Stochastic Linear Quadratic Game Research Articles

Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games

In this paper, we examine a sampled-data Nash equilibrium strategy for a stochastic linear quadratic (LQ) differential game, in which admissible strategies are assumed to be constant on the interval between consecutive measurements. Our solution first involves transforming the problem into a linear stochastic system with finite jumps. This allows us to obtain necessary and sufficient conditions assuring the existence of a sampled-data Nash equilibrium strategy, extending earlier results to a general context with more than two players. Furthermore, we provide a numerical algorithm for calculating the feedback matrices of the Nash equilibrium strategies. Finally, we illustrate the effectiveness of the proposed algorithm by two numerical examples. As both situations highlight a stabilization effect, this confirms the efficiency of our approach.

Game theoretic-based optimal load frequency control of power systems with network-induced delays

This paper presents a game theoretic-based load frequency control (LFC) scheme for power systems with network-induced delays. First, a dynamic model of two-area LFC systems is developed under consideration of bounded network-induced delays. Second, the optimal control problem of power systems with network-induced delays is formulated as a stochastic linear quadratic game. Then, by using differential games and Lyapunov theories, the game theoretic-based optimal load frequency controllers are designed for the system under consideration, and an algorithm is presented to make the desired optimal LFC gains solvable. Finally, a case study is carried out to show the effectiveness of the proposed method.