Insensitizing controls for linear ODE's

Marcos López-García, Alberto Peña-García, Luz de Teresa

Abstract


In this paper we present some results regarding insensitizing controls for finite dimensional systems. The concept was introduced by J. L. Lions in the context of partial differential equations and, as far as we know, is a problem that has not been treated in literature for ordinary differential equations. The concept in this situation arises in a natural way when treating the semidiscrete one for the heat equation. We present some results in the linear framework.

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References


F. Boyer, V. Hernández-Santamaría, and L. de Teresa, Insensitizing controls for a semilinear parabolic equation: a numerical approach, Math. Control Relat. Fields 9 (2019), no. 1, 117-158. https://doi.org/10.3934/mcrf.2019007

A.E. Bashirov, N. Mahmudov, N. Semi, and H. Etikan, Partial controllability concepts, International Journal of Control 80 (2007), 1-7. https://doi.org/10.1080/00207170600885489

J.-M. Coron, Control and nonlinearity, American Mathematical Society, United States of America, 2007.

S. Lakshmivarahan, J.-M. Lewis, and R. Jabrzemski, Forecast Error Correction using Dynamic Data Assimilation, Springer, 2017.

J.-L. Lions, Sur les sentinelles des systèmes distribués. Conditions frontières, termes sources, coefficients incomplètement connus, C. R. Acad. Sci. Paris Ser. I Math. 307 (1988), no. 17, 865-870.

J.-L. Lions, Least regret control and real time, Indiana Univ. Math. J. 42 (1993), no. 3, 893-905.

J.-L. Lions, Remarques prèliminaires sur le contrôle des systèmes à données incomplètes, in Actas del Congreso de Ecuaciones Diferenciales y Aplicaciones (CEDYA), Universidad de Malaga: 43-54, 1989.

M. Sobral, Sensitivity in Optimal Control Systems, Proceedings of the IEEE 56 (1968), 1644-1652. https://doi.org/10.1109/PROC.1968.6700

L. de Teresa, Insensitizing controls for a semilinear heat equation, Comm. Partial Differential Equations 25 (2000), no. 1-2, 39–72. https://doi.org/10.1080/03605300008821507

W. J. Terrell, Stability and Stabilization: An introduction, Princeton University Press, 2009.

J. Zabczyk, Mathematical control theory: an introduction, Reprint of the 1995 edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008.




DOI: https://doi.org/10.52846/ami.v49i1.1636