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

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