A Switching Observer for a Class of Nonuniformly Observable Systems via Singular Time-Rescaling

Aguado-Rojas, Missie; Hoang, Trong-Bien; Pasillas-Lépine, William; Lorı́a, Antonio; Respondek, Witold

doi:10.1109/tac.2021.3062340

Cited by 7 publications

(14 citation statements)

References 34 publications

(63 reference statements)

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“…Assumption 1 relaxes the hypotheses imposed in [5]. Next, for the purpose of analysis, we introduce the new time scale-cf.…”

Section: Switched-observer Designmentioning

confidence: 99%

“…Note that the latter constitutes a linear time-invariant system with a bounded perturbation z2 . Indeed, after [5], one can compute a positive definite matrix P ∈ R 2×2 such that the time derivative of V obs (z) := z P z, (16) along the solutions to (3), verifies…”

Section: Observer-based Hybrid Control Algorithmmentioning

confidence: 99%

“…Thus, the controller is hybrid in nature and successfully stabilizes the origin semiglobally and asymptotically. Our contribution is a natural follow up on long-standing work led by the second author [5,13,15,17], but there no intellectual intersection with these references, devoted entirely to the observer-design problem. In addition, relatively to them, we provide here explicit exponential bounds on the observer's estimation errors.…”

mentioning

confidence: 99%

“…It is particularly meaningful when the control goal is to stabilize an equilibrium at, and near which, observability is lost. The study of such systems, for about three decades, has yielded an ever-growing literature-see, e.g., [1][2][3][4][5]. It is that beyond the significant mathematical difficulty imposed solely by designing observer design [6][7][8], the stabilization problem is well-motivated by concrete engineering applications, such as sensorless motor control [9], bioreactor systems [10,11], electrical systems [12], and automotive applications [13], in which stabilization covers importance beyond intellectual curiosity.…”

mentioning

confidence: 99%

See 3 more Smart Citations

On Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems via Hybrid and Smooth Control: a Case Study

Maghenem¹,

Pasillas-Lépine²,

Lorı́a³

et al. 2022

Preprint

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For systems that are not observable at the very equilibrium of interest to be stabilized, output-feedback stabilization is considerably challenging. In this paper we solve this control problem for the case-study of a second-order system that is bilinear and affine, both in the input and the output, but it is unobservable at the target equilibrium. The case-study is representative of a well-studied class of non-uniformly observable systems and stems from automotive control. Our main contribution is a novel certainty-equivalence hybrid controller that achieves asymptotic stabilization semiglobally. The controller relies on a switched observer that estimates the state, provided that the latter is 'kept away' from the singular equilibrium. To achieve both competing tasks, stabilization and estimation, the controller also relies on the keen construction of a piecewise-constant, converging, reference. Our main results are illustrated via numerical simulations on a meaningful example.

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“…Assumption 1 relaxes the hypotheses imposed in [5]. Next, for the purpose of analysis, we introduce the new time scale-cf.…”

Section: Switched-observer Designmentioning

confidence: 99%

Section: Observer-based Hybrid Control Algorithmmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

On Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems via Hybrid and Smooth Control: a Case Study

Maghenem¹,

Pasillas-Lépine²,

Lorı́a³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This statement is particularly meaningful when the control goal is to stabilize an equilibrium, at which, observability is lost. The study of such systems, for about three decades, has yielded an ever-growing literature-see, e.g., [1]- [5]. Beyond the mathematical difficulty imposed by designing an observer [6]- [8], the stabilization problem is well-motivated by concrete engineering applications, such as sensorless motor control [9], bioreactor systems [10], [11], electrical systems [12], and automotive applications [13].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Observer-based Controller for a Non-uniformly Observable System

Maghenem

Pasillas-Lépine

Lorı́a

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

For systems that are not observable at an equilibrium to be stabilized, output-feedback stabilization is considerably challenging. This paper solves this control problem for the case-study of a second-order system that is bilinear and affine, both in the input and the output, but it is unobservable at the target equilibrium. The case-study defines a class of non-uniformly observable systems and stems from automotivecontrol applications. Our main contribution is a novel observerbased hybrid controller that achieves asymptotic stabilization semiglobally. The controller relies on a switched observer that estimates the state, provided that the latter is 'kept away' from the singular equilibrium. To achieve both competing tasks, stabilization and estimation, the controller relies on the keen construction of a piecewise-constant, converging, output reference. Our main results are illustrated via numerical simulations on a meaningful example.

show abstract

Output feedback stabilization of non-uniformly observable systems by means of a switched Kalman-like observer

Brivadis,

Sacchelli

2023

IFAC-PapersOnLine

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A Switching Observer for a Class of Nonuniformly Observable Systems via Singular Time-Rescaling

Cited by 7 publications

References 34 publications

On Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems via Hybrid and Smooth Control: a Case Study

On Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems via Hybrid and Smooth Control: a Case Study

A Hybrid Observer-based Controller for a Non-uniformly Observable System

Output feedback stabilization of non-uniformly observable systems by means of a switched Kalman-like observer

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