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## Rafael Martínez Guerra

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## System Identification 2003

A particular robustness issue is the requirement for a control system to perform properly in the presence of input and state constraints. In the physical world every signal is limited. It could happen that a controller will send control signals that cannot be followed by the physical system, for example, trying to rotate a valve at excessive speed.

This can produce undesired behavior of the closed-loop system, or even damage or break actuators or other subsystems. Specific control techniques are available to solve the problem: model predictive control see later , and anti-wind up systems. The latter consists of an additional control block that ensures that the control signal never exceeds a given threshold.

For MIMO systems, pole placement can be performed mathematically using a state space representation of the open-loop system and calculating a feedback matrix assigning poles in the desired positions. In complicated systems this can require computer-assisted calculation capabilities, and cannot always ensure robustness. Furthermore, all system states are not in general measured and so observers must be included and incorporated in pole placement design. Processes in industries like robotics and the aerospace industry typically have strong nonlinear dynamics.

In control theory it is sometimes possible to linearize such classes of systems and apply linear techniques, but in many cases it can be necessary to devise from scratch theories permitting control of nonlinear systems. These, e. Differential geometry has been widely used as a tool for generalizing well-known linear control concepts to the non-linear case, as well as showing the subtleties that make it a more challenging problem. Control theory has also been used to decipher the neural mechanism that directs cognitive states. When the system is controlled by multiple controllers, the problem is one of decentralized control.

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Decentralization is helpful in many ways, for instance, it helps control systems to operate over a larger geographical area. The agents in decentralized control systems can interact using communication channels and coordinate their actions. A stochastic control problem is one in which the evolution of the state variables is subjected to random shocks from outside the system.

A deterministic control problem is not subject to external random shocks. Every control system must guarantee first the stability of the closed-loop behavior. For linear systems , this can be obtained by directly placing the poles. Non-linear control systems use specific theories normally based on Aleksandr Lyapunov 's Theory to ensure stability without regard to the inner dynamics of the system. The possibility to fulfill different specifications varies from the model considered and the control strategy chosen.

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