Finite-time controllability and stabilization of probabilistic logical systems with state-dependent constraint via subset transition method

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. (c) 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This study proposes a novel technique, called the subset transition method, for finite-time controllability and stabilization of probabilistic logical dynamic control systems (PLDCS) with a state-dependent control constraint. The main idea is to construct an unconstrained deterministic logical control system, called the subset transition system (SubSTS), characterizing the transitional dynamics between subsets under common admissible controls. Necessary and sufficient conditions for set controllability and set stabilizability are obtained based on the SubSTS. Examples are presented to demonstrate the application of the obtained results.