Set Stabilization and Optimal Control of Switched Multi-Valued Logical Control Networks With State-Dependent Switching Signals

This brief studies the set stabilization and optimal control problem of switched multi-valued logical control networks (SMLCNs) with state-dependent switching signals. Firstly, based on the algebraic expression of SMLCNs, a sufficient and necessary condition for the set stabilization of SMLCNs is given. Then by using the principle of Dijkstra algorithm in graph theory, the Lagrange-type optimization problem for the set stabilization of SMLCNs is considered, and an algorithm for the design of optimal control sequence is presented, by which the state of the SMLCN can transfer to the given set with the minimal cost. Finally, a numerical example is given to demonstrate validity and effectiveness of the obtained results, in where we can see that by using the above results, one can not only judge the set stabilization of SMLCNs but also obtain an optimal control sequence on the premise that the system is set stabilization.