Application of graph theory in hybrid control systems using state space mesh

Abstract

In this paper, a novel method is developed to control hybrid dynamical systems which contain both continuous and discrete dynamics. The objective of the controller is to drive the system from its initial state to the desired final state. The hybrid controller consists of two independent parts. To design the first part, the abstract controller, a regular mesh of the continuous state space is constructed. Then, a behaviour graph of the system is derived by choosing a finite family of control signals and considering the discrete dynamic of the system. Subsequent application of the Floyd–Warshall algorithm, which was originally developed to find the minimum length path in a graph, allows the abstract controller to be constructed. A new algorithm is proposed to derive the control command for the second part, which constructs a bisimulation relation and finalizes the control process. Finally, the controller is applied to a dynamic system, and the obtained results show the effectiveness of the proposed control methodology.