Adaptive Stabilization for High‐Order Time‐Delay Systems With Asymmetric Output Constraints and Nonlinear Parametrization

ABSTRACT This paper addresses the fixed‐time adaptive control problem for nonlinearly parametrized high‐order systems with unknown time delays and asymmetric output constraints. A suitable Lyapunov‐Krasovskii functional combined with a backstepping control method forms the foundation for developing a fixed‐time control framework, complemented by a piecewise barrier Lyapunov function capable of dealing with symmetric and asymmetric output constraints or unconstrained outputs without redesigning the controller structure. During the procedure of control design, the tuning function is constructed to remove the overparametrization of unknown parameters. The presented adaptive control strategy ensures that system states are globally bounded and converge to the origin in an adjustable time through selected design parameters. Meanwhile, the system output can always be kept within prespecified output constraints. Notably, unlike existing schemes that handle symmetric constraints or known time delays, the proposed controller offers a unified framework capable of accommodating asymmetric time‐varying constraints and completely unknown delays without requiring any redesign. Finally, the effectiveness of the proposed control scheme is validated through two simulation studies: a mass‐spring system and a numerical example.