%0 Journal Article
%T 基于零和博弈的部分未知线性离散系统多智能体分布式最优跟踪控制<br>The Multiagent Distributed Optimal Tracking Control of Partially Unknown Linear Discrete Systems Based on Zero-Sum Games
%A 熊天娇
%A 王朝立
%J Advances in Applied Mathematics
%P 158-179
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.111022
%X 本文考虑了具有外部扰动的不确定线性离散系统分布式最优跟踪控制问题。现有的研究要求系统动力学已知且未证明最优解就是纳什均衡解。由于控制策略和干扰之间的竞争关系，该问题首先转变为多智能体零和博弈。本文根据所提出的新性能指标，采用内外循环算法对哈密顿雅可比艾萨克斯(HJI)方程进行迭代求解，并验证了收敛性。此外，它表明该算法得到的最优解是零和博弈的纳什均衡解。本文进一步表明，每当系统不完全已知时，单层神经网络可用于近似实值函数，与现有的三层网络相比，这可以降低计算复杂性。最后，通过仿真验证了该方法的有效性。<br />
The paper studies the distributed optimal tracking control problem by considering linear discrete systems with unknown disturbances. The existing research requires that the system dynamics are known and have not proved that the optimal solution is the Nash equilibrium. Such a problem is first transformed into a multiagent zero-sum game due to the competitive situation among inputs and disturbances. According to the proposed new performance index, the internal and external loop algorithm is adopted to solve the Hamilton Jacobi Isaacs (HJI) equations iteratively, and the convergence is also proven. In addition, it shows that the optimal solution obtained by the algorithm is the Nash equilibrium of the zero-sum game. This paper further shows that, whenever the system is not fully known, the single-layer neural network could be used to approximate the real value function, which can reduce the computational complexity compared with the prevalent three-layer networks. Finally, simulations are provided to show the effectiveness of the method.
%K 零和博弈，L<sub>2-</sub>增益，纳什均衡，线性离散系统<br>Zero-Sum Game
%K L<sub>2-</sub>Gain
%K Nash Equilibrium
%K Linear Discrete Systems
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=48070