Constrained robust model predictive control based on periodic invariance

Authors:
Young Il Lee;Basil Kouvaritakis
Affiliations:
Department of Control and Instrumentation, Seoul National University of Technology, Gongneung-dong, Nowon-gu, Seoul, Korea;Department of Engineering Science, Oxford University, Parks Road, OX1 3PJ, UK
Venue:
Automatica (Journal of IFAC)
Year:
2006

Citing 4
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Brief An improved approach for constrained robust model predictive control

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Technical communique: Extended invariance and its use in model predictive control

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Correspondence: Robust stabilization of uncertain time-varying discrete systems and comments on "an improved approach for constrained robust model predictive control"

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Brief paper: Receding horizon control of switching systems

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Brief paper: MPC of constrained discrete-time linear periodic systems - A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

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Stability of periodically time-varying systems: Periodic Lyapunov functions

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Abstract

In this paper, a receding-horizon control method for input/state constrained systems with polyhedral uncertainties is proposed. The dual-mode prediction strategy is adopted to deal with the constraints and periodically-invariant sets are used to derive a target invariant set of the dual-mode prediction strategy. The proposed control method is shown to have novel characteristics earlier approaches do not have i.e.: (i) the convex-hull of all the periodically invariant sets are invariant in the sense that there are feasible feedback gains guaranteeing invariance for any elements of the convex-hull and it provides larger target sets than other methods based on ordinary invariant sets. (ii) A particular convex-hull of periodically invariant sets, that is computable off-line, can be used as an invariant target set. In this case the number of on-line variables is only equal to the period of invariance and thus the proposed algorithm is computationally very efficient. These on-line variables provide interpolation between different feedback gains to yield best performance.