[en] This paper addresses the experimental control of time-harmonic electromagnetic waves. The underlying optimal control problem aims to find a set of values to apply to control sources, located in the controlled region or on its boundary, allowing any electromagnetic field caused by an undesired noise source to be suppressed or replaced by any other field map. After a presentation of the control method, illustrated with a few numerical applications, two experimental setups are considered. The first setup aims to control the voltage within a mixed microstrip/coaxial transmission line. In the second setup, the electric field inside a cross-shaped waveguide network is controlled. For both setups, the working frequency is chosen in the ultra-high frequency range, and a comparison is made to the results given by the equivalent numerical models.
Research center :
Montefiore Institute - Montefiore Institute of Electrical Engineering and Computer Science - ULiège
Disciplines :
Electrical & electronics engineering
Author, co-author :
Spirlet, Maxime ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Geuzaine, Christophe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Beauvois, Véronique ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Dép. d'électric., électron. et informat. (Inst.Montefiore)
Language :
English
Title :
Optimal Control Theory Applied to Unintended Source Control and Field Shaping for Time-Harmonic Electromagnetic Waves
Publication date :
January 2020
Journal title :
IEEE Transactions on Electromagnetic Compatibility
ISSN :
0018-9375
eISSN :
1558-187X
Publisher :
Institute of Electrical and Electronics Engineers, United States
J. Lions, "Exact controllability, stabilization and perturbations for distributed systems, " SIAM Rev., vol. 30, no. 1, pp. 1-68, 1988. [Online]. Available: http://dx.doi.org/10.1137/1030001
R. Glowinski, C.-H. Li, and J.-L. Lions, "A numerical approach to the exact boundary controllability of the wave equation (i) Dirichlet controls: Description of the numerical methods, " Jpn. J. Appl. Math., vol. 7, no. 1, pp. 1-76, 1990. [Online]. Available: http://dx.doi.org/10.1007/BF03167891
J. E. Lagnese, "Exact boundary controllability of Maxwell's equations in a general region, " SIAM J. Control Optim., vol. 27, no. 2, pp. 374-388, Mar. 1989. [Online]. Available: https://search.proquest.com/docview/925975700?accountid=14630
M. Darbas, O. Goubet, and S. Lohrengel, "Exact boundary controllability of the second-order maxwell system: Theory and numerical simulation, " Comput. Math. Appl., vol. 63, no. 7, pp. 1212-1237, 2012. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0898122111011023
A. Cozza, "Emulating an anechoic environment in a wave-diffusive medium through an extended time-reversal approach, " IEEE Trans. An-tennas Propag., vol. 60, no. 8, pp. 3838-3852, Aug. 2012.
J. Benoit, C. Chauvière, and P. Bonnet, "Source identification in time domain electromagnetics, " J. Comput. Phys., vol. 231, no. 8, pp. 3446-3456, 2012. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0021999112000411
M. Spirlet, "Correction of electromagnetic measurements and active shaping of electromagnetic fields in complex and reverberating environments, " Ph.D. dissertation, Dept. Elect., Electron. Inform., Univ. Liege, Liege, Belgium, 2018. [Online]. Available: http://hdl.handle.net/2268/221244
P. Courilleau, T. H. Molinaro, and I. G. Stratis, "On the controllability of time-harmonic electromagnetic fields in chiral media, " Adv. Math. Sci. Appl., vol. 16, no. 2, pp. 491-502, 2006.
K. Ito and K. Kunisch, Lagrange Multiplier Approach to Variational Problems and Applications. Philadelphia, PA, USA: SIAM, 2008. [Online]. Available: http://epubs.siam.org/doi/abs/10.1137/1.9780898718614
Leugering, Constrained Optimization and Optimal Control for Partial Differential Equations, G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, and S. Ulbrich, Eds. Basel, Switzerland: Birkhäuser, 2012.
H. Maurer and H. D. Mittelmann, "Optimization techniques for solving elliptic control problems with control and state constraints: Part 1. boundary control, " Comput. Optim. Appl., vol. 16, no. 1, pp. 29-55, 2000. [Online]. Available: http://dx.doi.org/10.1023/A:1008725519350
H. Maurer and H. D. Mittelmann, "Optimization techniques for solving elliptic control problems with control and state constraints. Part 2: Distributed control, " Comput. Optim. Appl., vol. 18, no. 2, pp. 141-160, 2001. [Online]. Available: http://dx.doi.org/10.1023/A:1008774521095
C. Bardos, G. Lebeau, and J. Rauch, "Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, " SIAM J. Control Optim., vol. 30, no. 5, pp. 1024-1065, Sep. 1992. [Online]. Available: https://search.proquest.com/docview/925912210?accountid=14630
M. Selvanayagam and G. V. Eleftheriades, "An active electromagnetic cloak using the equivalence principle, " IEEE Antennas Wireless Propag. Lett., vol. 11, pp. 1226-1229, 2012.
F. G. Vasquez, G. W. Milton, and D. Onofrei, "Active exterior cloaking for the 2D Laplace and Helmholtz equations, " Phys. Rev. Lett., vol. 103, Aug. 2009, Art. no. 073901. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.103.073901
M. Selvanayagam and G. V. Eleftheriades, "Experimental demonstration of active electromagnetic cloaking, " Phys. Rev. X, vol. 3, 2013, Art. no. 041011. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevX.3.041011
D. Schurig et al., "Metamaterial electromagnetic cloak at microwave fre-quencies, " Science, vol. 314, no. 5801, pp. 977-980, 2006. [Online]. Available: http://science.sciencemag.org/content/314/5801/977
E. Casas, "Second order analysis for bang-bang control problems of PDEs, " SIAM J. Control Optim., vol. 50, no. 4, pp. 2355-2372, 2012. [Online]. Available: https://search.proquest.com/docview/1034868642?accountid=14630
M. Bergounioux, K. Ito, and K. Kunisch, "Primal-dual strategy for constrained optimal control problems, " SIAM J. Control Optim., vol. 37, no. 4, pp. 1176-1194, 1999. [Online]. Available: https://search.proquest.com/docview/925817182?accountid=14630
E. Casas, "Control of an elliptic problem with pointwise state constraints, " SIAM J. Control Optim., vol. 24, no. 6, pp. 1309-1318, Nov. 1986. [Online]. Available: https://search.proquest.com/docview/926026152?accountid=14630
E. Casas, "Boundary control of semilinear elliptic equations with pointwise state constraints, " SIAM J. Control Optim., vol. 31, no. 4, pp. 993-1006, Jul. 1993. [Online]. Available: https://search.proquest.com/docview/925868452?accountid=14630
E. Casas, F. Troltzsch, and A. Unger, "Second order sufficient optimal-ity conditions for some state-constrained control problems of semilinear elliptic equations, " SIAM J. Control Optim., vol. 38, no. 5, pp. 1369-1391, 2000. [Online]. Available: https://search.proquest.com/docview/925816040?accountid=14630
P. Monk, Finite Element Methods for Maxwell's Equations (ser. Numerical Mathematics and Scientific Computation). Oxford, U.K.: Clarendon Press, 2003.
J. A. Stratton and L. J. Chu, "Diffraction theory of electromagnetic waves, " Phys. Rev., vol. 56, pp. 99-107, Jul. 1939. [Online]. Available: http://link.aps.org/doi/10.1103/PhysRev.56.99
P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, "A general environment for the treatment of discrete problems and its application to the finite element method, " IEEE Trans. Magn., vol. 34, no. 5, pp. 3395-3398, Sep. 1998.
C. Geuzaine and J.-F. Remacle, "Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities, " Int. J. Numer. Methods Eng., vol. 79, no. 11, pp. 1309-1331, 2009. [Online]. Available: http://dx.doi.org/10.1002/nme.2579
E. Joy and D. Paris, "Spatial sampling and filtering in near-field measurements, " IEEE Trans. Antennas Propag., vol. AP-20, no. 3, pp. 253-261, May 1972.