Economic model predictive control with terminal set dynamic programming for tracking control

This paper focuses on vehicle tracking control issues with consideration of energy efficiency, ride comfort and tracking performance. To address this issue, an economic model predictive control (EMPC) framework is proposed by taking average performance into account and introducing a time-varying terminal set. We integrate an economic model predictive controller and a terminal controller with a feedback gain related to the time-varying terminal set into the proposed EMPC framework. An acceleration-dependent average constraint is designed and incorporated into the MPC optimization problem to facilitate the convergence of the actual acceleration to the desired one, which enables the vehicle to implement a smooth driving style that boosts energy economy. A tuning factor in the average constraint has the capacity to balance energy consumption and control performance. Under the premise of invariance constraints, a dynamic terminal set is constructed by solving a dynamic programming problem online, which enables an arbitrary location and scale of the terminal set at each iteration by taking the current and predicted tracking errors into account. This allows a reduction in the conservativeness of an economic model predictive controller in the sense of both the region of attraction and the cost bound. Recursive feasibility of the MPC optimization problem and the terminal set dynamic programming is ensured, and average performance is not worse than the performance with an optimal steady-state operation. Moreover, the convergence of the closed-loop tracking error to the optimal steady-state is guaranteed by using the dissipativity theory. The effectiveness of the proposed algorithm is verified by numerical comparisons with different controller parameters and standard EMPC.