Robust control design for nonlinear uncertain systems with an unknown time-varying control direction

Kaloust, J.; Qu, Zhihua

doi:10.1109/9.557583

Cited by 48 publications

(33 citation statements)

References 19 publications

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“…Similar to [6,7], the system is chosen to be scalar in order to highlight the design of robust controller. The proposed results can be readily extended to a vector system where a(x) is a diagonal matrix of proper dimensions.…”

Section: Promblem Formulationmentioning

confidence: 99%

“…Undoubtedly, this problem is more general and technically challenging than the previous one. The first attempt in addressing this problem was reported in [6], where an online estimator of the unknown and time-varying control direction was proposed and integrated with a robust controller to stabilize the uncertain nonlinear system. However, in order to successfully device the online estimation mechanism, several assumptions are made in their work.…”

Section: Introductionmentioning

confidence: 99%

“…Due to the virtue of the Nussbaum technique, the proposed controller successfully removes above assumptions required by the online estimator [6]. In fact, it only requires that the control direction is bounded when its argument is bounded.…”

Section: Introductionmentioning

confidence: 99%

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Robust control for uncertain nonlinear systems with unknown and changing control direction

Yang

Yam

et al. 2009

2009 17th Mediterranean Conference on Control and Automation

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This paper studies the robust control problem for uncertain nonlinear systems with unknown and changing control direction. The control direction is the multiplier of the control term, and is allowed to cross zero and change its sign for unlimited number of times. Based on the analysis of system dynamics at the points where the control direction is zero, a robust controller is proposed by integrating with a Nussbaum-type gain. Under the proposed controller, the system converges to zero if zero is accessible, or to the accessible point closest to zero if zero is not accessible by any control. The control performance is illustrated by the simulated example.

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Section: Promblem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust control for uncertain nonlinear systems with unknown and changing control direction

Yang

Yam

et al. 2009

2009 17th Mediterranean Conference on Control and Automation

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“…The proposed controller is able to drive the system approaching zero, if zero is accessible; otherwise, it drives the system to the accessible point closest to zero, if zero is inaccessible by any control. In addition, due to the virtue of the Nussbaum technique, the proposed controller successfully removes the above assumptions required by the online estimator [17]. In fact, it only requires that the control direction is finite when its argument is finite.…”

Section: Introductionmentioning

confidence: 99%

Robust control for uncertain nonlinear systems with state‐dependent control direction

Yang

Yam

et al. 2010

Intl J Robust & Nonlinear

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SUMMARYThe control direction is the multiplier of the control term. In this study, the control direction is considered as an unknown function of state and allowed to cross zero and change its sign smoothly. Based on the analysis of system dynamics at the points where the control direction is zero, a robust controller is proposed by integrating with a bounding function and a Nussbaum-type gain. Under the proposed controller, the system approaches zero if zero is accessible, or to the accessible point closest to zero if zero is not accessible by any control. The control performance is illustrated by simulated examples.

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“…Such case has not being fully solved yet in the reported literature. A first attempt is dated from Kaloust and Qu (1997), where an online estimator of the control direction was proposed but effective only for scalar nonlinear plants. More recently, Yang, Yam, Li, and Wang (2011) studied the control problem for a state-dependent sign-switching control direction by assuming state-feedback design.…”

Section: Introductionmentioning

confidence: 99%

Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

Oliveira

Peixoto

Hsu

2015

International Journal of Control

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This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

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Robust control design for nonlinear uncertain systems with an unknown time-varying control direction

Cited by 48 publications

References 19 publications

Robust control for uncertain nonlinear systems with unknown and changing control direction

Robust control for uncertain nonlinear systems with unknown and changing control direction

Robust control for uncertain nonlinear systems with state‐dependent control direction

Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

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