Model predictive control of non-linear discrete time systems: a linear matrix inequality approach

Using a non-linear model in model predictive control (MPC) changes the control problem from a convex quadratic programme to a non-convex non-linear problem, which is much more challenging to solve. In this study, we introduce an MPC algorithm for non-linear discrete-time systems. The systems are composed of a linear constant part perturbed by an additive state-dependent non-linear term. The control objective is to design a state-feedback control law that minimises an infinite horizon cost function within the framework of linear matrix inequalities. In particular, it is shown that the solution of the optimisation problem can stabilise the non-linear plants. Three extensions, namely, application to systems with input delay, non-linear output tracking and using output-feedback, are followed naturally from the proposed formulation. The performance and effectiveness of the proposed controller is illustrated with numerical examples.