On the control of the final speed for a class of finite-dimensional linear systems: controllability and regulation

• Autorzy: Rachik Mostafa , Khaloufi Issam , Benfatah Youssef , Boutayeb Hamza , Laarabi Hassan

Identyfikatory

DOI

10.24425/acs.2023.146956

• Języki publikacji: EN

Abstrakty

EN

In this article, we extended the concept of controllability, traditionally used to control the final state of a system, to the exact control of its final speed. Inspired by Kalman’s theory, we have established some conditions to characterize the control that allows the system to reach a desired final speed exactly. When the assumptions ensuring speed-controllability are not met, we adopt a regulation strategy that involves determining the control law to make the system’s final speed approach as closely as possible to the predefined final speed, and this at a lower cost. The theoretical results obtained are illustrated through three examples.

Słowa kluczowe

EN

speed-controllability; controllability; continuous systems; regulation; Kalman’s condition

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 3
• Strony: 497--525
• Opis fizyczny: Bibliogr. 18 poz., wzory

Twórcy

autor

Rachik Mostafa

• Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco

• https://orcid.org/0000-0002-5118-2786

autor

Khaloufi Issam

• Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco

• https://orcid.org/0000-0002-9416-8300

autor

Benfatah Youssef

• Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco

• https://orcid.org/0000-0001-9497-003X

autor

Boutayeb Hamza

• Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco

• https://orcid.org/0000-0003-4775-4814

autor

Laarabi Hassan

• Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco

• https://orcid.org/0000-0001-7735-6935

Bibliografia

• [1] R.E. Kalman, Y.C. Ho and K.S. Narendra: Controllability of linear dynamical systems. Contributions to Differential Equations, 1 (1963), 189-213. DOI: 10.21136/MB.2012.142861.
• [2] E.D. Sontag: Kalman’s Controllability Rank Condition: From Linear To Nonlinear. In Mathematical System Theory, A.C. Antoulas Ed., Springer, 1996, 453-462. DOI: 10.1007/978-3-662-08546-2_25.
• [3] D.L. Lukes: Global controllability of nonlinear systems. SIAM Journal on Control, 10 (1972), 112-126. DOI: 10.1137/0310011.
• [4] A. El Bhih, Y. Benfatah and M. Rachik: Exact determinations of maximal output admissible set for a class of semilinear discrete systems. Archives of Control Sciences, 30(3), (2020), 523-552, DOI: 10.24425/acs.2020.134676.
• [5] D. Cabada, K. Garcia, C. Guevara and H. Leiva: Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions. Archives of Control Sciences, 32(2), (2022), 335-357. DOI: 10.24425/acs.2022.141715.
• [6] J. Klamka and A. Czornik: Stochastic controllability of linear systems with delay in control. 17th International Carpathian Control Conference (ICCC), (2016). DOI: 10.1109/CarpathianCC.2016.7501118.
• [7] Zhijian Ji, Zidong Wang, Hai Lin and Zheng Wang: Controllability of multi-agent systems with time-delay in state and switching topology. International Journal of Control, 83(2), (2010), 371-386. DOI: 10.1080/00207170903171330.
• [8] Y. Benfatah, A. El Bhih, M. Rachik and A. Tridane: On the maximal output admissible set for a class of bilinear discrete-time systems. International Journal of Control Automation and Systems, 19 (2021), 1-18. DOI: 10.1007/s12555-020-0486-6.
• [9] A. Abdelhak and M. Rachik: Model reduction problem of linear discrete systems: Admissibles initial states. Archives of Control Sciences, 29(1), (2019), 41-55. DOI: 10.24425/acs.2019.127522.
• [10] M. Rachik and M. Lhous: An observer-based control of linear systems with uncertain parameters. Archives of Control Sciences, 26(4), (2016), 565-576. DOI: 10.1515/acsc-2016-0031.
• [11] S. Guermah, S. Djennoune and M. Bettayeb: Controllability and observability of linear discrete-time fractional-order systems. International Journal of Applied Mathematics and Computer Science, 18(2), (2008), 213-222. DOI: 10.2478/v10006-008-0019-6.
• [12] Hai Zhang, Cao Jinde and Jiang Wei: Controllability criteria for linear fractional differential systems with state delay and impulses. Journal of Applied Mathematics, 2013 Art. ID 146010. DOI: 10.1155/2013/146010.
• [13] B.S. Vadivoo, R. Raja, Cao Jinde, G. Rajchakit and A.R. Seadawy: Controllability criteria of fractional differential dynamical systems with non-instantaneous impulses. Journal of Mathematical Control and Information, 37(3), (2020), 777-793. DOI: 10.1093/imamci/dnz025.
• [14] A. Larrache, M. Lhous, S. Ben Rhila, M. Rachik and A. Tridane: An output sensitivity problem for a class of linear distributed systems with uncertain initial state. Archives of Control Sciences, 30(1), (2020), 139-155. DOI: 10.24425/acs.2020.132589.
• [15] M. Gueye: Exact boundary controllability of 1-D parabolic and hyperbolic degenerate equations. SIAM Journal of Control and Optimization, 52(4), (2014), 2037-2054. DOI: 10.1137/120901374.
• [16] B. Allal, A. Hajjaj, J. Salhi and A. Sbai: Boundary controllability for a coupled system of degenerate/singular parabolic equations. Evolution Equations and Control Theory, 11(5), (2022), 1579-1604. DOI: 10.3934/eect.2021055.
• [17] H. Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer New York, 2011.
• [18] A. El Jai: Eléments d’analyse et de contrôle des systemes. Presses Universitaires de Perpignan, 2004. In French.