Model Predictive Control for Uncertain Stochastic Systems

Jie Sheng, Liqian Zhang, and Shengyuan Xu


Discrete-time systems, linear matrix inequalities, stochastic systems, Spatial-Temporal


This paper investigates the problem of robust model predictive control for uncertain discrete-time stochastic systems. The uncertainties on the system matrices are assumed to belong to a class of norm bounded time-varying matrices with a certain structure. The hard constraints on the variances of the inputs and outputs are considered. The control scheme is characterized as a constrained optimization problem of the worst-case quadratic cost over infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the robust stochastic stability of the closed-loop system for all admissible uncertainties.

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