Adaptive fixed-time control for nonlinear systems with positive odd rational powers

Abstract

In this paper, for strict-feedback nonlinear systems with positive odd rational powers, the problem of adaptive fixed-time tracking control (FTTC) is considered. With the support of fixed-time theorem and adaptive backstepping method, this paper proposes a new globally adaptive FTTC strategy, which can overcome the singular problems caused by the derivation of virtual control signal. In addition, the proposed control scheme is a universal approach that can be applied to other types of nonlinear systems. Furthermore, the designed adaptive fixed-time tracking controller ensures the boundedness of all signals in the controlled system, and it guarantees the tracking error converges to a small neighbourhood near equilibrium in fixed-time. Finally, the simulation result further verifies the feasibility of the presented control scheme.

KEYWORDS:

• Adaptive control
• fixed-time control
• high-order nonlinear systems
• backstepping control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (62173046, 61627809), National Key R&D Program of China under grant (2018YFA0702200), Liaoning Revitalization Talents Program (XLYC1801005), and the Nature Science Foundation of Liaoning Province of China (2022JH25/10100008).