Modeling and optimal control of multi-hop control networks based on the MLD framework

A multi-hop control network (MHCN) is a control system in which plants and controllers are connected through a multi-hop wireless network modeled by a directed graph. In this paper, based on the MLD (Mixed Logical Dynamical) framework, which is one of the powerful methods in hybrid systems control, we propose a modeling method and an optimal control method of MHCNs. First, a directed graph in MHCNs is modeled by a pair of linear equation and inequality with binary variables, and the MLD model of MHCNs is derived. Next, by using the MLD model, the optimal control problem is transformed into a mixed integer quadratic programming problem. Finally, a numerical simulation on optimal control of a simple MHCN is shown.