Stability of Finite Horizon Optimisation based Control without Terminal Weight
This work provides a new stability condition and algorithm for model predictive control, which is important for control engineers designing systems without terminal cost functions.
This paper addresses the stability analysis of model predictive control (MPC) with a finite horizon and no terminal weight. It proposes a new stabilising MPC algorithm (CMPC) that achieves asymptotic stability if an optimal one-step value function (OSVF) acts as a local control Lyapunov function (CLF).
This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm.