Controllability of Linear Time-Varying Control System Based on Non-Cooperative Dynamic Games

When we face a complex, evolving artificial system, there are "rational" individuals in the system who pursue their own interests. This paper we regulate the individuals in order to avoid significant pitfalls. First, we introduce hierarchical structure model of a game-based control system for macro-regulation and formulate the model by forward differential equation. Then we analyze the system with the extreme value principle and give the unique solution known as the Nash equilibrium. Moreover, we converse the model to the forward and backward equation to study the necessary and sufficient condition on the controllability of the system. Finally, we give the dual model of the system to study the observability inequality.