Constructive robust model predictive control for constrained non-linear systems with disturbances

This study presents a new robust model predictive control (MPC) scheme for constrained continuous-time non-linear systems subject to unknown but bounded disturbances. The performance index is a function on disturbance-free state and input profiles, and the predictions are parameterised by an analytic controller with a small number of adjustable parameters. In particular, input-to-state stable control Lyapunov functions techniques are used to construct a variation of Freeman´s formula with some tunable parameters, which yields an MPC with guaranteed input-to-state stability in some estimated invariant sets w.r.t the disturbance. It is further derived that the MPC here is inverse optimal for a class of dynamic game problems and has a sector margin (0.5, ∞). Finally, two numerical examples are used to illustrate the performance and effectiveness of the results obtained here.