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

Abstract

Performance 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.

A Transferable Force Controller based on Prescribed Performance for Contact Establishment in Robotic Assembly Tasks

“…Further research will aim at investigating the phenomenon that the original prescribed performance bounds are violated in some cases. Convergence analysis should account for non-negligible velocity control dynamics, and methods for discrete-time design of PPC should be developed, which is inline with [16]. Besides, further experiments will be conducted to evaluate the performance of the proposed controller within a benchmarking contour-following task [17].…”

An overview of prescribed performance control and its application to spacecraft attitude system

“…15 While, PPC is not due to its monotonically increasing control gain. 16 In the existing works, FC is usually restricted to nonlinear systems with low relative degree. However, PPC can be extended to nonlinear systems with high relative degree.…”