Controllability and Observability of Game-Based Logical Control Systems
Changxi Li, Xiao Zhang · SIAM Journal on Control and Optimization · 2025
Abstract. Game-based control systems (GBCSs) are proposed to describe the situation where there is a controller and multiple agents in a hierarchical decision-making structure. However, in most situations, the dynamics of the agents in the hierarchical decision-making system are described by a logical decision-making process. To combine logical control systems and GBCSs, in this paper we propose game-based logical control systems (GBLCSs) to describe such systems. First, the mathematical model of GBLCS is formulated. Then, necessary and sufficient matrix conditions for the controllability and observability of the GBLCSs are derived by using the semitensor product-based algebraic state-space representation method. Finally, the effectiveness of the theoretical results is demonstrated by an example.