Prescribed performance control approaches, applications and challenges: A comprehensive survey

Abstract

As to control systems, transient performance is as important as steady‐state performance. For some special dynamic systems, transient performance is a more prior index in comparison with the steady‐state one. Prescribed performance control (PPC) has been proved to be a powerful tool that guarantees control system outputs/errors with desired transient performance as well as steady‐state performance. The purpose of this paper is to give a comprehensive review on the latest developments of PPC theories and applications. The existing performance functions are classified into five different categories, and their features are comprehensively compared, providing a useful guidance for further applications. Then, the latest developments of PPC's applications in all kinds of control systems are recalled. Specially, the faced challenges and theoretical defects of PPC are discussed, which is expected to point out the further research direction for PPC.

Nonfragile Quantitative Prescribed Performance Control of Waverider Vehicles With Actuator Saturation

“…THEOREM 2: Consider the closed-loop system consisting of plant (14) with controller (26) and adaptive law (27). Then all the signals involved in (30) are ultimately bounded, and satisfies the prescribed performance (16).…”

“…Finally, the superiority is verified by the presented compared simulation results. Our future work will focus on overcoming the fragility of PPC to states constraints and actuator faults [28]- [30].…”

Interaction Motion Control on Tri-finger Pneumatic Grasper using Variable Convergence Rate Prescribed Performance Impedance Control with Pressure-based Force Estimator

“…Comparable modification and association of PPC to data driven methods were also ventured for improved precision of model-based control systems [41,42]. Alternatively, a diverged outlook was exempted by Luo et al, Cao et al and Bu on the adaptation of intelligent control towards enhance sensory tracking of said error transformation control approach [43][44][45]. With a wide range of formulations being undertaken towards PPC, in-depth priority was further relocated to the system's PPF on its immense potential for enhanced real-time applications [46][47][48][49][50][51][52][53][54].…”

Funnel-based Reachability Control of Unknown Nonlinear Systems using Gaussian Processes

“…In the past few decades, there have been several works in the literature addressing reachability problem (see [10], [11], [12], [13], [14]) for known dynamical systems. To solve this problem, we leverage the funnel-based control approaches [15] that have been extensively used for controlling systems with prescribed performance constraints (see [16] and references therein for examples). We first employ the Gaussian process learning to approximate the system dynamics using the noisy measurements along a probabilistic bound on approximation.…”