Convergence of a Stochastic Adaptive MPC

This paper presents an adaptive model predictive control(MPC) for discrete-time linear stochastic systems. The proposed adaptive MPC is designed by combining the weighted least squares(WLS) estimation algorithm with the receding horizon LQG control. For unconstrained systems, it is proven that the closed-loop system with the proposed adaptive MPC is stable under some natural conditions on the true systems. Moreover, by adding a diminishing excitation to the adaptive MPC, the parameters converge to the true ones and the performance of the system can be optimized asymptotically.