Solution of min-max optimization problem for LPV systems via dynamic programming

Abstract

A feedback control law is derived analytically for a linear parameter varying (LPV) discrete-time system with bounded rates of parameter variations subject to input-saturated constraints in this paper. As the uncertain region of such a LPV system in the future changes corresponding to the parameters which can be predicted in the future stage due to the information on the parameters value, magnitude bounds and the variation rate bounds, the control law is presented in the paper by solving a min-max MPC problem based on a dynamic programming viewpoint. By exploiting the dynamic nature of the min-max optimal problem and showing the convexity of the dynamic cost-to-go, the intrinsic structure of the feedback control law has been obtained which is proved to be efficient for an LPV system with bounded rates of parameter variations by an example at last.