Terminal Constraint-Free Model Predictive Control for Max-Plus Linear Systems

In this paper, terminal constraint-free model predictive control (MPC) is established to track a reference signal for a max-plus linear system. Due to unconvex characteristics of max-plus linear systems, the existence of terminal constraints severely increases the difficulty in solving the optimal control problems. A weighted objective function is designed to make terminal states reach a positively invariant set of a standard max-plus linear system equivalent to the max-plus linear system. A lower bound on the prediction horizon is proposed to maintain exponential stability of the standard max-plus linear system using the terminal constraint-free MPC. Simulation results are given to illustrate effectiveness of the theoretical results on the terminal constraint-free MPC for a max-plus linear system.