Probabilistic Constrained Model Predictive Control for Linear Discrete-time Systems with Additive Stochastic Disturbances

Model predictive control (MPC) is a kind of optimal feedback control in which the control performance over a finite future is optimized and its performance index has a moving initial time and a moving terminal time. The objective of this study is to propose a design method of MPC for linear discrete-time systems with stochastic disturbances under probabilistic constraints. For this purpose, the two-sided Chebyshev's inequality is applied to successfully handle probabilistic constraints with less computational load. A necessary and sufficient condition for the feasibility of the stochastic MPC is shown here. Moreover, a sufficient condition for the stability of the closed-loop system with stochastic MPC is derived by means of a linear matrix inequality.