Algorithm and stability of ATC receding horizon control

Receding horizon control (RHC), also known as model predictive control (MPC), is a suboptimal control scheme that solves a finite horizon open-loop optimal control problem in an infinite horizon context and yields a measured state feedback control law. A lot of efforts have been made to study the closed-loop stability, leading to various stability conditions involving constraints on either the terminal state, or the terminal cost, or the horizon size, or their different combinations. In this paper, we propose a modified RHC scheme, called adaptive terminal cost RHC (ATC-RHC). The control law generated by ATC-RHC algorithm converges to the solution of the infinite horizon optimal control problem. Moreover, it ensures the closed-loop system to be uniformly ultimately exponentially stable without imposing any constraints on the terminal state, the horizon size, or the terminal cost. Finally we show that when the horizon size is one, the underlying problems of ATC-RHC and heuristic dynamic programming (HDP) are the same. Thus, ATC-RHC can be implemented using HDP techniques without knowing the system matrix A.