Observer-Based Sequential Control of a Nonlinear Two-Time-Scale System with Multiple Slow and Fast States

Saha, Dipanjan; Valasek, John

doi:10.1016/j.ifacol.2016.10.245

Cited by 5 publications

(11 citation statements)

References 12 publications

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“…In this manuscript, we verify that [1] covers another class of systems and an observer that cannot be covered by [2]. We have also checked that our results apply for plants in which the reduced (slow) system is such that nonlinear observers in [4] - [10] can be used to estimate the slow variables. As far as we are aware, there are no existing results dealing with SPA stability.…”

Section: Introductionmentioning

confidence: 61%

Convergence of full-order observers for the slow states of a singularly perturbed system (Part II: Applications)

Cuevas

Nešić

Manzie

2018

2018 Australian &Amp; New Zealand Control Conference (ANZCC)

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Many natural and engineered systems exhibit a singularly perturbed structure where different time scales inherently lead to difficulties in the design of observers for the system. In our related work [1], we have shown that, under appropriate assumptions, an observer designed for the slow part of the system can be applied and results in semiglobal practical asymptotical (SPA) stability of the estimation error. In this paper, we show that assumptions from [1] hold for two classes of plants and nonlinear observers. In fact, we show that the provided framework in [1] covers current results in the literature and also other cases that are not covered by existing results. Hence, we demonstrate that we generalise existing results in the literature.

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Section: Introductionmentioning

confidence: 61%

Convergence of full-order observers for the slow states of a singularly perturbed system (Part II: Applications)

Cuevas

Nešić

Manzie

2018

2018 Australian &Amp; New Zealand Control Conference (ANZCC)

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“…Although boundedness of solutions of the full system can be assumed, we state it for two reasons, 1) this result is of interest in its own right and 2) some of the assumptions we state for this result are also needed to prove much stronger conclusion on the stability of the error dynamics. In our analysis, we compute the derivatives of 1 ( , ) and ( , , ), given in Assumptions 2 and 3, along the trajectories of (6). This leads to some terms representing the interconnections between the slow and the fast dynamics.…”

Section: Boundedness Of Solutions Of the Plantmentioning

confidence: 99%

“…Nevertheless, those observers are valid only locally and only work well when the system is evolving close to the equilibrium point considered for the linearisation. To counteract this problem, a wide variety of nonlinear observer design methods have been developed [1][2][3][4][5][6][7][8][9][10] , but these approaches may lead to ill-conditioned gains when used for systems exhibiting multiple time scales.…”

Section: Introductionmentioning

confidence: 99%

“…The authors in Kazantzis et al 1 only consider a particular class of plants and a specific nonlinear observer that exhibits linear error dynamics for the slow system. An observer for spring-mass-damper systems with singularly perturbed structure is given in Saha and Valasek 6,7 ; however, those results apply to a very specific class of systems and observers. Other results on observer design for nonlinear singularly perturbed systems are available in Wang and Liu 20 , and Darrogheh et al 21 .…”

Section: Introductionmentioning

confidence: 99%

“…Then, in Section 5 we illustrate and demonstrate the applicability of our results by presenting three classes of plants and observers for which our results hold. Although not presented here, the results cover the situation when the reduced (slow) system is such that reduced-order 2 , full-order [1][2][3][4][5][6][7] , and higher-order 8 observers can be used to estimate the slow variables. Finally, to demonstrate the theoretical findings, we test the results on a simulation of a suspension system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robustness analysis of nonlinear observers for the slow variables of singularly perturbed systems

Cuevas

Nešić

Manzie

2020

Intl J Robust & Nonlinear

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Estimation of unmeasured variables is a crucial objective in a broad range of applications. However, the estimation process turns into a challenging problem when the underlying model is nonlinear and even more so when additionally it exhibits multiple time scales. The existing results on estimation for systems with two-time scales apply to a limited class of nonlinear plants and observers. We focus on analysing nonlinear observers designed for the slow state variables of nonlinear singularly perturbed systems. Moreover, we consider the presence of bounded measurement noise in the system. We generalise current results by considering broader classes of plants and estimators to cover reduced-order, full-order and higher-order observers. First, we show that the singularly perturbed system has bounded solutions under an appropriate set of assumptions on the corresponding boundary layer and reduced systems.We then exploit this property to prove that, under reasonable assumptions, the error dynamics of the observer designed for the reduced system are semi-globally inputto-state (ISS) practically stable when the observer is implemented on the original plant. We also conclude  2 stability results when the measurement noise belongs to  2 ∩  ∞ . In the absence of measurement noise, we state results on semi-global practical asymptotical (SPA) stability for the error dynamics. We illustrate the generality of our main results through three classes of systems with corresponding observers and one numerical example.

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Output feedback control of a class of two-time-scale nonlinear systems using high-gain observers

Raza,

Malik,

Mazhar

et al. 2023

International Journal of Control

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Observer-Based Sequential Control of a Nonlinear Two-Time-Scale System with Multiple Slow and Fast States

Cited by 5 publications

References 12 publications

Convergence of full-order observers for the slow states of a singularly perturbed system (Part II: Applications)

Convergence of full-order observers for the slow states of a singularly perturbed system (Part II: Applications)

Robustness analysis of nonlinear observers for the slow variables of singularly perturbed systems

Output feedback control of a class of two-time-scale nonlinear systems using high-gain observers

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