Control design for timed Petri nets based on LMIs and structure expansion

This paper concerns the design of optimal control sequences for timed Petri nets under earliest firing policy. Optimality is defined with respect to the sequences duration. The proposed method computes the control firing sequence and its duration by solving integer linear problems constrained by a set of matrix inequalities that must be fulfilled by a sequence of elementary firing count vectors. To reduce the error that may affect the estimation of the sequence duration, an expansion of the net structure is proposed with respect to the time parameters. The estimation error is proved to be bounded depending on a granularity parameter used for expansion.