Asymptotic Tracking Control With Prescribed-Time Prescribed Performance for Uncertain Nonlinear Systems: A Fully Actuated System Approach

In this article, a robust adaptive tracking control scheme is developed for fully actuated systems (FASs) in the presence of nonlinear uncertainties, input disturbances, and multiplicative input matrices perturbation, capable of achieving the adjustable transient and steady-state performance. In comparison with the conventional and finite-time prescribed performance control (PPC) methods subject to the initial value constraint, the proposed prescribed-time PPC scheme blends the FAS approach with the speed transformation, guaranteeing the full-state asymptotic tracking with prescribed-time prescribed performance. First, a basic fully actuated controller is introduced, yielding a closed-loop tracking error system with a linear dominant part. Second, the speed transformation is applied to the closed-loop system, converting the initial PPC problem into the asymptotic convergence problem of the transferred error system and completely eliminating the initial value constraint. Third, the auxiliary control input and adaptive law embedded with positive integrable time-varying functions are devised, ensuring the boundedness of all closed-loop signals and the desired performance. Simulation studies are conducted to demonstrate the effectiveness and superiority of the presented control strategy.