Constrained robust distributed model predictive control for uncertain discrete-time Markovian jump linear system

Abstract

This paper is concerned with the robust distributed model predictive control (MPC) problem for a class of uncertain discrete-time Markovian jump linear systems (MJLSs), subject to constraints on the inputs and states. Polytopic uncertainties both in system matrices and transition probability matrices of Markov process are taken into consideration. The global system is decomposed into several subsystems, and in this way these subsystems are able to exchange information with each other via internet. Furthermore, by constructing a novel Lyapunov functional, a sufficient condition is derived to guarantee the robust stability in the mean square sense for each subsystem with admissible constraints and uncertainties. In terms of the Cauchy–Schwarz inequality, the constrained problem of minimizing an upper bound on the worst-case infinite horizon cost function is transformed into a convex optimization problem involving linear matrix inequalities (LMIs). By solving a series of LMIs, a novel Jacobi iterative algorithm is proposed to design a distributed mode-dependent state-feedback controller, which ensures the local optimality at each sampling instant. Finally, compared with centralized and decentralized control schemes, two numerical simulation examples are employed to show the effectiveness of the proposed distributed algorithm.