A Novel Adaptive Fixed-Time Tracking Control Approach of Uncertain Nonlinear Systems

The issue of fixed-time tracking control of nonlinear systems subject to time-varying uncertain parameters is investigated in this article. In contrast to previous adaptive approach-based fixed-time control results which focus on driving the tracking error to a bounded region, it is technically challenging yet highly desired to achieve zero-error trajectory tracking. The primary difficulty lies in how to construct and analyze adaptive estimation schemes to completely compensate for uncertain parameters within the fixed-time convergence setting. Furthermore, the presence of time-varying uncertainties renders the systems fundamentally different from those in existing works. To tackle this challenge, a new fixed-time stability lemma utilizing an exponential decay function is proposed. Then, we develop an adaptive fixed-time controller design framework, it is demonstrated that the tracking error ultimately converges to zero after converging to a small neighborhood around zero within a fixed time, with all the closed-loop signals remaining bounded. Besides, the singularity problem in fixed-time control is circumvented. Finally, simulation results substantiate the effectiveness of the proposed strategy.