Updated terminal cost RHC for continuous-time systems

Receding horizon control (RHC) or model predictive control (MPC) solves online a finite horizon open-loop optimal control problem repeatedly in an infinite horizon context and provides a suboptimal control solution. It has been widely used in industry. For continuous-time (CT) systems, two categories of RHC have been investigated in literature, namely instantaneous RHC and sampled-data RHC. This paper focuses on the sampled-data RHC for continuous linear time-invariant (LTI) systems. The usual way to ensure stability of RHC scheme is to impose some constraints on the terminal cost and/or the terminal state and/or the horizon length. A new RHC algorithm is proposed, which we call updated terminal cost receding horizon control (UTC-RHC). Compared with the standard RHC which uses the same terminal cost all the time, our algorithm updates the terminal cost at each sampling instant. The advantage of UTC-RHC is that the uniform exponential stability of the closed-loop system can be guaranteed without imposing the usual constraints on the terminal state or the terminal cost or the horizon size. Moreover, the UTC-RHC control gain approaches the optimal value associated with the infinite horizon optimal control problems.