Global output-feedback tracking for nonlinear cascade systems with unknown growth rate and control coefficients

Abstract

This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth. The systems investigated are substantially different from the closely related works, and have zero-dynamics, unknown growth rate, and unknown time-varying control coefficients. This makes the problem much more difficult to solve. Motivated by the authors' recent works, this paper proposes a new adaptive control scheme to achieve the global practical tracking. It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. This is achieved by combining the methods of universal control and dead zone with backstepping technique, and using the framework of performance analysis in the closely related works. A numerical example demonstrates the effectiveness of the theoretical results.

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

“…Assumptions to , particularly Assumption , make the problem become much more difficult and the system under study essentially different from those in the related results on tracking . Assumption indicates that the growth of nonlinear functions depends on unmeasurable states, possesses an unknown growth rate, and satisfies the triangular bounds condition, which offers the possibility for integrating backstepping design into universal control.…”

“…Among those existing output‐feedback works, most of the results focus on nonlinear systems with unmeasured state‐dependent growth . Specifically, in the work of Bullinger and Allgöwer, it is only required that the lower bound of control coefficients should be known; however, the reference signal is a completely known bounded function and its first r derivatives are essentially bounded.…”

Global Output Feedback Stabilization for a Class of Nonlinear Cascade Systems

“…The contribution of these assumptions is that 0 contains all of states of nonlinear cascade systems. Meanwhile, a unified Lyapunov function is successfully constructed and we proposed a novel observer that is different from [24,26].…”

“…However, when zerodynamics exist and obey mild conditions, the tracking problem cannot be solved by trivially extending the corresponding results without zero-dynamics; that is, there do not exist appropriate observers to tracking states of cascade systems. As further investigation, researchers now consider cascade connections in which the nonlinear systems are globally stable, but the input subsystem is more complex than just an integrator; for instance, [24][25][26] successfully investigated output feedback stabilization for uncertain cascade systems under growth condition. Regrettably, their approaches are only suitable for lower-triangular cascade systems.…”

Further results on global practical tracking via adaptive output feedback for uncertain nonlinear systems

“…Assumption 1 shows that the control coefficients of system (1) can be a polynomial of output, rather than a known constant in [3,5], though where the system growth rates are allowed to be an unknown polynomial of output. Moreover, Assumption 3 is much standard for practical tracking [1,[3][4][5]9], which is weaker than those in [6][7][8] where the constant upper bound of y r andẏ r is used as a design parameter in the controller forms.…”