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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.

International Journal of Robust and Nonlinear Control, Volume 4, Number 14, Pages 395--413, 2004

Abstract

In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min-max model predictive control problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the optimal control law is piecewise affine, and can be explicitly pre-computed so that the linear program does not have to be solved on-line. We assume that the plant model is known, is discrete-time and linear time-invariant, is subject to unknown but bounded state disturbances and that the states of the system are measured. 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

@Article{kerrigan:maciejowski:2004a,: author = {Kerrigan E. C. and Maciejowski J. M.},; journal = {International Journal of Robust and Nonlinear Control},; title = {Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution},; year = {2004},; bibkey = {kerrigan:maciejowski:2004a},; number = {14},; pages = {395--413},; volume = {4}
}



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