Region minimised monitor design for deadlock-prevention of S4PR nets

Constructing P-invariants is a typical way to design deadlock-prevention monitors for systems of sequential systems with shared resources (S⁴PR) nets in the existing siphon-based methods. When there are some certain structures in S⁴PR nets, the existing siphon-based methods are not suitable for monitor designing. This study advances siphon´s max-controlled conditions for P-invariant construction. Accordingly, a region minimised optimisation (RMO) method for deadlock-prevention monitor design is proposed, which is realised by using standardised mixed integer programming tool. In order to lower the limitation of monitors on system behaviour, the region under supervision is minimised. The RMO method is able to design monitors for S⁴PR nets in which the existing methods are not suitable, is free of trivial construction of P-invariants, and is applicable to S⁴PR nets with unobservable transitions. Since RMO is originated from the basic idea of siphon control, it remains the advantage of high computational efficiency, and also can replace the existing siphon-based monitor design methods.