Output regulation for a class of nonlinear systems using the observer based output feedback control

Xu, Dabo; Huang, Jie

doi:10.1109/acc.2009.5159933

Cited by 11 publications

(35 citation statements)

References 13 publications

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“…It can be verified that Assumptions A1–A7 are all satisfied. Explicit expressions of z 1 ( v , w , σ ), z 2 ( v , w , σ ), x 1 ( v , w , σ ), x 2 ( v , w , σ ), and u ( v , w , σ ) can be found in . In particular, we have

\begin{matrix} \frac{\partial^{4} {boldx}_{2} (v, w, σ)}{\partial t^{4}} & = - 9 σ^{4} {boldx}_{2} (v, w, σ) - 10 σ^{2} \frac{\partial^{2} {boldx}_{2} (v, w, σ)}{\partial t^{2}}, \\ \frac{\partial^{4} boldu (v, w, σ)}{\partial t^{4}} & = - 9 σ^{4} boldu (v, w, σ) - 10 σ^{2} \frac{\partial^{2} boldu (v, w, σ)}{\partial t^{2}} . \end{matrix}

The simulation results are presented in Figure with

scriptN (k) = k^{2} \cos k

, σ = π /20, w i ∈[−1,1], and initial conditions v (0)=[1,0] T , z 1 (0)=2, z 2 (0)=−1, x 1 (0)=0.5, and x 2 (0)=0.…”

Section: Examplesmentioning

confidence: 98%

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A result on output regulation of lower triangular systems with unknown high‐frequency gain sign

Guo

Liu

2017

Intl J Robust & Nonlinear

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Summary This paper concerns global robust output regulation of a class of nonlinear lower triangular systems with an unknown high‐frequency gain as well as an unknown exosystem. A novel class of internal model candidates is integrated with the output regulation framework. As a result, stabilization of the augmented system can be performed without parameter estimators. However, the new internal models bring challenges to the stabilization of the augmented system. To overcome these challenges, we propose a new recursive controller design procedure and use it to develop a Nussbaum‐gain‐based controller. This work extends the existing results on nonlinear output regulation of lower triangular systems to the case where both the high‐frequency gain sign and the exosystem are unknown. Copyright © 2017 John Wiley & Sons, Ltd.

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\begin{matrix} \frac{\partial^{4} {boldx}_{2} (v, w, σ)}{\partial t^{4}} & = - 9 σ^{4} {boldx}_{2} (v, w, σ) - 10 σ^{2} \frac{\partial^{2} {boldx}_{2} (v, w, σ)}{\partial t^{2}}, \\ \frac{\partial^{4} boldu (v, w, σ)}{\partial t^{4}} & = - 9 σ^{4} boldu (v, w, σ) - 10 σ^{2} \frac{\partial^{2} boldu (v, w, σ)}{\partial t^{2}} . \end{matrix}

The simulation results are presented in Figure with

scriptN (k) = k^{2} \cos k

, σ = π /20, w i ∈[−1,1], and initial conditions v (0)=[1,0] T , z 1 (0)=2, z 2 (0)=−1, x 1 (0)=0.5, and x 2 (0)=0.…”

Section: Examplesmentioning

confidence: 98%

“…It can be verified that Assumptions A1-A7 are all satisfied. Explicit expressions of z 1 .v; w; /, z 2 .v; w; /, x 1 .v; w; /, x 2 .v; w; /, and u.v; w; / can be found in [33]. In particular, we have @ 4 x 2 .v; w; / @t 4 D 9 4 x 2 .v; w; / 10 2 @ 2 x 2 .v; w; / @t 2 ; @ 4 u.v; w; / @t 4 D 9 4 u.v; w; / 10 2 @ 2 u.v; w; / @t 2 :…”

Section: Examplementioning

confidence: 99%

A result on output regulation of lower triangular systems with unknown high‐frequency gain sign

Guo

Liu

2017

Intl J Robust & Nonlinear

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“…The first condition for time-invariant nonlinear systems was given in [5] where a time-invariant linear internal model is constructed under the assumption that u is a polynomial in v and the exosystem is linear. Condition (19) with all coefficients a i constant was proposed in [4] for time-invariant nonlinear systems. For the time-invariant plant with a linear exosystem, it was shown in [16] that the condition in [4] is equivalent to the condition that u is a polynomial in v. However, for time-varying systems, condition (15) may not be satisfied even if the solution u of the regulator equations is a polynomial in v and the exosystem is linear.…”

Section: Construction Of Steady-state Generator and Internal Modelmentioning

confidence: 99%

“…System (40) is now in the same form as system (11) of [19] except that the functionsf ,ĝ i , i = 1, . .…”

Section: Assumption Iv2 For Any Compact Subsetmentioning

confidence: 99%

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Output regulation of time‐varying nonlinear systems

Yang

Huang

2011

Asian Journal of Control

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Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

Liu

Huang

2019

Intl J Robust & Nonlinear

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Summary In this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.

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Output regulation for a class of nonlinear systems using the observer based output feedback control

Cited by 11 publications

References 13 publications

A result on output regulation of lower triangular systems with unknown high‐frequency gain sign

A result on output regulation of lower triangular systems with unknown high‐frequency gain sign

Output regulation of time‐varying nonlinear systems

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

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