In this article, a decentralized optimal tracking control strategy is proposed for a class of nonlinear systems with tracking error constraints by utilizing adaptive dynamic programming (ADP). It should be noted that ADP technology cannot be directly used to solve decentralized optimal tracking problem of large-scale interconnected nonlinear system with nonzero equilibrium points, since that an infinite domain performance index function may result in an unsolvable solution. In addition, by introducing a smooth function, the constrained tracking error is transformed into an unconstrained one. Then, the error dynamics and a new infinite domain performance index function are designed, such that ADP technology can be used. Following the designed performance index function, the tracking error can be ensured within a small neighborhood of zero. Finally, the feasibility and the effectiveness of the proposed decentralized optimal control scheme are verified through two simulation examples.

中文翻译：

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具有跟踪误差约束的大规模非线性系统的分散最优跟踪控制

在本文中，利用自适应动态规划（ADP），针对一类具有跟踪误差约束的非线性系统，提出了一种分散的最优跟踪控制策略。需要注意的是，ADP 技术不能直接用于解决具有非零平衡点的大规模互联非线性系统的分散最优跟踪问题，因为无限域性能指标函数可能会导致无法解决。此外，通过引入平滑函数，将有约束的跟踪误差转化为无约束的跟踪误差。然后，设计了误差动力学和新的无限域性能指标函数，以便可以使用 ADP 技术。按照设计的性能指标函数，跟踪误差可以保证在很小的零邻域内。最后，