Self-Adjustable Performance-Based Adaptive Tracking Control of Uncertain Nonlinear Systems

This paper is concerned with the problem of prescribed performance tracking control for strict-feedback systems with parametric uncertainties and unmatched disturbances. An adaptive command-filtered control approach with performance guarantees is put forward to address the problem. By means of a new-type self-adjustable performance function and a barrier function, it is capable of achieving the practical prescribed time tracking and enhancing the reliability of control implementation simultaneously, without yet the requirement for the specific initial condition. In the control design, a class of finite-time command filters is adopted to solve the “explosion of complexity” problem, and the error compensation mechanism with practical finite-time stability is introduced to remove the impact of filtered errors. Moreover, considering that the overshoot of the tracking error fails to be quantified by the majority of performance functions with infinite initial values, a pair of asymmetric performance functions is constructed such that the trajectory tracking with the predefined overshoot, settling time, and accuracy is achieved, while preserving the capability of relaxing the initial condition. It turns out that the proposed approach warrants the performance-related constraint satisfaction and the boundedness of all the closed-loop signals. Three simulation studies are carried out to demonstrate the theoretical findings.
Note to Practitioners
—This paper is motivated by the potential fragility problem exhibited in the traditional constraint-handling methods in the presence of paroxysmal factors such as suddenly strong disturbances or highly fluctuating target trajectories. For practical applications (e.g., satellite docking, automobile production, target interception, and network congestion control) suffering from the above scenario, it might be favorable to widen prescribed performance boundaries in a proactive way from the perspective of the safe and reliable operation of the controlled system. On this basis, a novel command filter-based adaptive tracking control solution with self-adjustable performance guarantees is proposed. It not only achieves trajectory tracking with the preassigned overshoot, settling time, and accuracy in the context of raising the reliability of control implementation but also possesses the attributes of inexpensive computation burden and easy acceptability in practical applications.