Abstract
This paper proposes an optimal inverse system for a max-plus linear system with a linear parameter-varying structure. For the design of inverse systems of max-linear systems, the prediction equation using max-plus linear systems and the greatest subsolution for the linear algebraic equation are required. Hence, this paper newly gives a prediction equation and the greatest sub-solution for the linear parameter-varying system. In addition to those, this paper shows an optimization method for the system parameters in the inverse systems, and this optimization problem can be reduced to the linear programming. Finally, the proposed method is applied to a two-inputs, two-outputs production system with four machines, and the efficiency of the proposed method is demonstrated by using numerical simulations.
