This article addresses the distributed optimal fault-tolerant control (FTC) issue by using the two-level game approach for a class of nonlinear interconnected systems, in which each subsystem couples with its neighbors through not only the states but also the inputs. At the first level, the FTC problem for each subsystem is formulated as a zero-sum differential game, in which the controller and the fault are regarded as two players with opposite interests. At the second level, the whole interconnected system is formulated as a graphical game, in which each subsystem is a player to achieve the global Nash equilibrium for the overall system. The rigorous proof of the stability of the interconnected system is given by means of the cyclic-small-gain theorem, and the relationship between the local optimality and the global optimality is analyzed. Moreover, based on the adaptive dynamic programming (ADP) technology, a distributed optimal FTC learning scheme is proposed, in which a group of critic neural networks (NNs) are established to approximate the cost functions. Finally, an example is taken to illustrate the efficiency and applicability of the obtained theoretical results.

中文翻译：

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非线性互联系统基于两级博弈的分布式最优容错控制。

本文通过对两类非线性互连系统使用两级博弈方法来解决分布式最优容错控制（FTC）问题，其中每个子系统不仅通过状态而且通过输入与邻居耦合。在第一层，每个子系统的FTC问题被表述为零和微分博弈，其中控制器和故障被视为具有相反利益的两个参与者。在第二级，整个互连系统被表述为图形游戏，其中每个子系统都是一个参与者，以实现整个系统的全局Nash平衡。利用循环小增益定理给出了互联系统稳定性的严格证明，并分析了局部最优与全局最优之间的关系。此外，基于自适应动态规划（ADP）技术，提出了一种分布式最优FTC学习方案，在该方案中建立了一组评论神经网络（NNs）来近似成本函数。最后，以一个例子来说明所获得理论结果的效率和适用性。