Regional constrained controllability problem: Approaches and simulations

The aim of this paper is to deal with an output controllability problem. It consists in driving the state of a distributed parabolic system toward a state between two prescribed functions on a boundary subregion of the system evolution domain with minimum energy control. Two necessary conditions are derived. The first one is formulated in terms of subdifferential associated with a minimized functional. The second one is formulated as a system of equations for arguments of the Lagrange systems. Numerical illustrations show the efficiency of the second approach and lead to some conjectures. Recommended by Editorial Board member Fumitoshi Matsuno under the direction of Editor Jae Weon Choi. Zerrik El Hassan is a Professor at the university Moulay Ismail of Meknes in Morocco. He was an Assistant Professor in the faculty of sciences of Meknes and researcher at the university of Perpignan (France). He got his doctorat d etat in system regional analysis (1993) at the University Mohammed V of Rabat, Morocco. Professor Zerrik wrote many papers and books in the area of systems analysis and control. Now he is the Head of the research team MACS (Modeling Analysis and Control of Systems) at the university Moulay Ismail of Meknes in Morocco. Ghafrani Fatima is a Researcher at team MACS at the University Moulay Ismail of Meknes in Morocco. She wrote many papers in the area of systems analysis and control.