Adaptive Tracking with Prescribed Performance and Parameter Estimation for Nonlinear Systems

This paper studies the tracking problem for a class of uncertain strict-feedback systems (SFSs) with guaranteed transient performance and parameter estimation. To cope with the unknown parameters of the strict-feedback systems, a forgetting-factor-based parameter estimation error reconstruction mechanism is introduced for the online identification of the unknown system parameters. To achieve the prescribed performance, some novel functions are introduced to transform the constrained tracking control problem into an equivalent stabilization problem which is independent of the initial conditions. To avoid the "differential explosion" in the backstepping controller design procedure, the dynamic surface control (DSC) method is employed. It is shown that all signals of the closed-loop systems are uniformly ultimately bounded and the tracking error satisfies the prescribed transient performance. Finally, the benefits and effectiveness of the proposed scheme are verified in terms of the single-link manipulator actuated by a brush DC motor.