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.