Model predictive control of nonlinear systems: Computational burden and stability

Implementation of model predictive control (MPC) for nonlinear systems requires the online solution of a nonconvex, constrained nonlinear optimisation problem. Computational delay and loss of optimality arise in the optimisation procedures. The 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 online optimisation procedure, the nonlinear system under the proposed nonlinear MPC is asymptotically stable. The stability condition presented in the paper enables the 'fictitious' terminal control to be nonlinear, rather than only linear, 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.