Piecewise-linear constrained control for timed continuous Petri nets

Timed Continuous Petri Net (TCPN) systems are piecewise linear models with input constraints that can approximate the dynamical behavior of a class of timed discrete event systems. This paper concentrates in the development of a control structure for TCPN that transfers the system from the initial state to another desired one. The resulting control law consists in a Linear Programming Problem, which is solved on-line, and a set of gain matrices, one for each configuration. This approach allows the use of any classical pole assignment technique for the computation of the gain matrices. Furthermore, convergence to the desired marking and input boundedness are demonstrated.