Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties

Abstract

This paper considers the global practical tracking for a class of uncertain nonlinear systems. Remarkably, the systems under investigation admit rather inherent nonlinearities, and especially allow arguably the most severe uncertainties: unknown control directions and non-parametric uncertainties. Despite this, a refined tracking objective, rather than a reduced one, is sought. That is, not only pre-specified arbitrary tracking accuracy is guaranteed, but also certain prescribed transient performance (e.g., arrival time and maximum overshoot) is ensured to better meet real applications. To solve the problem, a new tracking scheme is established, crucially introducing delicate time-varying gains to counteract the severe uncertainties and guarantee the prescribed performance. It is shown that the designed controller renders the tracking error to forever evolve within a prescribed performance funnel, through which the desired tracking objective is accomplished for the systems. Particularly, by subtly specifying the funnel, global fixed-time practical tracking (i.e., that with prescribed arrival time) and semiglobal practical tracking with prescribed maximal overshoot can be achieved for the systems. Moreover, the tracking scheme remains valid in the presence of rather less-restrictive unmodeled dynamics.

Global practical tracking for nonlinear systems with unknown input powers using dual high‐gain‐based adaptive feedback

“…We next give the estimations for the last four terms on the right-hand side of (19) (denoted by 1 , 2 , 3 , and 4 , respectively). From (12), (13) and Lemma 1, it follows that…”

“…Tracking control is one of the core and classic issues in control domain, and there have developed numerous types of control schemes in different circumstances, such as high-gain adaptive control one for system with parameter unknowns, 10 active disturbance rejection control one for system with large uncertainties, 11 L 1 adaptive control one to guarantee robustness in the presence of fast adaptation, 12 and funnel control one to improve the transient and steady state performance. 13 In the last decades, much progress has been made on global practical tracking for systems with uncontrollable and unobservable linearization, that is, a class of systems with inherent nonlinearities (see, eg, other works 10,[13][14][15][16][17] and references therein). It has been pointed out in the work of Qian and Lin 14 that, for such systems, there exist counterexamples that no continuous feedback exists to achieve global asymptotic tracking, and global practical tracking scheme was first established therein.…”

“…Subsequently, works of Lin and Pongvuthithum 10 and Sun and Liu 15 considered the case with serious parametric unknowns by designing adaptive controllers. Works of Yan and Liu 16 and Li and Liu 13 studied the case with unknown control directions, and particularly, in the work of Li and Liu, 13 prescribed transient performance was also guaranteed. Remarkably, the input powers of the system in the closely related works 10,[13][14][15][16] are precisely known, and the methods proposed therein are inapplicable for the case with unknown input powers.…”

“…Works of Yan and Liu 16 and Li and Liu 13 studied the case with unknown control directions, and particularly, in the work of Li and Liu, 13 prescribed transient performance was also guaranteed. Remarkably, the input powers of the system in the closely related works 10,[13][14][15][16] are precisely known, and the methods proposed therein are inapplicable for the case with unknown input powers. Towards the limitation, our recent work 17 successfully solved the global practical tracking for systems with unknown input powers belonging to a known constant interval.…”

Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances

“…On the other hand, the finite-time stability problem has been attracted more attention of researchers to achieve fast transient performance [36][37][38][39][40]. Based on the technology of adding a power integrator, in [41], the authors concentrated on a global finite-time stabilization problem for a class of switched nonlinear systems.…”