Model predictive control with missing data

This paper is concerned with the problem of robust model predictive control for discrete-time systems with packet losses. A stochastic process satisfying Bernoulli random binary distribution is utilized to model the packet losses, and a parameter dependent Lyapunov function is adopted to reduce the conservatism. The aim is to design a state feedback controller which minimizes an upper bound on a quadratic objective function at each sampling instant for all admissible packet losses and system parameter uncertainties, and the robust stochastic stability of the closed-loop system is guaranteed. The hard constraints on the variances of the inputs and outputs are also considered. All the conditions to solve the proposed problem are formulated in the framework of linear matrix inequalities (LMIs). A simulation example is given to illustrate the effectiveness of the proposed control methodology.