Piecewise-linear constrained control for timed continuous Petri nets

Abstract

Abstract-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.

Performance control of Markovian Petri nets via fluid models: A stock-level control example

“…However, only three transitions exhibit significant, and almost constant, delays: t 5 , t 8 and t 11 . Furthermore, t 6 must fire faster than t 7 whenever both are enabled.…”

“…Uncontrollable transitions were considered in [10], where a gradient-based controller was proposed for driving the output towards the desired value. In [11], uncontrollable transitions were also considered. There, the classical linear feedback control structure was adapted (computing a gain matrix for each region), avoiding computational complexity problems and providing feasibility and effectiveness.…”

“…Since the covariance matrix of the error (P k+1 ) is used for the next time step, a feedback-loop with the unit delay z −1 is added in the Block Diagram. Then, block EKF computes the gain K k e k , with which the estimation for the next time step m k+1 can be obtained by using (11). In this way, with the output of the M P N system and block EKF it is possible to obtain an estimation for the state as if it were a T CP N system, i.e., it is obtained m that evolves like the T CP N system but approximates the mean value of the M P N one in agreement to its output values Y.…”

“…By using the techniques introduced in [11], a control law was designed for the T CP N system ( fig. 3), and then interpreted and applied to the original one, according to the control scheme described in the previous section ( fig.…”

“…In this work, timed continuous Petri net (T CP N ) models under infinite server semantics are considered, since it has been found that such systems approximate interesting classes of DES. In fluid models more analytical techniques can be used for the analysis of some interesting properties, like controllability [6] and the synthesis of controllers, either for the optimal steady-state control problem [7] or dynamic control for reaching a desired marking in models in which all transitions are controllable [8], [9] or with some uncontrollable transitions [10], [11].…”