Constructive robust MPC scheme for constrained nonlinear systems with disturbances

This paper presents a new robust model predictive control (MPC) scheme for continuous-time nonlinear systems subject to unknown but bounded disturbances and constraints on the state and input. The performance index is a function on disturbance-free state and input profiles, and the predictions are parameterized by one analytic controller with a small number of adjustable parameters. Using the methods of input-to-state stable control Lyapunov functions (ISS-CLFs), a variation of Freeman´s formula is constructed, with a single tunable parameter reflecting `decay rate´ of the ISS-CLF. It is shown that the formula has the properties of ISS with respect to all admissible disturbances in an explicitly estimated region of attraction. With the results, we prove that the constrained closed-loop MPC system is ISS for all admissible disturbances. The applicability of the proposed MPC scheme is illustrated to control an open-loop unstable system.