This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights’ updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example.

中文翻译：

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针对具有规定性能和执行器故障的非线性系统的基于命令过滤器的事件触发固定时间控制

本文研究了基于命令滤波器的自适应神经网络（NN）最小学习实用固定时间控制，用于具有规定性能和执行器故障的随机非线性系统。所考虑的系统是一个高阶非严格反馈随机结构，具有未知的动态和外部干扰。通过将神经网络与最小学习参数方法相结合，消除了对非线性函数先验知识的需要，并且无论系统的阶数和神经节点的数量如何，神经网络的权重更新律的数量都减少到一个。这种减少显着降低了计算负担。此外，神经网络高斯基函数的独特性质被应用于解决非严格反馈结构的代数环问题。提出了一种新颖的事件触发控制机制来节省通信资源。为了克服“复杂性爆炸”和“奇异性”问题，提出了一种新颖的固定时间命令过滤器，然后提出了一种改进的补偿机制来减轻命令过滤器中出现的错误。此外，为了改善跟踪误差的瞬态和稳态性能，考虑了规定的性能函数。通过Lyapunov稳定性理论，表明所开发的自适应反步控制方案保证闭环系统信号在固定时间内概率有界，收敛时间与初始值无关，并且跟踪误差始终保持在衰减的规定性能范围内。最后通过实际仿真算例验证了理论结果的有效性和实用性。