Optimisation of attraction domains of nonlinear MPC via LMI methods

This paper addresses the attraction domain of Model-Based Predictive Control (MPC) for nonlinear systems with control input and state constraints. Based on a stability condition of nonlinear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilising control law to maximise the domain of attraction of the nonlinear MPC is proposed. The problem of maximisation of the attraction region is recast as a well-defined optimisation problem. By an LMI based optimisation approach, the terminal weighting item and fictitious terminal stabilising control law are optimised to enlarge the attraction domain and hence the feasibility domain of the nonlinear MPC method. The proposed method is illustrated by a numerical example and favourably compared with existing results.