Time-Optimal Stabilization of Switched Boolean Control Networks Under Constraints: An Efficient Graphical Approach

In this paper, an efficient graph-theoretic approach for state-feedback time-optimal stabilization of switched Boolean control networks (SBCNs) under constrains is proposed. Initially, the dynamic properties of the SBCN are represented through a state transition graph (STG). The equivalence between the shortest-time state trajectory and the shortest path within the STG is then established. An efficient algorithm based on the breadth-first search of the STG is developed to rapidly identify the set of reachable states, calculate the distance to each reachable state, and collect the shortest-time control information for every state. Furthermore, the state-feedback gain matrices for time-optimal stabilization are constructed. Finally, constraints handling is presented by modifying the STG according to a variety of constraints while reusing the core graph-theoretical algorithms. Overall, the proposed approach is distinguished by its graphical perspective and its lowest time complexity in theory.