Abstract The problem of adaptive neural network (NN) control and the dynamic surface control (DSC) method for a series of nonlinear systems with uncertainty is discussed in this paper. Unknown smooth functions can be approximated by radial basis function-neural networks (RBF-NNs) with arbitrary accuracy in nonlinear systems. The DSC scheme is introduced for nonlinear systems with uncertainty to overcome the “explosion of complexity” compared with the conventional backstepping approach. Meanwhile, the global asymptotic stability of nonlinear systems is manifested via the Lyapunov stability theory, which indicates the uniform boundedness of all closed-loop signals is ensured and dynamic surface errors are arbitrarily small in the compact set by selecting proper parameters. Finally, the effectiveness of the proposed control technique is validated by two simulation examples.

中文翻译：

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基于动态曲面控制的不确定非线性系统自适应神经网络控制

摘要 本文讨论了一系列具有不确定性的非线性系统的自适应神经网络（NN）控制问题和动态表面控制（DSC）方法。未知平滑函数可以通过径向基函数神经网络 (RBF-NN) 在非线性系统中以任意精度逼近。DSC 方案是针对具有不确定性的非线性系统引入的，以克服与传统反步方法相比的“复杂性爆炸”。同时，非线性系统的全局渐近稳定性是通过李雅普诺夫稳定性理论表现出来的，这表明通过选择合适的参数，可以保证所有闭环信号的一致有界性和动态表面误差在紧集合中任意小。最后，