Model Predictive Control of Spatially Distributed Systems with Spatio-Temporal Logic Specifications

In this paper, for spatially distributed systems, we propose a new method of model predictive control with spatio-temporal logic specifications. We formulate the finite-time control problem with specifications described by SSTLf (signal spatio-temporal logic over finite traces) formulas. In the problem formulation, the feasibility is guaranteed by representing control specifications as a penalty in the cost function. Time-varying weights in the cost function are introduced to satisfy control specifications as well as possible. The finite-time control problem can be written as a mixed integer programming (MIP) problem. According to the policy of model predictive control (MPC), the control input can be generated by solving the finite-time control problem at each discrete time. The effectiveness of the proposed method is presented through a numerical example.