Download Optimal Control of Discrete Time Stochastic Systems by Dr. Charlotte Striebel (auth.) PDF

By Dr. Charlotte Striebel (auth.)

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Sample text

13). 18). 2. 5) are possible. 2. t+l are a-finite t+l t measures, and Ht' Qt ,and Gt are stochastic kernels. 2). 13). 9) is measurable and non- negative. 11) holds. 1, and the Fubini Theorem for At+l X ~t+l and (zt,ut ) fixed. 2. 16) A E~ where ht' qt ,and ~t ' At ,and . 9). 1. stochastic kernel. 8) is a stochastic kernel. 2 and the measurability of j~ Then 32 is measurable. 17) is measurable. jt is non-negative so that gt+l is non-negative. 5). 5) for these values. 6). 1. 9). ~ ,and rt Qt and Ht are non-singular.

S.

1 is a sufficient statistic. 8), and it follows from is sufficient for xt • For certain loss functions it will be possible to reduce the sufficient statistic further. Let t = 0,1, ... 6) , define is an r provided r Xn matrix. < n. o t ut(z ) The dimension of {R} Let will be less than that be a control law that satisfies = u0 t +l (zt+l ) = ... that is, no control from t at onwards. s. 3. The statistic available at time at is the expected miss t and assuming that ton. 1. 10) where and u t are fixed.

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