Null controllability of heat equation with switching controls under Robin’s boundary condition

Yıl 2016, Cilt: 45 Sayı: 2, 373 - 379, 01.04.2016

Ali Hamidoğlu

Öz

In this paper, we consider the null controllability of 1-d heat equation
endowed with Robin’s boundary conditions, when the operator −
d
2
dx2
has positive eigenvalues and try to find sufficient conditions for building switching controls. In [1], the author developed a first analysis of
this problem with Dirichlet’s boundary conditions and obtain sufficient
conditions for switching controls. We firstly consider 1-d heat system
endowed with two controls. Then we try to build switching control
strategies guaranteeing that, at each instant of time, only one control
is activated. 

Anahtar Kelimeler

Heat equation, Robin’s boundary condition, variational approach, switching control

Kaynakça

• E. Zuazua, Switching control, J. Eur. Math. Soc. 13, pp. 85–117, 2011.
• Walter A. Strauss, Partial Differential Equations: An Introduction, Wiley, 1992.
• E. Zuazua, Controllability and observability of partial differential equations: Some results and open problems, In: Handbook of Differential Equations: Evolutionary Equations, Vol.3, pp. 527–621, 2006.
• E. Zuazua, S. Micu, On the controllability of a fractional order parabolic equation, SIAM J. Control Optim., Vol.44, pp. 1950–1972, 2006.
• D.L. Russell, Controllability and stabilizability theory for linear partial differential equations. Resent progress and open questions, SIAM Rev., Vol.20, pp. 639–739., 1978.
• J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, SpringerVerlang Berlin Heidelberg, 1971.
• J.L. Lions, Exact Controllability, Stabilizability and Perturbations for Distributed Systems", SIAM Rev., Vol. 30, pp. 1–68, 1988.
• E.B. Lee, L. Markus, Foundations of Optimal Control Theory, John Wiley and Sons, Inc., New York, 1967.