Algorithms enhancement for optimal triggering control in logical dynamic systems: Leveraging data structure storage

Abstract

This paper studies stabilization of logical control systems (LCSs) using an event-triggered control strategy. First, an LCS is converted into its algebraic state-space representation. In this framework, a stabilizability criterion for LCSs is established, and the optimal triggering control problem is formulated. The goal of the optimal triggering control is to drive the LCS to a desired state while minimizing the number of states that trigger the control action. Then, the equivalence between designing the optimal triggering controller for an LCS and finding the minimum-weight arborescence in the corresponding transition graph is proved. Subsequently, based on the depth-first search and utilizing a Fibonacci-heap-typed data structure, algorithms are established to determine the stabilizability of LCSs and to design the optimal triggering controller. Finally, an example involving the lac operon in the bacterium Escherichia coli is presented to illustrate the obtained results.