Inverse optimal tracking control of non‐affine nonlinear systems with unmatched disturbances using singular perturbation theory

This paper presents a novel optimal tracking control strategy for a category of non‐affine nonlinear systems that encounter both unmatched and matched disturbances. Traditional inverse optimal control methods typically require systems to be affine‐in‐control in order for explicit inversion and cost function determination, precluding direct application to non‐affine nonlinear systems. In this study, a fast subsystem is built through a backstepping procedure to transform the original system into the standard singular perturbation model. Within the fast time scale, the boundary‐layer subsystem is designed to stabilize the fast states around the desired manifold. Rather than acting as a pseudo controller, the desired manifold serves to simplify the original system in the slow time scale. Thereafter, an observer‐based inverse optimal control law is employed for the resulting order‐reduced slow subsystem. Finally, singular perturbation theory is leveraged to simultaneously achieve optimal performance and disturbance rejection while preserving non‐affine structure, without introducing heavy computation overhead. The efficacy of the proposed method is demonstrated using two simulation examples.