Switching Model Predictive Control for Perturbed Max-Plus Linear Systems via Minimum Dwell-Time

In this article, switching model predictive control (MPC) is proposed for a perturbed max-plus linear system with a reference signal. The lack of stability guarantee for MPC brings difficulties in reducing tracking errors caused by perturbations in the perturbed max-plus linear system. To reduce tracking errors, the perturbed max-plus linear system is partitioned into a switching max-plus linear system by a permutation matrix. Based on a local maximum terminal set, each mode of the switching max-plus linear system is assigned with an optimal control problem to track the reference signal. Minimum dwell-time is designed to ensure the feasibility of the switching MPC and the stability of the switching max-plus linear system via Hausdorff metric analyses and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\infty$</tex-math></inline-formula>-norm hypercube invariance. Numerical simulations show the effectiveness and superiority of the switching MPC for a perturbed max-plus linear system.