Nonsmooth nonlinear systems can model many practical processes with discontinuous property and are difficult to be stabilized by classical control methods like smooth nonlinear systems. This article considers the output-feedback adaptive neural network (NN) control problem for nonsmooth nonlinear systems with input deadzone and saturation. First, the nonsmooth input deadzone and saturation is converted to a smooth function of affine form with bounded estimation error by means of the mean-value theorem. Second, with the help of approximation theorem and Filippov’s differential inclusion theory, the given nonsmooth system is converted to an equivalent smooth system model. Then, by introducing a proper logarithmic barrier Lyapunov function (BLF), an output-feedback adaptive NN strategy is set up by constructing an appropriate observer and adopting the adaptive backstepping technique. A new stability criterion is established to guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, comparative simulations through Chua’s oscillator are offered to verify the effectiveness of the proposed control algorithm.

中文翻译：

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具有输入死区和饱和度的不确定非光滑非线性系统的输出反馈自适应神经网络控制


非光滑非线性系统可以模拟许多具有不连续特性的实际过程，并且很难通过光滑非线性系统等经典控制方法来稳定。本文考虑具有输入死区和饱和的非光滑非线性系统的输出反馈自适应神经网络 (NN) 控制问题。首先，利用中值定理将非光滑输入死区和饱和度转换为具有有限估计误差的仿射形式的光滑函数。其次，借助逼近定理和Filippov的微分包含理论，将给定的非光滑系统转换为等效光滑系统模型。然后，引入合适的对数势垒Lyapunov函数（BLF），构造合适的观测器并采用自适应反步技术，建立输出反馈自适应神经网络策略。建立了一种新的稳定性准则来保证闭环系统中的所有信号都是半全局一致最终有界（SGUUB）。最后，通过蔡氏振荡器进行比较仿真，以验证所提出的控制算法的有效性。