Model predictive controller for perturbed nonlinear systems with bounded inputs

In this paper we develop the framework for optimal nonlinear model predictive controller (NMPC) with guaranteed stability for nonlinear systems with measurement errors. Newton´s method for solving constrained minimization problem, when the errors come from gradient and Hessian estimation procedure, is proposed and analyzed. More specifically, the solution to the problem of optimal control for state constrained dynamics with bounded input is characterized and the concepts that provide the tools to determine the value function and the optimal control feedback are presented. Under mild assumptions we require that NMPC keeps the state inside the vicinity of optimal steady state and introduce new constraints to ensure stability. Since, in general NMPC optimization procedure does not imply stability, the main idea is to design Lyapunov-based predictive controller which would allow the local control law, in the presence of bounded errors, to maintain the deviated trajectory inside the tolerable limits. It is pointed out that the properly defined procedure can improve the response since the chosen numerical approach implies sufficiently fast convergence. The optimal input is computed based on constrained optimal algorithm.