# American Institute of Mathematical Sciences

• Previous Article
Asymptotic approximation to a solution of a singularly perturbed linear-quadratic optimal control problem with second-order linear ordinary differential equation of state variable
• NACO Home
• This Issue
• Next Article
An alternate gradient method for optimization problems with orthogonality constraints
doi: 10.3934/naco.2020055

## Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach

 1 Department of Electrical engineering & Informatics, National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Route d'Imouzzer, BP 72, Fez, MA 2 TSI Team, Department of Mathematics, Faculty of Sciences, Moulay Ismail University, BP 11201, Avenue Zitoune, Meknes, MA

* Corresponding author: Touria Karite

Received  February 2019 Revised  October 2020 Published  November 2020

The aim of this paper is to study the problem of constrained controllability for distributed parabolic linear system evolving in spatial domain $\Omega$ using the Reverse Hilbert Uniqueness Method (RHUM approach) introduced by Lions in 1988. It consists in finding the control $u$ that steers the system from an initial state $y_{_{0}}$ to a state between two prescribed functions. We give some definitions and properties concerning this concept and then we resolve the problem that relays on computing a control with minimum cost in the case of $\omega = \Omega$ and in the regional case where $\omega$ is a part of $\Omega$.

Citation: Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2020055
##### References:

show all references

##### References:
 [1] Larbi Berrahmoune. Constrained controllability for lumped linear systems. Evolution Equations & Control Theory, 2015, 4 (2) : 159-175. doi: 10.3934/eect.2015.4.159 [2] Larbi Berrahmoune. Null controllability for distributed systems with time-varying constraint and applications to parabolic-like equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3275-3303. doi: 10.3934/dcdsb.2020062 [3] Venkatesan Govindaraj, Raju K. George. Controllability of fractional dynamical systems: A functional analytic approach. Mathematical Control & Related Fields, 2017, 7 (4) : 537-562. doi: 10.3934/mcrf.2017020 [4] Felipe Wallison Chaves-Silva, Sergio Guerrero, Jean Pierre Puel. Controllability of fast diffusion coupled parabolic systems. Mathematical Control & Related Fields, 2014, 4 (4) : 465-479. doi: 10.3934/mcrf.2014.4.465 [5] Guillaume Olive. Boundary approximate controllability of some linear parabolic systems. Evolution Equations & Control Theory, 2014, 3 (1) : 167-189. doi: 10.3934/eect.2014.3.167 [6] Farid Ammar Khodja, Franz Chouly, Michel Duprez. Partial null controllability of parabolic linear systems. Mathematical Control & Related Fields, 2016, 6 (2) : 185-216. doi: 10.3934/mcrf.2016001 [7] Lingyang Liu, Xu Liu. Controllability and observability of some coupled stochastic parabolic systems. Mathematical Control & Related Fields, 2018, 8 (3&4) : 829-854. doi: 10.3934/mcrf.2018037 [8] John E. Lagnese. Controllability of systems of interconnected membranes. Discrete & Continuous Dynamical Systems, 1995, 1 (1) : 17-33. doi: 10.3934/dcds.1995.1.17 [9] Yassine El Gantouh, Said Hadd, Abdelaziz Rhandi. Approximate controllability of network systems. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020091 [10] Lianwen Wang. Approximate controllability and approximate null controllability of semilinear systems. Communications on Pure & Applied Analysis, 2006, 5 (4) : 953-962. doi: 10.3934/cpaa.2006.5.953 [11] Thuy N. T. Nguyen. Uniform controllability of semidiscrete approximations for parabolic systems in Banach spaces. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 613-640. doi: 10.3934/dcdsb.2015.20.613 [12] Kuntal Bhandari, Franck Boyer. Boundary null-controllability of coupled parabolic systems with Robin conditions. Evolution Equations & Control Theory, 2021, 10 (1) : 61-102. doi: 10.3934/eect.2020052 [13] Andrei Halanay, Luciano Pandolfi. Lack of controllability of thermal systems with memory. Evolution Equations & Control Theory, 2014, 3 (3) : 485-497. doi: 10.3934/eect.2014.3.485 [14] Assia Benabdallah, Michel Cristofol, Patricia Gaitan, Luz de Teresa. Controllability to trajectories for some parabolic systems of three and two equations by one control force. Mathematical Control & Related Fields, 2014, 4 (1) : 17-44. doi: 10.3934/mcrf.2014.4.17 [15] Franck Boyer, Guillaume Olive. Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients. Mathematical Control & Related Fields, 2014, 4 (3) : 263-287. doi: 10.3934/mcrf.2014.4.263 [16] Damien Allonsius, Franck Boyer. Boundary null-controllability of semi-discrete coupled parabolic systems in some multi-dimensional geometries. Mathematical Control & Related Fields, 2020, 10 (2) : 217-256. doi: 10.3934/mcrf.2019037 [17] Antonio Marigonda. Second order conditions for the controllability of nonlinear systems with drift. Communications on Pure & Applied Analysis, 2006, 5 (4) : 861-885. doi: 10.3934/cpaa.2006.5.861 [18] Tatsien Li, Zhiqiang Wang. A note on the exact controllability for nonautonomous hyperbolic systems. Communications on Pure & Applied Analysis, 2007, 6 (1) : 229-235. doi: 10.3934/cpaa.2007.6.229 [19] Therese Mur, Hernan R. Henriquez. Relative controllability of linear systems of fractional order with delay. Mathematical Control & Related Fields, 2015, 5 (4) : 845-858. doi: 10.3934/mcrf.2015.5.845 [20] El Mustapha Ait Ben Hassi, Farid Ammar khodja, Abdelkarim Hajjaj, Lahcen Maniar. Carleman Estimates and null controllability of coupled degenerate systems. Evolution Equations & Control Theory, 2013, 2 (3) : 441-459. doi: 10.3934/eect.2013.2.441

Impact Factor:

Article outline