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Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution

Kerrigan E. C. and Maciejowski J. M.

October 2002
Technical Report: CUED/F-INFENG/TR.440

Abstract

In order to ensure robust feasibility and stability of model predictive control (MPC) schemes, it is often necessary to optimise over feedback policies rather than open-loop trajectories. All specific proposals to date have required the solution of nonlinear programs and/or the solution of a large number of optimisation problems. In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable MPC problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the receding horizon control (RHC) law is piecewise affine, and can be explicitly pre-computed, so that the linear program does not have to be solved on-line. Two numerical examples are presented; one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible.

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BibTex Entry

@TechReport{kerrigan:maciejowski:2002,: author = {Kerrigan E. C. and Maciejowski J. M.},; institution = {Department of Engineering, University of Cambridge},; title = {Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution},; year = {2002},; address = {Cambridge, UK},; bibkey = {kerrigan:maciejowski:2002},; month = {October},; note = {CUED/F-INFENG/TR.440}
}



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