Nonlinear model predictive control for periodic systems using LMIs

The problem of stabilizing constrained nonlinear discrete-time periodic systems using model predictive control (MPC) is considered in this paper. The results are based on a recently developed MPC scheme for linear periodic systems which is extended to the nonlinear case by using differential inclusion. Alternatively, it can be viewed as an extension of a well-known robust MPC scheme exploiting the periodicity of the system and therefore reducing conservatism. At each time instant, a new periodic linear state feedback law is obtained based on the repeated solution of a convex optimization problem involving a set of linear matrix inequalities (LMIs). The approach can therefore take advantage of existing efficient and reliable algorithms for LMIs. A numerical example demonstrates the effectiveness of the proposed scheme.