Model predictive control of nonlinear systems: computational burden and stability

Implementation of Model Predictive Control (MPC) for nonlinear systems requires on-line solution of a non-convex, constrained nonlinear optimisation problem. Computational delay and loss of optimality arise in the optimisation procedures. This paper presents a practical MPC scheme for nonlinear systems with guaranteed asymptotic stability. It is shown that when an initial control profile is chosen to satisfy an inequality condition in each on-line optimisation procedure, the nonlinear system under the proposed nonlinear MPC is asymptotically stable. The stability condition presented in this paper enables the “fictitious” terminal control to be nonlinear, rather than only linear, and thus the stability region is greatly enlarged. Furthermore it is pointed out that nominal stability is still guaranteed even though the global, or even the local, minimisation of the objective cost is not achieved within the prescribed computational time