Mixed H 2 /H ∞ Control for Nonlinear Closed-Loop Stackelberg Games With Application to Power Systems

作者：Zhongyang Ming, Huaguang Zhang, Yushuai Li, Yuling Liang · 发表于：IEEE Transactions on Automation Science and Engineering · 年份：2022 · DOI：10.1109/tase.2022.3216733 · 被引用次数：45 · 研究领域：Adaptive Dynamic Programming Control、Stability and Controllability of Differential Equations、Frequency Control in Power Systems

This paper studies the mixed$H_{2}/H_{\infty} $control problem for nonlinear closed-loop Stackelberg games via adaptive dynamic programming (ADP) technology. Firstly, by constructing a cost function with the Lagrange multiplier, the hierarchical Stackelberg game problem is transformed into a coupled Hamilton-Jacobi-Isaacs (HJI) equations problem. In the second place, the critic-actor neural networks (NNs) framework is established to approximate the cost functions and control strategies of Stackelberg game. The corresponding algorithm flow is given. This is a novel idea that NNs are used to approximate the control strategies in Stackelberg game that cannot be given a specific form. Finally, the algorithm is applied to the load frequency control (LFC) problem of single-area power system. The optimal neural network weights are obtained by the designed ADP algorithm. And the comparison results of the three control schemes show that the mixed$H_{2}/H_{\infty} $based on Stackelberg game can not only achieve better frequency response, but also have better performance indicators for leader. Note to Practitioners—$H_{\infty} $control studies the anti-interference ability of the system, and the designed controller should attenuate the suppression coefficient of adjusting error and external disturbance to a given minimum level.$H_{2}$control is optimal control, and the controller is designed to minimize the cost function of system state and system input. In general, in$H_{\infty} $or$H_...