Global finite‐time stabilization via time‐varying output‐feedback for uncertain nonlinear systems with unknown growth rate

Abstract

Summary This paper considers the global finite‐time output‐feedback stabilization for a class of uncertain nonlinear systems. Comparing with the existing related literature, two essential obstacles exist: On the one hand, the systems in question allow serious parametric unknowns and serious time variations coupling to the unmeasurable states, which is reflected in that the systems have the unmeasurable states dependent growth with the rate being an unknown constant multiplying a known continuous function of time. On the other hand, the systems possess remarkably inherent nonlinearities, whose growth allows to be not only low‐order but especially high‐order with respect to the unmeasurable states. To effectively cope with these obstacles, we established a time‐varying output‐feedback strategy to achieve the finite‐time stabilization for the systems under investigation. First, a time‐varying state‐feedback controller is constructed by adding an integrator method, and by homogeneous domination approach, a time‐varying reduced‐order observer is designed to precisely rebuild the unmeasurable states. Then, by certainty equivalence principle, a desired time‐varying output‐feedback controller is constructed for the systems. It is shown that, as long as the involved time‐varying gain is chosen fast enough to overtake the serious parametric unknowns and the serious time variations, the output‐feedback controller renders that the closed‐loop system states converge to zero in finite time. Copyright © 2017 John Wiley & Sons, Ltd.

Output‐feedback control strategies of lower‐triangular nonlinear nonholonomic systems in any prescribed finite time

“…On the other hand, when the control system satisfies the known time-varying incremental rate, both the control strategies proposed in Theorem 1 and Theorem 2 can achieve the output-feedback stabilization problem in any prescribed finite time, but the control strategy proposed in Theorem 2 has a faster convergence speed. Moreover, when the control system satisfying both an unknown and a known incremental rate, 32,35 and combining with Theorem 1 and Theorem 2, we can propose the output-feedback regulation control strategy in any prescribed finite time of such systems with relatively fast convergence speed.…”

“…Then, because the controller u 0 (t) is bounded and convergent to 0, as t → t 0 + t * , thus we can achieve that the x-subsystem can be stabilized at the equilibrium point in any prescribed finite time under controller u 1 (t). Correspondingly, the observation states of the x-subsystem in any prescribed finite time can be recorded aŝ= (̂1, … ,̂i, … ,̂n) T = (u n 0 1 , … , u n−i+1 0 i , … , u 0 n ) T , and combining with (35) and (44), the controller…”

Output feedback stabilization for a class of high‐order planar systems with an asymmetric output constraint

“…Based on the framework of the backstepping method, a special version of the backstepping design named as adding a power integrator was recently presented in References 9 and 10 for deriving solutions to the stabilization problem for a class of high‐order nonlinear systems (also referred to as p ‐normal form systems). As shown in References 9 and 10, the technique of adding a power integrator not only contributes to a technological breakthrough in coping with the intrinsic obstacles of high‐order nonlinear systems stemming from inherent nonlinearities and the non‐existence and/or the lack of controllability/observability of the Jacobian linearization around the origin but also provides further insights into the construction of an observer for output feedback design without utilizing the separation principle, thereby motivating numerous important works dedicated to the state/output feedback stabilization of high‐order nonlinear systems; see, for example, References 11‐24 and the references therein.…”

“…The asymmetric constraint on the output is depicted by − ε l < y ( t ) < ε u for all t ≥ t 0 with two pre‐specified positive constants ε l and ε u . Being aware of the fact that suitable conditions on nonlinearities and uncertainties are intrinsically necessary for output feedback stabilization, 1‐4,12,14,20 the following mild assumptions are imposed on system (1) so as to provide a solution to this unsolved problem:…”

“…Then, a continuous state feedback controller is designed for system (1) by means of revamping the technique of adding a power integrator (ie, a special version of the backstepping design) with the skillful implantation of the proposed tangent ‐type asymmetric BLF as well as a delicate manipulation of sign functions. Furthermore, partially inspired by but substantially different from those used in References 12,14,16, and 20, a reduced‐order nonsmooth observer equipped with a nonlinear gain function is constructed by deliberating the inherent nonlinearities of system (1). By subtly combining the state feedback controller with the developed observer and appropriately selecting the observer gain function, an output feedback stabilizer can be explicitly synthesized, thereby achieving the stabilization task while ensuring the fulfillment of the asymmetric output constraint.…”