Model Predictive Control for Uncertain Stochastic Systems

Jie Sheng, Liqian Zhang, and Shengyuan Xu


Discretetime systems, linear matrix inequalities, stochastic systems, SpatialTemporal


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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