Receding horizon-based feedback optimization for mix-valued logical networks: The imperfect information case

The optimization problem of mix-valued logical system is investigated. Firstly, a recursive solution is obtained for the finite horizon case. Subsequently, it is proved that as long as the filter length is large enough, the optimal control sequence obtained by the receding horizon-based method, coincides with the best strategy of the infinite horizon case. Based on this observation, we certify that the infinite horizon optimization problem is solvable by a one unit delayed feedback control. Therefore, instead of searching optimal control for infinite times, we can solve the infinite optimization problem by calculating the optimal feedback matrix, which can be obtained from a finite horizon optimization problem. Several examples are presented to illustrate the proposed theory.