Inverse optimal control is a widely used technique for solving various optimal problems arising in the controlled system. However, this method becomes inapplicable to optimal problems when the system has disturbances. In this article, we propose a novel anti-disturbance inverse optimal controller design for a class of high-dimensional chain structure systems with any disturbances, matched, or mismatched. First, a disturbance observer is employed to get the estimates of the disturbances in the system. Then using backstepping approach, the disturbance estimation is incorporated in the virtual control laws, and consequently a control Lyapunov function (CLF) is obtained. Finally, a composite controller is designed by developing an inverse optimal control method using the obtained CLF function. We show the stability analysis of the anti-disturbance controller with rigorous proofs, which minimizes an optimal index while the output converges. Moreover, simulation study and analysis for real application to DC–DC buck converters reveal that the proposed composite controller achieves good performance and stabilizes the system with disturbances.

中文翻译：

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有扰动系统的抗扰动逆最优控制

逆最优控制是一种广泛使用的技术，用于解决受控系统中出现的各种优化问题。然而，当系统存在扰动时，该方法不适用于优化问题。在本文中，我们针对一类具有任意扰动、匹配或不匹配的高维链结构系统提出了一种新颖的抗扰动逆最优控制器设计。首先，使用扰动观测器来估计系统中的扰动。然后使用反步法，将扰动估计纳入虚拟控制律，从而获得控制李雅普诺夫函数（CLF）。最后，通过使用获得的 CLF 函数开发逆最优控制方法来设计复合控制器。我们通过严格的证明展示了抗扰动控制器的稳定性分析，它在输出收敛的同时最小化了一个最优指标。此外，针对 DC-DC 降压转换器实际应用的仿真研究和分析表明，所提出的复合控制器具有良好的性能，并且可以稳定系统的扰动。