On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems

Given a discrete-time controlled bilinear systems with initial state x(0) and output function y(i), we investigate the maximal output set Θ(Ω) = {x(0) ∈ ℝ(n), y(i) ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝ(p). Using some stability hypothesis, we show that Θ(Ω) can be deter...

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Detalles Bibliográficos
Autores principales: Benfatah, Youssef, El Bhih, Amine, Rachik, Mostafa, Tridane, Abdessamad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 2021
Materias:
Regular Papers
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8412393/
https://www.ncbi.nlm.nih.gov/pubmed/34493935
http://dx.doi.org/10.1007/s12555-020-0486-6
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author Benfatah, Youssef
El Bhih, Amine
Rachik, Mostafa
Tridane, Abdessamad
author_facet Benfatah, Youssef
El Bhih, Amine
Rachik, Mostafa
Tridane, Abdessamad
author_sort Benfatah, Youssef
collection PubMed
description Given a discrete-time controlled bilinear systems with initial state x(0) and output function y(i), we investigate the maximal output set Θ(Ω) = {x(0) ∈ ℝ(n), y(i) ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝ(p). Using some stability hypothesis, we show that Θ(Ω) can be determined via a finite number of inequations. Also, we give an algorithmic process to generate the set Θ(Ω). To illustrate our theoretical approach, we present some examples and numerical simulations. Moreover, to demonstrate the effectiveness of our approach in real-life problems, we provide an application to the SI epidemic model and the SIR model.
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spelling pubmed-84123932021-09-03 On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems Benfatah, Youssef El Bhih, Amine Rachik, Mostafa Tridane, Abdessamad Int J Control Autom Syst Regular Papers Given a discrete-time controlled bilinear systems with initial state x(0) and output function y(i), we investigate the maximal output set Θ(Ω) = {x(0) ∈ ℝ(n), y(i) ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝ(p). Using some stability hypothesis, we show that Θ(Ω) can be determined via a finite number of inequations. Also, we give an algorithmic process to generate the set Θ(Ω). To illustrate our theoretical approach, we present some examples and numerical simulations. Moreover, to demonstrate the effectiveness of our approach in real-life problems, we provide an application to the SI epidemic model and the SIR model. Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 2021-09-02 2021 /pmc/articles/PMC8412393/ /pubmed/34493935 http://dx.doi.org/10.1007/s12555-020-0486-6 Text en © ICROS, KIEE and Springer 2021 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Regular Papers
Benfatah, Youssef
El Bhih, Amine
Rachik, Mostafa
Tridane, Abdessamad
On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
title On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
title_full On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
title_fullStr On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
title_full_unstemmed On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
title_short On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems
title_sort on the maximal output admissible set for a class of bilinear discrete-time systems
topic Regular Papers
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8412393/
https://www.ncbi.nlm.nih.gov/pubmed/34493935
http://dx.doi.org/10.1007/s12555-020-0486-6
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