Prescribed Performance Adaptive Control of Uncertain Nonlinear Systems: State‐of‐the‐art and Open Issues

Abstract

AbstractPerformance in adaptive control designs for uncertain nonlinear systems, whose uncertainty is not purely parametric, was traditionally restricted to enforcing, besides stability, desirable behavior at steady‐state. In the literature, rigorous proofs have been provided guaranteeing tracking error convergence to residual sets, whose size depends on design parameters and some bounded though unknown terms. Therefore, even controllable, steady‐state accuracy was impossible to be a priori selected by any systematic procedure. Furthermore, transient performance such as maximum overshoot and convergence rate, was difficult to be established analytically even for known systems. The problem was approached via minimizing certain performance indices, which unfortunately were connected only indirectly with the actual system response. Hence, even though performance improvement is anticipated, no connection to a priori specified trajectory oriented metrics could be achieved. For classes of nonlinear systems Funnel Control has been proposed to provide solution. However, the problem remained largely unsolved for the case of adaptive closed‐loop uncertain systems. To fill in the gap, the Prescribed Performance Control (PPC) methodology was presented. This work is a review on PPC, highlighting on its main advantages and discussing on probably the most important open issues.