In this paper, we propose a novel differential-game based neural network (NN) control architecture to solve an optimal control problem for a class of large-scale nonlinear systems involving N-players. We focus on optimizing the usage of the computational resources along with the system performance simultaneously. In particular, the N-players' control policies are desired to be designed such that they cooperatively optimize the large-scale system performance, and the sampling intervals for each player are desired to reduce the frequency of feedback execution. To develop a unified design framework that achieves both these objectives, we propose an optimal control problem by integrating both the design requirements, which leads to a multi-player differential-game. A solution to this problem is numerically obtained by solving the associated Hamilton-Jacobi (HJ) equation using event-driven approximate dynamic programming (E-ADP) and artificial NNs online and forward-in-time. We employ the critic neural networks to approximate the solution to the HJ equation, i.e., the optimal value function, with aperiodically available feedback information. Using the NN approximated value function, we design the control policies and the sampling schemes. Finally, the event-driven N-player system is remodeled as a hybrid dynamical system with impulsive weight update rules for analyzing its stability and convergence properties. The closed-loop practical stability of the system and Zeno free behavior of the sampling scheme are demonstrated using the Lyapunov method. Simulation results using a numerical example are also included to substantiate the analytical results.

中文翻译：

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具有多种资源的大型非线性系统的具有资源意识的差分博弈近似最优控制。

在本文中，我们提出了一种新颖的基于差分博弈的神经网络（NN）控制体系结构，以解决一类涉及N个参与者的大型非线性系统的最优控制问题。我们专注于同时优化计算资源的使用和系统性能。特别地，期望设计N个玩家的控制策略，使得它们协同地优化大型系统性能，并且期望每个玩家的采样间隔以减少反馈执行的频率。为了开发实现这两个目标的统一设计框架，我们通过综合两个设计要求提出了一个最优控制问题，这导致了多人游戏的差异化。该问题的解决方案是通过使用事件驱动的近似动态规划（E-ADP）和人工NN在线实时地求解相关的Hamilton-Jacobi（HJ）方程来数值获得的。我们使用批评者神经网络，利用非周期性的反馈信息，对HJ方程（即最优值函数）的解进行近似。使用NN近似值函数，我们设计了控制策略和采样方案。最后，将事件驱动的N玩家系统重构为具有脉冲权重更新规则的混合动力系统，以分析其稳定性和收敛性。使用Lyapunov方法论证了系统的闭环实际稳定性和采样方案的Zeno自由行为。