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Titlebook: Constrained Control of Uncertain, Time-Varying, Discrete-Time Systems; An Interpolation-Bas Hoai-Nam Nguyen Book 2014 Springer Internationa

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Lecture Notes in Computer Scienceoidal, and depending on the objective functions, i.e. linear or quadratic, at most two LPs or one QP or one LMI problems are solved on-line at each time instant. In the explicit case, the control law is shown to be a piecewise affine function of state.
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Interpolating Control—Output Feedback Casehrough measurement and storage of appropriate previous measurements. Even if the state might be ., it is directly measurable and will provide an appropriate model for the control design with constraint handling guarantees. Finally, it will be shown how the interpolating control principles can lead to an output-feedback control design procedure.
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Set Theoretic Methods in Controlinvariant sets are introduced. Some algorithms are proposed for computing such sets. The chapter ends with the problem of estimating the domain of attraction for uncertain and/or time-varying linear discrete-time systems with saturated input.
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Interpolating Control—Nominal State Feedback Caseiant sets and semi-definite programming in the case of using ellipsoidal invariant sets. Proof of recursive feasibility and asymptotic stability are provided. Several numerical examples are given to support the algorithms with illustrative simulations.
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Interpolating Control—Nominal State Feedback Casein the next chapter. The main idea is to interpolate between high-performance (unconstrained) feedback with constraint-aware low-gain feedback strategies in order to respect the constraints. The algorithms are based on linear programming or quadratic programming in the case of using polyhedral invar
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