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Robust optimal feedback control design for uncertain systems based on artificial neural network approximation of the Bellman's value function

机译:基于人工神经网络近似的贝尔曼价值函数的不确定系统鲁棒最优反馈控制设计

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In this study, a local approximated solution for the Hamilton-Jacobi-Bellman equation based on differential neural networks is proposed. The approximated Value function is used to obtain a feedback control law for a class of uncertain dynamical systems. The approach to deal with the uncertainties of the dynamical system is a min-max method that yields obtaining a robust-like solution for an optimal control problem. The proposed cost functional is presented in the Bolza form and the necessary and sufficient conditions for getting the min-max optimal solution with the designed robust version of the dynamic programming approach are provided. Moreover, the effect of the neural network approximation is studied. All the analysis considers a smoothness assumption regarding the Value function. The practical stability of the system with the neural network feedback optimal control is formally demonstrated by means of the Lyapunov method. Finally, the performance of the control law is compared in simulation with a classical optimal controller. The proposed controller overcomes the results produced by the classical controller, which is confirmed by the functional evaluation. (C) 2020 Elsevier B.V. All rights reserved.
机译:在该研究中,提出了基于差分神经网络的汉密尔顿 - 雅各比 - 贝尔曼方程的局部近似解。近似值函数用于获得一类不确定动力系统的反馈控制规律。处理动态系统的不确定性的方法是MIN-MAX方法,产生获得鲁棒状解决方案以获得最佳控制问题。提供了拟议的成本函数在Bolza形式中介绍,提供了通过设计的强大版本的动态编程方法进行最小最大最佳解决方案的必要和充分条件。此外,研究了神经网络近似的效果。所有分析都考虑了有关价值函数的平滑度。通过Lyapunov方法正式证明了系统具有神经网络反馈最佳控制的系统的实际稳定性。最后,在具有经典的最佳控制器的模拟中比较了控制法的性能。所提出的控制器克服了经典控制器产生的结果,该结果由功能评估确认。 (c)2020 Elsevier B.v.保留所有权利。

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