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Optimization Over State Feedback Policies for Robust Control with Constraints

Goulart P. J. and Kerrigan E. C. and Maciejowski J. M.

March 2005
Technical Report: CUED/F-INFENG/TR.494

Abstract

This paper is concerned with the optimal control of linear discrete-time systems, which are subject to unknown but bounded state disturbances and mixed constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with memory of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This result implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods without having to introduce any conservatism in the problem formulation. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and for all allowable disturbance sequences. The cost that is chosen to be minimized in the associated finite horizon optimal control problem is a quadratic function in the disturbance-free state and input sequences. It is shown that the value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic or given by a 1-norm or infinity-norm bound, or a second-order cone program (SOCP) if the disturbance set is ellipsoidal or given by a 2-norm bound.

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BibTex Entry

@TechReport{goulart:kerrigan:maciejowski:2005,: author = {Goulart P. J. and Kerrigan E. C. and Maciejowski J. M.},; institution = {Department of Engineering, University of Cambridge},; title = {Optimization Over State Feedback Policies for Robust Control with Constraints},; year = {2005},; bibkey = {goulart:kerrigan:maciejowski:2005},; month = {March},; note = {CUED/F-INFENG/TR.494}
}



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