Anti‐disturbance inverse optimal control for systems with disturbances

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.