Attractors and limit cycles of discrete-time switching affine systems: Nominal and uncertain cases

Serieye, Mathias; Albea-Sánchez, Carolina; Seuret, Alexandre; Jungers, Marc

doi:10.1016/j.automatica.2022.110691

Cited by 11 publications

(32 citation statements)

References 31 publications

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“…Note that the property of of being a set-value map comes from the fact that ∈ . A model-driven solution to this problem was provided in 24 and will be summarized hereafter. Interestingly, this paper provides a solution for robust stabilization of switched affine systems, which consists of proving that the solutions to the closed-loop system converge to a robust limit cycle which is composed of the union of shifted ellipsoid.…”

Section: System Datamentioning

confidence: 99%

“…Following the ideas developed in 24 , the notion of limit cycles 25,26 is adapted to the problem under consideration. Before presenting the concept of robust limit cycles, let us first introduce the following definitions.…”

Section: Cycles and Robust Limit Cyclesmentioning

confidence: 99%

“…Note that the idea of studying limit cycles for switched affine systems has been considered in 18 for the case of constant and known matrices and . In this case, necessary and sufficient constructive conditions for the existence of { } ∈ , for a given cycle , have been provided in 24 , while it was only an assumption in 18 . It is also worth noting that the structure of the control law provided in 18 complicates the study of robust limit cycles since their control law requires exact knowledge of the system matrices.…”

Section: Definition 1 (Cycle)mentioning

confidence: 99%

“…A solution to the stabilization of switched affine systems subject to external disturbances to a robust limit cycle is presented here following the idea and concept borrowed from 24 . The main difference with respect to 24 is the addition of the bounded external disturbance in (6). The robust stabilization problem is formalized as follows.…”

Section: Robust Model-based Stabilization Of Switched Affine Systemsmentioning

confidence: 99%

“…In contrast to these works, here we consider a data-driven control design method for switched affine systems, where the control variable is the switching signal. Following the framework provided in 24 dealing with an uncertain model-based method, this paper will present a robust data-driven control design for this class of systems. To do so the following objectives will be addressed in the paper • Provide a technical generic tool that allows transforming a model-based criteria for discrete-time systems into a data-driven one.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

LMI relaxations and its application to data-driven control design for switched affine systems

Seuret¹,

Albea-Sánchez²,

Gordillo³

2023

Preprint

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The problem of data-driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine, etc. Still in the view of practical applications, providing an accurate model for this class of systems can be a hard task, and it might be more relevant to work on data issued from some trajectories obtained from experiments and to deploy a new branch of tools to stabilize the systems that are compatible with the processed data. Following the recent concept of data-driven control design, this paper first presents a generic equivalence lemma that shows a matrix constraint based on data, instead of the system parameter. Then, following the concept of robust hybrid limit cycles for uncertain switched affine systems, robust model-based and then data-driven control laws are designed based on a Lyapunov approach. The proposed results are then illustrated and evaluated on an academic example.

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Section: System Datamentioning

confidence: 99%

Section: Cycles and Robust Limit Cyclesmentioning

confidence: 99%

Section: Definition 1 (Cycle)mentioning

confidence: 99%

Section: Robust Model-based Stabilization Of Switched Affine Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

LMI relaxations and its application to data-driven control design for switched affine systems

Seuret¹,

Albea-Sánchez²,

Gordillo³

2023

Preprint

View full text Add to dashboard Cite

show abstract

Linear matrix inequality relaxations and its application to data‐driven control design for switched affine systems

Seuret

Albea-Sánchez

Gordillo

2023

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

The problem of data-driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine and so forth. Still in the view of practical applications, providing an accurate model for this class of systems can be a hard task, and it might be more relevant to work on data issued from some trajectories obtained from experiments and to deploy a new branch of tools to stabilize the systems that are compatible with the processed data. Following the recent concept of data-driven control design, this paper first presents a generic equivalence lemma that shows a matrix constraint based on data, instead of the system parameter. Then, following the concept of robust hybrid limit cycles for uncertain switched affine systems, robust model-based and then data-driven control laws are designed based on a Lyapunov approach. The proposed results are then illustrated and evaluated on an academic example.

show abstract

Local stabilization conditions for discrete-time switched affine systems

Khodja,

Fiter,

Hetel

et al. 2024

Automatica

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Attractors and limit cycles of discrete-time switching affine systems: Nominal and uncertain cases

Cited by 11 publications

References 31 publications

LMI relaxations and its application to data-driven control design for switched affine systems

LMI relaxations and its application to data-driven control design for switched affine systems

Linear matrix inequality relaxations and its application to data‐driven control design for switched affine systems

Local stabilization conditions for discrete-time switched affine systems

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