A gain scheduled model predictive control for linear-parameter-varying max-plus-linear systems

This paper proposes a design method of model predictive control (MPC) for linear-parameter-varying max-plus-linear (LPV-MPL) systems. The LPV-MPL system is an extended description of max-plus-linear (MPL) systems, and the system matrices are linear representations in terms of system parameters in the max-plus algebra. Using the greatest subsolution for a linear polynomial matrix equation for the derivation of the control law, the system parameters are represented explicitly in the control law. Hence, the proposed MPC is called the gain-scheduled MPC for LPV-MPL systems because the control law is suitable for the gain-scheduled control. The gain-scheduled MPC is effective when the parameters variation is widely changed, and they are scheduled beforehand.