Dynamics and steady state analysis of controlled Generalized Batches Petri Nets

This paper is dedicated to an extended class of hybrid Petri nets called controlled Generalized Batches Petri Nets. The novel feature of these nets is that the firing flow of continuous and batch transitions and the transfer speed of batch places are control variables. First we propose a linear programming problem to compute the instantaneous firing flow vector and the instantaneous transfer speed vector solving an optimization problem, where the objective function depends on the control goal. Second we analyze and characterize the steady state of this model solving a programming problem that takes into account the net structure and the initial marking. This problem is linear if the transfer speeds are preassigned while it is nonlinear if the transfer speeds are control variables. In such a last case, a viable technique to compute a family of solutions by linear relaxation of the non linear problem is presented. The optimality of steady states for given linear objective functions is also addressed.