A zero-sum electromagnetic evader–interrogator differential game with uncertainty

References

• Banks , HT , Ito , K , Kepler , GM and Toivanen , JA . 2006 . Material surface design to counter electromagnetic interrogation of targets . SIAM J. Appl. Math. , 66 : 1027 – 1049 .
   Web of Science ®Google Scholar
• Banks , HT , Ito , K and Toivanen , JA . 2006 . Determination of interrogating frequencies to maximize electromagnetic backscatter from objects with material coatings . Commun. Comput. Phys. , 1 : 357 – 377 .
   Google Scholar
• von Neumann , J and Morgenstern , O . 1944 . Theory of Games and Economic Behavior , Princeton , NJ : Princeton University Press .
   Google Scholar
• Banks , HT , Grove , SL , Ito , K and Toivanen , JA . 2006 . Static two-player evasion–interrogation games with uncertainty . Comput. Appl. Math. , 25 : 289 – 306 .
   Web of Science ®Google Scholar
• Banks , HT , Hu , S , Ito , K and Muccio , SG . 2011 . Dynamic electromagnetic evasion-pursuit games with uncertainty . Numer. Math.: Theory, Methods Appl. , 4 : 399 – 418 .
   Google Scholar
• Colton , D and Kress , R . 1998 . “ Inverse Acoustic and Electromagnetic Scattering Theory ” . In Applied Mathematical Sciences , 2nd , Vol. 93 , Berlin : Springer-Verlag .
   Google Scholar
• Jackson , JD . 1975 . Classical Electrodynamics , New York : Wiley & Sons .
   Google Scholar
• How , H and Vittoria , C . 2004 . Microwave impedance control over a ferroelectric boundary layer . IEEE Trans. Microwave Theory Tech. , 52 : 2177 – 2182 .
   Web of Science ®Google Scholar
• How , H , Zuo , X , Hokanson , E , Kempel , L and Vittoria , C . 2002 . Calculated and measured characteristics of a microstrip fabricated on a Y-type hexaferrite substrate . IEEE Trans. Microwave Theory Tech. , 50 : 1280 – 1288 .
   Web of Science ®Google Scholar
• Banks , HT , Smith , RC and Wang , Y . 1996 . Smart Material Structures: Modeling, Estimation and Control , Paris/Chichester : Masson/John Wiley .
   Google Scholar
• Basar , T and Olsder , GJ . 1999 . Dynamic Noncooperative Game Theory , Philadelphia , PA : SIAM .
   Google Scholar
• Oksendal , B . 2000 . Stochastic Differential Equations , 5th , Berlin : Springer .
   Google Scholar
• Ethier , SN and Kurtz , TG . 1986 . Markov Processes: Characterization and Convergence , New York : Wiley & Sons .
   Google Scholar
• Elliott , RJ and Kalton , NJ . 1972 . “ The existence of value in differential games ” . In Mem. AMS Vol. 126 , 67
   Google Scholar
• Kocan , M , Soravia , P and Swiech , A . 1997 . On differential games for infinite-dimensional systems with nonlinear unbounded operators . J. Math. Anal. Appl. , 211 : 395 – 423 .
   Web of Science ®Google Scholar
• Berkovitz , LD . 1985 . The existence of value and saddle point in games of fixed duration . SIAM J. Control Optim , 23 : 173 – 196; . Errata and addendum, ibid., 26 (1988), 740-742
   Web of Science ®Google Scholar
• Isaacs , R . 1965 . Differential Games , New York : Wiley . Reprint by Dover, 1999
   Google Scholar
• Friedman , A . 1970 . On the definition of differential games and the existence of value and saddle points . J. Differ. Eqns , 7 : 69 – 91 .
   Web of Science ®Google Scholar
• Friedman , A . 1971 . Differential Games , New York : Wiley .
   Google Scholar
• Krasovskii , NN and Subbotin , AI . 1988 . Game Theoretical Control Problems , New York : Springer .
   Google Scholar
• Ghosh , MK and Shaiju , AJ . 2004 . Existence of value and saddle point in infinite-dimensional differential games . J. Optim. Theory Appl. , 121 : 301 – 325 .
   Web of Science ®Google Scholar
• Shaiju , AJ . 2003 . Infinite horizon differential games for abstract evolution equations . Comput. Appl. Math. , 22 : 335 – 357 .
   Web of Science ®Google Scholar
• Ramaswamy , M and Shaiju , AJ . 2009 . Construction of approximate saddle-point strategies for differential games in a Hilbert space . J. Optim. Theory Appl , 141 : 349 – 370 .
   Web of Science ®Google Scholar
• Elliott , RJ , Kalton , NJ and Markus , L . 1973 . Saddle points for linear differential games . SIAM J. Control , 11 : 100 – 313 .
   Web of Science ®Google Scholar
• Parthasarathy , T and Raghavan , TES . 1975 . Existence of saddle points and Nash equilibrium points for differential games . SIAM J. Control , 13 : 977 – 980 .
   Web of Science ®Google Scholar
• Wilson , DJ . 1977 . Differential games with no information . SIAM J. Control Optim. , 15 : 233 – 246 .
   Web of Science ®Google Scholar
• Young , LC . 1937 . Generalized curves and the existence of an attained absolute minimum in the calculus of variations . C. R. Soc. Sci. Lett. Varsovie, Cl. III , 30 : 212 – 234 .
   Google Scholar
• Young , LC . 1938 . Necessary conditions in the calculus of variations . Acta Math. , 69 : 239 – 258 .
   Google Scholar
• McShane , EJ . 1940 . Necessary conditions in generalized-curve problems of the calculus of variations . Duke Math. J. , 7 : 1 – 27 .
   Google Scholar
• McShane , EJ . 1940 . Generalized curves . Duke Math. J. , 6 : 513 – 536 .
   Google Scholar
• McShane , EJ . 1967 . Relaxed controls and variational problems . SIAM J. Control , 5 : 438 – 485 .
   Google Scholar
• Filippov , AF . 1962 . On certain questions in the theory of optimal control . SIAM J. Control , 1 : 76 – 84 .
   Google Scholar
• Warga , J . 1962 . Relaxed variational problems . J. Math. Anal. Appl. , 4 : 111 – 128 .
   Google Scholar
• Warga , J . 1967 . Functions of relaxed controls . SIAM J. Control , 5 : 628 – 641 .
   Google Scholar
• Warga , J . 1972 . Optimal Control of Differential and Functional Equations , New York : Academic Press .
   Google Scholar
• Bahlali , S . 2008 . Necessary and sufficient optimality conditions for relaxed and strict control problems . SIAM J. Control Optim. , 47 : 2078 – 2095 .
   Web of Science ®Google Scholar
• Chryssoverghi , I and Bacopoulos , A . 1990 . Discrete approximation of relaxed optimal control problems . J. Optim. Theory Appl. , 65 : 395 – 407 .
   Web of Science ®Google Scholar
• Chryssoverghi , I and Bacopoulos , A . 1993 . Approximation of relaxed nonlinear parabolic optimal control problems . J. Optim. Theory Appl. , 77 : 31 – 50 .
   Web of Science ®Google Scholar
• Marco , SCD and Gonzalez , RLV . 1999 . Relaxation of minimax optimal control problems with infinite horizon . J. Optim. Theory Appl. , 101 : 285 – 306 .
   Web of Science ®Google Scholar
• Billingsley , P . 1968 . Convergence of Probability Measures , New York : Wiley & Sons .
   Google Scholar
• V , Yu . 1956 . Prohorov, Convergence of random processes and limit theorems in probability theory . Theor. Prob. Appl. , 1 : 157 – 214 .
   Google Scholar
• Lions , JL . 1971 . Optimal Control of Systems Governed by Partial Differential Equations , New York : Springer-Verlag .
   Google Scholar
• Banks , HT and Hu , S . A zero-sum electromagnetic evader–interrogator differential game with uncertainty, 2011
   Google Scholar
• Banks , HT and Ito , K . 1997 . Approximation in LQR problems for infinite dimensional systems with unbounded input operators . J. Math. Syst. Estimation, Control , 7 : 1 – 34 .
   Google Scholar
• Temam , R . 1977 . Navier-Stokes Equations , New York : North-Holland .
   Google Scholar
• Yu , J and Yuan , XZ . 1998 . New saddle point theorem beyond topological vector spaces . J. Optim. Theory Appl. , 96 : 211 – 219 .
   Web of Science ®Google Scholar
• Dautray , R and Lions , JL . 2000 . Mathematical Analysis and Numerical Methods for Science and Technology , Vol. 5 , Berlin : Part 1, Springer-Verlag .
   Google Scholar
• Crandall , MG and Lions , PL . Viscosity Solution of Hamilton–Jacobi Equations in Infinite Dimensions, Part VI, Evolution Equations, Control Theory, and Biomathematics . Lecture Notes in Pure and Applied Mathematics , Vol. 155, Dekker, New York, NY, 1994, pp. 51–89
   Google Scholar
• Berkovitz , LD . 1988 . Characterizations of the values of differential games . Appl. Math. Optim. , 17 : 177 – 183 .
   Web of Science ®Google Scholar