Finite-time controllability and stabilization of probabilistic logical systems with state-dependent constraint via subset transition method |
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| Institution: | 1. LAJ Laboratory, University of Jijel, Algeria;2. Université Paris-Saclay, Univ Evry, IBISC, Evry 91020, France;1. Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu 241000, China;2. Key Laboratory of Smart Manufacturing in Energy Chemical Process (East China University of Science and Technology), Ministry of Education, Shanghai 200237, China;1. Department of Electrical Engineering, Shiraz University of Technology, Shiraz, Iran;2. Department of Electrical and Computer Engineering, Windsor University, Windsor, ON, Canada;1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China;2. Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University, Ministry of Education, China;3. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China;1. School of Electrical Engineering, Hunan University of Technology, Zhuzhou 412000, China;2. School of Mathematical Science, Sunway University, Selangor Darul Ehsan 47500, Malaysia;1. Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;2. School of Business, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | Constraints are very common for practical control systems. For logical systems, the existing technique of pre-feedback is an effective way of treating state-dependent constraints in control when the state is measurable. However, it is inapplicable for the case when measurement information is not available. In this situation, in order for the control input to not violate the state-dependent constraint, the control at each step must be selected from the common admissible controls of all possible states. Motivated by this observation, in this study, we propose a novel technique, termed the subset transition method, for finite-time controllability and stabilization of probabilistic logical dynamic control system (PLDCS) with a state-dependent control constraint. The main idea of this method is to construct an unconstrained deterministic logical control system over the power set of the state space, called the subset transition system (SubSTS), characterizing the transitional dynamics between subsets under common admissible controls. We prove that a control sequence is admissible with respect to all states in an initial subset if and only if it does not steer the SubSTS from the initial subset to the empty set. Based on this, necessary and sufficient conditions for set controllability and set stabilizability are obtained. Examples are presented to demonstrate the application of the obtained results. |
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