An extension of the linear integer program approach for controller synthesis of DES modeled by Petri nets

In the literature, linear algebraic approaches are always attractive and important tools for solving the supervisory control problem of discrete event systems (DES) modeled by Petri nets with linear inequation constraints. Especially, linear integer programming (LIP) is an efficient technique for the on-line computation of the control policy when the maximal uncontrollable subnet is loop-free. However, if there are some loops in the maximal uncontrollable subnet, the computational difficulty of nonlinear integer programming (NIP) is a great obstacle to the online computation of the control policy. The paper proposes an extension of the LIP method (ELIP) to deal with the problem of NIP. The main idea is to decompose the maximal uncontrollable subnet into two small uncontrollable subnets, i.e. loop-free subnet and loop-in subnet. Because the loop-free subnet can be solved by LIP and reachability analysis can be used for the loop-in subnet, NIP is avoided for online computing the control policy. The technique of optimal decomposition is also presented in the paper.