Robust Explicit Solution of Multirate Predictive Control System with External Disturbances

Abstract

This paper considers the problem of robust predictive control for a class of uncertain multirate systems, in which the output sampling period is several times larger than the one of input updating. By means of dynamic programming and multiparametric quadratic programming (mp-QP) techniques, this work proposes a novel robust explicit model predictive control (REMPC) algorithm such that the higher on-line updating speed of input can be attained. Firstly, the optimization problem is decomposed into several subproblems. For each subproblem, a constraint condition only involving current state and input is constructed. Then taking current state and future inputs as parameter variables we can obtain a robust explicit solution for the new reformulated optimization subproblem by mp-QP method. Especially, by choosing a maximal robust positive invariant set as the terminal constraint set of the optimization problem, closed-loop robust stability of the multirate control system subject to external disturbance can be guaranteed. Finally, a numerical simulation is given to show the effectiveness of the proposed method.