Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

Abstract

Summary This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

“…Assumptions 1 and 2 are standard conditions required in many adaptive state feedback DSC schemes, which can be commonly found in the existing literature. [14][15][16][17][18][19][20][21][22][23]60…”

“…Theorem 1. Consider the closed-loop system consisting of the plant (1); the nonlinear filters (8) and (16); the control law (18); and the adaptive laws (5), (13), and (19). Suppose that Assumptions 1 and 2 hold, for any initial conditions satisfying V(0) ≤ p, where p is a given positive constant, then there exist design parameters k i , γ i , i = 1, … , n, τ j , and β j , j = 1, … , n − 1, such that the following statements hold:…”

“…To handle the time‐delay effects, adaptive DSC schemes were developed for nonlinear time‐delay systems with parametric uncertainties in the works of Yoo et al( ) and Wu et al() In the work of Yoo et al, the result of decentralized adaptive DSC was proposed for interconnected nonlinear systems subject to nonsymmetric dead‐zone control inputs. For nonaffine pure‐feedback systems, an adaptive dynamic surface approach was presented by using the modified linear filters . In the work of Chen et al, an adaptive robust DSC with composite adaptation laws was designed for uncertain nonlinear systems in semistrict‐feedback form, where the persistent excitation (PE) condition has to be satisfied to ensure the convergence of parameter estimates.…”

“…For nonaffine pure-feedback systems, an adaptive dynamic surface approach was presented by using the modified linear filters. 19 In the work of Chen et al, 20 an adaptive robust DSC with composite adaptation laws was designed for uncertain nonlinear systems in semistrict-feedback form, where the persistent excitation (PE) condition has to be satisfied to ensure the convergence of parameter estimates. Furthermore, result based on multiple models and switching was exploited to improve the transient response of a adaptive DSC system, 21 but the PE condition still exists.…”

Model‐assisted extended state observer and dynamic surface control–based trajectory tracking for quadrotors via output‐feedback mechanism

“…To retain the excellent tracking performance of the back‐stepping design while eliminating the problem of explosion of complexity, dynamic surface control (DSC) is proposed as an effective alternative by introducing a first‐order filtering of the synthetic input at each step of the back‐stepping design and has provided a systematic solution for the tracking control problem of uncertain nonlinear systems. (–) However, the output‐feedback controller design for quadrotors via the DSC method is still open to be solved.…”