Analysis of the Clinton Critical Experiment [declassified]

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Et 11 i*Ut-JDcps ds, u;" = i*utyo,. e. e. t E [O,IJ. 39) In order to show the existence of the saddle point, we will verify it on the pair (u 1 , u2 ). 34) hold. Hence, (U 1 ,U 2 ) E Uad. 27) holds. 34). For, take any u 2 with (ul,u 2 +u2 ) E Uad. Then J(ul, u2 + u 2 ) - J(u 1 , u2 ) = 2E\U Yo,. + 11 U -JDcps ds, 11 u 1 1 1- tiu;" dt) x + EI111 U1- t iut,. , u;")£2(0,1) dt - E11 IluUI~2(0,1) dt S 2E r 1 / io \ - 2E + i*utyo,. ) io 1 dt £2(0,1) r i*utyo,. II~2(0,1) dt (11IIUl-till~(£2(0,1),X) dt - 1) S O.

5. 55). 72) are satisfied. 4. 1. uv = Hv(x, Du), uvlao = O. 1) The functions Hv(x,p) satisfy first H v (x, p) are Caratheodory functions. 1). 3) where H (x, p) represents the vector H v (x, p). zv = HE(x, Dz), zvlao O. 1) is imbedded in a family of equivalent problems, indexed by the transformation r. All matrices r to be considered will be invertible, so we shall not mention it explicitly. A matrix r satisfies the maximum principle if ru 2:: 0 :::} u 2:: O. 6) We begin by stating two alternative sets of assumptions: L Hv(x,p) 2:: -A.

Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. ColI. , Vol. , 1957. [8] RS. Joseph, Filtering for Stochastic Processes with Application to Guidance, Interscience Publishers, New York, 1968. E. Bashirov, On linear filtering under dependent wide band noises, Stochastics, 23 (1988), 413-437. E. R Mishne, On linear filtering under dependent white noises, Stochastics and Stochastics Reports, 35 (1991), 1-23. [11] RF. J. Zwart, An Introduction to Infinite Dimensional Linear Systems Theoty, Springer Verlag, New York, 1995.

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