Abstract
Given a discrete-time controlled bilinear systems with initial state x0 and output function yi, we investigate the maximal output set Θ(Ω) = {x0 ∈ ℝn, yi ∈ Ω, ∀ i ≥ 0} where Ω is a given constraint set and is a subset of ℝp. 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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Recommended by Associate Editor Ohmin Kwon under the direction of Editor Jessie (Ju H.) Park
The authors would like to thank the reviewer for his time to help improve this paper. Research reported in this paper was supported by the Moroccan Systems Theory Network.
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The authors declare that they have no conflicts of interest.
Youssef Benfatah is a Ph.D. student. He received his M.S. degree in applied mathematics in 2017 from Faculty of Sciences and Techniques of Settat, Hassan I University, Morocco. Since 2019, he is a member of the Analysis, Modeling and Simulation Laboratory at Faculty of Sciences Ben M’sik, University of Hassan II. His research interests include optimal control, dynamical systems, mathematical modeling and distributed systems.
Amine El Bhih is a Ph.D. student. He received his M.S. degree in applied mathematics in 2017 from Faculty of Sciences Ben Máik, Hassan II University, Casablanca, Morocco. Since 2019, he is a member of the Analysis, Modeling and Simulation Laboratory at the same faculty. His research interests include optimal control, dynamical systems, mathematical modeling distributed systems.
Mostafa Rachik is a Professor of Mathematics and Computer Science at Faculty of Sciences Ben Máik, Casablanca (Morocco). He received his Ph.D. degree in control systems. Professor Rachik wrote many papers in the area of systems analysis and control. Now he is the Head of the research team LAMS (Analysis, Modeling and Simulation Laboratory) at the same faculty. His main research interests are dynamical systems, mathematical modelling, stochastic epidemic systems, robotics, optimization, distributed systems, optimal control, and its applications.
Abdessamad Tridane is an Associate Professor in the Department of Mathematical Sciences at United Arab Emirates University, Al Ain, UAE. He received his Ph.D. degree in control systems theory. Dr. Tridane wrote many papers in the area of control systems, mathematical epidemiology and mathematical medicine. His main research interests are dynamical systems, control systems, mathematical epidemiology and medicine.
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Benfatah, Y., El Bhih, A., Rachik, M. et al. On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems. Int. J. Control Autom. Syst. 19, 3551–3568 (2021). https://doi.org/10.1007/s12555-020-0486-6
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DOI: https://doi.org/10.1007/s12555-020-0486-6