TY - JOUR
T1 - Petri-Net Controller Synthesis for Partially Controllable and Observable Discrete Event Systems
AU - Luo, Ji Liang
AU - Zhou, Meng Chu
N1 - Funding Information:
This work was supported in part by National Science Foundation of China under Grant No. 61573158, Promotion Program for Young and Middle-aged Teacher in Science and Technology funded by Huaqiao University under Grant No. 11FJRC01, the FDCT (Fundo para o Desenvolvimento das Ciencias e da Tecnologia) under Grant no. 119/2014/A3, and Natural Science Foundation of Fujian Province of China under Grant no. 2014J01241.
PY - 2017/3
Y1 - 2017/3
N2 - To enforce linear constraints on Petri nets that are partially controllable and observable, this work proposes an approach based on constraint transformation. First, a state-space equation of a Petri net control system based on event feedback is obtained by expressing a control action as a matrix, and the optimal control policy is designed. However, this policy needs to solve a nonlinear program on line. Second, pre-transition-gain-transformation is proposed to equivalently transform a constraint into a disjunction of new ones for an uncontrollable transition, and, similarly, post-transition-gain-transformation to transform a constraint into a disjunction of new ones for an unobservable transition. An algorithm is then given to transform a constraint into a disjunction of admissible ones, and, consequently, an efficient policy, which may not be optimal, can be designed. Third, in order to guarantee that the policy be both efficient and optimal, a dynamic linear constraint is introduced. Further, observing-transformation is proposed to simplify a dynamic constraint for an unobservable transition, and an algorithm is given to equivalently transform a class of linear constraints into admissible dynamic ones. As a result, an optimal controller requiring little online computation can be designed accordingly for some class of Petri nets. Finally, a maze system is used to illustrate the theoretical results.
AB - To enforce linear constraints on Petri nets that are partially controllable and observable, this work proposes an approach based on constraint transformation. First, a state-space equation of a Petri net control system based on event feedback is obtained by expressing a control action as a matrix, and the optimal control policy is designed. However, this policy needs to solve a nonlinear program on line. Second, pre-transition-gain-transformation is proposed to equivalently transform a constraint into a disjunction of new ones for an uncontrollable transition, and, similarly, post-transition-gain-transformation to transform a constraint into a disjunction of new ones for an unobservable transition. An algorithm is then given to transform a constraint into a disjunction of admissible ones, and, consequently, an efficient policy, which may not be optimal, can be designed. Third, in order to guarantee that the policy be both efficient and optimal, a dynamic linear constraint is introduced. Further, observing-transformation is proposed to simplify a dynamic constraint for an unobservable transition, and an algorithm is given to equivalently transform a class of linear constraints into admissible dynamic ones. As a result, an optimal controller requiring little online computation can be designed accordingly for some class of Petri nets. Finally, a maze system is used to illustrate the theoretical results.
KW - Forbidden states
KW - Petri nets
KW - generalized mutual exclusion constraints
KW - linear constraints
KW - supervisory control
UR - http://www.scopus.com/inward/record.url?scp=85015105428&partnerID=8YFLogxK
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U2 - 10.1109/TAC.2016.2586604
DO - 10.1109/TAC.2016.2586604
M3 - Article
AN - SCOPUS:85015105428
SN - 0018-9286
VL - 62
SP - 1301
EP - 1313
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 3
M1 - 7502164
ER -