American Institute of Mathematical Sciences

January  2008, 4(1): 107-123. doi: 10.3934/jimo.2008.4.107

A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback

 1 School of Management, Fudan University, Shanghai 200433, China 2 School of Science, Shenzhen University, Guang Dong 518060, China 3 Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501

Received  October 2006 Revised  July 2007 Published  January 2008

This paper presents a new basic model based on automatons for the state feedback control of discrete event systems (DES), including (repeated) concurrent DES. So, this new model unifies the Ramadge-Wonham framework and the controlled Petri nets, with or without concurrency or repeated concurrency. The repeated concurrent model under Ramadge-Wonham framework is first presented here. We study relationships between the concurrent models and the basic model. Based on this, we show that the uniqueness of the maximal permissive state feedback (PSF) of a predicate $P$ is equivalent to the weak interaction of $P$, which is also equivalent to that the set of PSF is closed under a disjunction. These results are also true for the concurrent systems, but the weak interaction may be difficult to be verified. Hence, we try to simplify the weak interaction by introducing concepts of cover, transitivity and local concurrently well-posedness (CWP). We show that the local CWP can ensure that the set of PSF for the concurrent systems equals that for the basic system.
Citation: Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback. Journal of Industrial & Management Optimization, 2008, 4 (1) : 107-123. doi: 10.3934/jimo.2008.4.107
 [1] Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems II: Control synthesis problems. Journal of Industrial & Management Optimization, 2008, 4 (4) : 713-726. doi: 10.3934/jimo.2008.4.713 [2] Qiying Hu, Wuyi Yue. Optimal control for resource allocation in discrete event systems. Journal of Industrial & Management Optimization, 2006, 2 (1) : 63-80. doi: 10.3934/jimo.2006.2.63 [3] Anthony M. Bloch, Melvin Leok, Jerrold E. Marsden, Dmitry V. Zenkov. Controlled Lagrangians and stabilization of discrete mechanical systems. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 19-36. doi: 10.3934/dcdss.2010.3.19 [4] Qiying Hu, Wuyi Yue. Two new optimal models for controlling discrete event systems. Journal of Industrial & Management Optimization, 2005, 1 (1) : 65-80. doi: 10.3934/jimo.2005.1.65 [5] Qiying Hu, Wuyi Yue. Optimal control for discrete event systems with arbitrary control pattern. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 535-558. doi: 10.3934/dcdsb.2006.6.535 [6] Michel Duprez, Guillaume Olive. Compact perturbations of controlled systems. Mathematical Control & Related Fields, 2018, 8 (2) : 397-410. doi: 10.3934/mcrf.2018016 [7] Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479-502. doi: 10.3934/jgm.2014.6.479 [8] Changzhi Wu, Kok Lay Teo, Volker Rehbock. Optimal control of piecewise affine systems with piecewise affine state feedback. Journal of Industrial & Management Optimization, 2009, 5 (4) : 737-747. doi: 10.3934/jimo.2009.5.737 [9] Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301 [10] Haiying Jing, Zhaoyu Yang. The impact of state feedback control on a predator-prey model with functional response. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 607-614. doi: 10.3934/dcdsb.2004.4.607 [11] Huawen Ye, Honglei Xu. Global stabilization for ball-and-beam systems via state and partial state feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 17-29. doi: 10.3934/jimo.2016.12.17 [12] Peng Cui, Hongguo Zhao, Jun-e Feng. State estimation for discrete linear systems with observation time-delayed noise. Journal of Industrial & Management Optimization, 2011, 7 (1) : 79-85. doi: 10.3934/jimo.2011.7.79 [13] Dorothy Bollman, Omar Colón-Reyes. Determining steady state behaviour of discrete monomial dynamical systems. Advances in Mathematics of Communications, 2017, 11 (2) : 283-287. doi: 10.3934/amc.2017019 [14] Mariko Arisawa, Hitoshi Ishii. Some properties of ergodic attractors for controlled dynamical systems. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 43-54. doi: 10.3934/dcds.1998.4.43 [15] Changyan Di, Qingguo Zhou, Jun Shen, Li Li, Rui Zhou, Jiayin Lin. Innovation event model for STEM education: A constructivism perspective. STEM Education, 2021, 1 (1) : 60-74. doi: 10.3934/steme.2021005 [16] Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 209-226. doi: 10.3934/dcdsb.2017011 [17] Nguyen H. Sau, Vu N. Phat. LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback. Journal of Industrial & Management Optimization, 2018, 14 (2) : 583-596. doi: 10.3934/jimo.2017061 [18] Sang-Heon Lee. Development of concurrent structural decentralised discrete event system using bisimulation concept. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 305-317. doi: 10.3934/naco.2016013 [19] Shohel Ahmed, Abdul Alim, Sumaiya Rahman. A controlled treatment strategy applied to HIV immunology model. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 299-314. doi: 10.3934/naco.2018019 [20] Qizhen Xiao, Binxiang Dai. Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1065-1081. doi: 10.3934/mbe.2015.12.1065

2020 Impact Factor: 1.801