Adaptive Semiglobal Nonlinear Output Regulation:An Extended-State Observer Approach

TL;DR

The paper addresses adaptive nonlinear output regulation for nonlinear plants with uncertain parameters within the nonequilibrium framework of Byrnes and Isidori. It introduces an extended-state observer–based adaptive internal model that can handle nonlinearly parameterized immersion conditions by simultaneously estimating the uncertain parameter vector $\theta$ and reconstructing augmented states. Under mild assumptions, the extended zero dynamics are shown to be semiglobal (or locally exponentially) stable, yielding bounded trajectories and asymptotic regulation ($y_e\to 0$) for large observer gains. This approach relaxes linear-immersion and linear-parameterization requirements, broadening the class of exosystems and controlled systems and demonstrated on a nonlinear oscillator example. The work provides a principled method to achieve adaptive regulation in more general nonlinear settings with nonequilibrium theory.

Abstract

This paper proposes a new extended-state observer-based framework for adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an extended-state observer with an internal model, one is able to obtain an estimate of the term containing uncertain parameters, which then makes it possible to design an adaptive internal model in the presence of a general nonlinearly parameterized immersion condition.

Figures (3)

• Figure 1: Left: plot of function $\hbox{sat}_i$ with $l_i=3$; and right: plot of function $\hbox{dz}_i$ with $c_i=1.2,a_{0,i}=4, \epsilon_{0,i}=2$.
• Figure 2: Phase portrait of (\ref{['example-exosys']}) at $\rho=0.2$, $\rho=0$ and $\rho=-0.2$.
• Figure 3: Trajectories of regulated output $y_e(t)$ and parameter estimate $\hat{\theta}(t)$.

Theorems & Definitions (13)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6
• Lemma 1
• proof
• Lemma 2
• proof