An Optimal inverse system for max-plus linear system taking account of local dynamical system

Abstract

Recently, we have proposed an optimal inverse system for linear-parameter-varying max-plus-linear (LPV-MPL) system by extending the conventional inverse systems for fixed parameter MPL systems. In the design method, the linear parametrized control law is given, and the parameters are optimized by solving the linear programming successively. However, from the applicational point of view, there are many cases where the behaviour of parameters has dynamical properties and cannot be changed directly. Therefore, this paper gives the optimal inverse system for LPV-MPL with the counter k-dependent parameters in order that we could take account of the dynamical behavior of the parameters.