A New Arbitrary-Time Guaranteed-Performance Adaptive Tracking Control Scheme Design for Uncertain Nonlinear Systems

The arbitrary-time (AT) nonovershoot adaptive tracking control issue is investigated for uncertain high-order nonlinear systems with guaranteed-performance (GP). Superior to the existing prescribed-time prescribed-performance control strategies that are vulnerable to suddenly unexpected external disturbances, a novel globally segmented AT guaranteed-performance (ATGP) function is proposed to overcome such limitations. First, the tracking errors of the system are driven to zero not only within the GP constraints but within an AT, which greatly enhances the execution efficiency. Then, a robust error-induced time-triggered disturbance-rejection mechanism is proposed to eliminate the singularity issue in conventional prescribed-performance control and enable a stabilized system to regain ATGP convergence under unexpected disturbances. Furthermore, compared with traditional adaptive algorithms that only achieve the ultimately uniform boundedness, an AT parameter adaptive law is proposed, driving the adaptive estimation error to zero. Finally, a practical example on a manipulator and a numerical example on a general nonlinear system are taken to authentically corroborate the efficacy of the proposed control algorithm.