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Volume 4, Issue 3
Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagnetics

H. T. Banks, Shuhua Hu, K. Ito & Sarah Grove Muccio

DOI: 10.4208/nmtma.2011.m1025

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 359-378.

Published online: 2011-04

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  • Abstract

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent. In this paper, the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator. The problem is formulated in two different ways. One is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation. The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations. In addition, a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.

  • Keywords

Electromagnetic evasion-pursuit, uncertainty, feedback control, computational methods, Kolmogorov and Fokker-Planck equations.

  • AMS Subject Headings

35Q61, 83C50, 83C22, 65M32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-359, author = {H. T. Banks, Shuhua Hu, K. Ito and Sarah Grove Muccio}, title = {Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagnetics}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {3}, pages = {359--378}, abstract = {

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent. In this paper, the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator. The problem is formulated in two different ways. One is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation. The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations. In addition, a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1025}, url = {http://global-sci.org/intro/article_detail/nmtma/5973.html} }
TY - JOUR T1 - Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagnetics AU - H. T. Banks, Shuhua Hu, K. Ito & Sarah Grove Muccio JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 359 EP - 378 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1025 UR - https://global-sci.org/intro/article_detail/nmtma/5973.html KW - Electromagnetic evasion-pursuit, uncertainty, feedback control, computational methods, Kolmogorov and Fokker-Planck equations. AB -

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent. In this paper, the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator. The problem is formulated in two different ways. One is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation. The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations. In addition, a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.

H. T. Banks, Shuhua Hu, K. Ito and Sarah Grove Muccio. (2011). Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagnetics. Numerical Mathematics: Theory, Methods and Applications. 4 (3). 359-378. doi:10.4208/nmtma.2011.m1025
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