Robust adaptive model predictive control with persistent excitation conditions

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy online parameter estimation. Constraints enforcing persistently exciting closed loop actions are introduced for set-membership identification scheme. The algorithm requires the solution of convex program, satisfies constraints robustly, ensures recursive feasibility input-to-state stability. Almost sure convergence to actual system parameters is demonstrated under assumptions on stabilizability, reachability, tight disturbance bounds.