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首页> 外文期刊>International Journal of Adaptive Control and Signal Processing >Adaptive neural network-based optimal control of nonlinear continuous-time systems in strict-feedback form
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Adaptive neural network-based optimal control of nonlinear continuous-time systems in strict-feedback form

机译：基于自适应神经网络的严格反馈非线性连续时间系统的最优控制

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摘要

This paper focuses on neural network (NN) based optimal control of nonlinear continuous-time systems in strict-feedback form when the system dynamics are known by using an adaptive backstepping approach. A single NN-based adaptive approach is designed to learn the solution of the infinite horizon continuous-time Hamilton-Jacobi-Bellman (HJB) equation while the corresponding optimal control input that minimizes the HJB equation is calculated in a forward-in-time manner without using value and policy iterations. First, the optimal control problem is solved for a generic multi-input and multi-output nonlinear system with a state feedback approach. Then the approach is extended to a single-input and single-output nonlinear system by using output feedback via a nonlinear observer. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signals approach the optimal control inputs with small bounded error both for the state and output feedback-based controller designs. In the absence of NN reconstruction errors, asymptotic convergence to the optimal control is demonstrated. Finally, simulation examples are provided to validate the theoretical results.
机译：当使用自适应反步方法获知系统动态时，本文将重点关注基于神经网络（NN）的严格连续形式的非线性连续时间系统的最优控制。设计了一种基于NN的自适应方法来学习无限地平线连续时间Hamilton-Jacobi-Bellman（HJB）方程的解，同时以提前方式计算使HJB方程最小化的相应最佳控制输入无需使用价值和政策迭代。首先，通过状态反馈方法解决了通用多输入多输出非线性系统的最优控制问题。然后，通过使用通过非线性观察器的输出反馈，该方法扩展到单输入单输出非线性系统。使用李雅普诺夫（Lyapunov）技术表明，对于状态和基于输出反馈的控制器设计，所有信号均最终均匀地受到限制，并且近似控制信号以较小的有限误差逼近最佳控制输入。在没有神经网络重构错误的情况下，证明了渐近收敛到最优控制。最后，通过仿真实例验证了理论结果。

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