3r (talk) 01:09, 10 September 2015 (UTC)

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title: Talk:Airport security


text:
Nero Multimedia Suite

Nero Platinum Suite is a software suite for Microsoft Windows that is developed and marketed by Nero AG. Version 2017 of this product was released in October 2016.

Version differences
Since its Version 10, Nero provides two variants of the suite – the Classic and the Platinum. The Platinum version includes the following additional functions:
 * Music recorder - to record MP3s from worldwide radios stations (since Nero 2016)
 * Video editing in Ultra-HD (since version 2014) and in HEVC (Since Nero 2017 but only available in Nero Video and not available in Nero Recode)
 * Additional video, transition and picture-in-picture effects
 * SecurDisc 4.0 Technology with 256 bit-encryption (since Nero 2017)
 * Additional film templates and disc menu templates
 * Blu-ray disc ripping and conversion
 * Blu-ray playback (not possible with Nero 2016, only with previous versions)

Included products
The following applications are included in Nero 2016:

Disc authoring and copying

 * Nero Burning ROM: an optical disc authoring program for CDs, DVDs, and Blu-rays by Nero AG and one of its first products. The product is also available separately. It includes several functions for audio format conversion, the creation of audio CDs, etc.. As of version 2015, Nero AirBurn App and Nero Burning ROM enable users to burn media via their mobile devices.
 * Nero Express: a simplified version of Nero Burning ROM targeted at novices. The Nero AirBurn app does not work with Nero Express.

Video editing and creating of video discs

 * Nero Video: is a software tool for creating and editing videos. It combines editing tools (including the addition of effects, music and themes) and video export as well as DVD and Blu-ray authoring. The product provides simple editing functions for novices (in Express mode) as well as advanced video editing (Advanced mode). It is available separately as a download.

Data conversion

 * Nero Recode: converts video and audio files as well as non-copyright-protected video DVDs and Blu-Rays into multiple video formats.
 * Nero Disc to Device is an easy-to-use application for converting video discs and audio CDs for playback on mobile devices or in the cloud.
 * Nero MediaHome enables users to manage and play their images, videos and music files. Alongside ripping and the creation of playlists and slideshows, MediaHome includes features that let users sort their media, including tagging, face recognition system in photos, geo location support and manual geotagging for photos and videos. Streaming to TVs and home media players is also included. Starting with Version 2015, users can stream media directly to their mobile devices (iOS, Android, Amazon) with the Nero MediaHome Receiver App. Nero MediaHome is also available with limited functionality as a free download from nero.com.
 * Nero Media Browser: simple tools for retrieving media content. It makes the Nero MediaHome media library also available to non-Nero programs using simple drag and drop.
 * Nero Blu-ray Player (not in Nero 2016 Platinum, only in the previous Platinum version. ): media player for Blu-ray discs

Data rescue

 * Nero RescueAgent: helps users to recover files from damaged or partially unreadable media (discs, hard disks, USB thumb drives and flash drives) and to restore files that were accidentally deleted.
 * Nero BackItUp: a system backup utility. It was integral part of Nero 6, 7, 8, 10 and 11 suites. With the introduction of Nero 9 Nero BackItUp 4 became a standalone backup product, while its successor, Nero BackItUp 5, was the main application of Nero BackItUp & Burn Later, the product was re-integrated into Nero Multimedia Suite 10 and is now included in Nero 11. The product can also be purchased separately.

Free Tools
The following components were part of the suite until Version 11. They are now available for download separately and are free of charge.
 * Nero CoverDesigner: enables users to design and print disc covers and labels
 * Nero BurnRights: enables administrators to provide other users with access to drives
 * Nero DiscSpeed: a disc speed measurement and performance diagnostics tool, including benchmarking and surface error scanning.
 * Nero WaveEditor: an audio editing tool capable of recording, editing, filtering, and exporting music files.
 * Nero SoundTrax: a tool for recording, mixing and digitizing music tracks.
 * Nero InCD Reader 5: this tools enables users to read CDs created with InCD
 * Nero SecurDisc Viewer: this tool enables users to read discs created with SecurDisc.
 * Nero InfoTool: Detailed system information browser
 * Nero AI tools: including Nero AI Image Upscaler, Nero AI Photo Colorize, Nero AI Photo restoration, Nero AI Face Animation, Nero AI Avatar Generator and Nero AI Image Compressor.

title: Nero Multimedia Suite