Prescribed-Time Tracking Control for Nonlinear Systems: A Nonvanishing Disturbance Observer-Based Approach

This article investigates the problem of observer-based prescribed-time tracking control (OPTC) for a class of nonlinear systems with uncertain nonvanishing disturbances. First, a prescribed-time observer (PTO) with a well-designed time-varying high gain is constructed to achieve zero-error observation of the uncertain nonvanishing disturbances within the prescribed observation time. Subsequently, a two-stage controller design framework is proposed to construct the desired control input, which consists of two distinct components: the first-stage controller and the second-stage controller. The first-stage controller is established to compensate for the effects of the system’s nonlinear dynamics, thereby providing a relatively satisfactory tracking performance. The second-stage controller, on the other hand, is constructed based on a sophisticated switching mechanism of the control gains, which not only ensures that the tracking error converges to zero within the prescribed tracking time but also guarantees a smooth transition between the two-stage controllers. Finally, the simulation example involving a disturbed single-link flexible-joint robotic manipulator is presented to demonstrate the effectiveness of the proposed control strategy.