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Minimum Energy Input Control Problem on a Constrained Boundary Subregion

Layla Ezzahri(1), Ali Boutoulout(2*), Fatima Zahrae El Alaoui(3)

(1) Moulay Ismail University, Morocco
(2) Moulay Ismail University, Morocco
(3) Moulay Ismail University, Morocco
(*) Corresponding author


DOI: https://doi.org/10.15866/ireaco.v8i1.4686

Abstract


In this paper we focus on solving the problem of minimum energy control using the subdifferential approach. We show how one can steers a hyperbolic system from an initial state to a final one between two prescribed profiles, only on a boundary subregion Γ of the system evolution domain Ω. First we give some definitions and properties of this new concept, and then we concentrate on the determination of the control which would realize a given final state with minimum energy.
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Keywords


Minimum Energy; Optimal Control; Subdifferential Approach; Hyperbolic Systems

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References


R. F. Curtain and A. J. Pritchard, Infinite Dimensional Linear Systems Theory (Springer-Verlag, 1978).
http://dx.doi.org/10.1007/bfb0006761

R.F. Curtain, and H. Zwart, An introduction to infinite dimentional linear systems theory (Springer Verlag, 1995).
http://dx.doi.org/10.1007/978-1-4612-4224-6

A. El Jai and A.J. Pritchard, Sensors and actuators in distributed systems analysis (Wiley, 1988).
http://dx.doi.org/10.1016/0924-4247(91)80026-l

A. El Jai, A.J. Pritchard, M.C. Simon and E. Zerrik, Regional Controlability of distributed system, International Journal of Control, Vol. 62(Issue 6):1351-1365, 1995.
http://dx.doi.org/10.1080/00207179508921603

E. Zerrik, A. El Jai and A. Boutoulout, Actuators and regional boundary controllability of parabolic system, International Journal of System Science, Vol. 31(Issue 1):73-82, 2000.
http://dx.doi.org/10.1080/002077200291479

D.Q. Mayne, J.B. Rawlings, C.V. Rao and P.O.M. Scokaert, Constrained Model Predictive Control: Stability and Optimality, Automatica Journal, Vol. 36(Issue 6):789-814, 2000.
http://dx.doi.org/10.1016/s0005-1098(99)00214-9

A. Boutoulout, H. Bourray, M. Baddi, F.Z. El Alaoui, Regional Boundary Observability with Constraints, (2011) International Review of Automatic Control (IREACO), 4 (6), pp. 846-854.

A. Boutoulout, H. Bourray, F. El Alaoui, L. Ezzahri, Constrained controllability for distributed hyperbolic systems, Mathematical science letters, Vol. 3(Issue 3): 207-214, 2014.
http://dx.doi.org/10.12785/msl/030312

E. Zerrik and F. Ghafrani, M. Raissouli An Extended Controllability Problem with Minimum Energy, Journal of Mathematical Sciences, Vol. 161(Issue 2):344-353, 2009.
http://dx.doi.org/10.1007/s10958-009-9558-0

A. Pazy, Semigroups of Linear Operators and Applications to Partial Dif-ferential Equations (Springer-Verlag, 1990).
http://dx.doi.org/10.1007/978-1-4612-5561-1

J. L. Lions, Contrôlabilité Exacte Perturbation et Stabilisation des systèmes distribués (Masson, 1988).
http://dx.doi.org/10.1007/bfb0007542

E. Zerrik and R. Larhrissi, Regional Boundary Controllability of Hyperbolic Systems: Numerical Approach, Journal of dynamical and control systems, Vol. 8(Issue 3):293—312, 2002.
http://dx.doi.org/10.1023/a:1016373003163

J.-P. Aubin, S. Wilson. Optima and Equilibria: An Introduction to Nonlinear Analysis (Springer, 2002).


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