11.11. Consider a 1-dimensional version of the stochastic linear regulator problem of Example 11.2.4: (s2) = inf E8,1 UE

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11 11 Consider A 1 Dimensional Version Of The Stochastic Linear Regulator Problem Of Example 11 2 4 S2 Inf E8 1 Ue 1 (171.01 KiB) Viewed 28 times

11.11. Consider a 1-dimensional version of the stochastic linear regulator problem of Example 11.2.4: (s2) = inf E8,1 UEK *** []] [ ((X4)? + bu?)dr + (11.3.9) where dx = uydt + odBt ; for t > s. X = , ut, B, ER, o, constants, 6 > 0, the infinum being over the space K of all Markov controls u satisfying E%;"[(X4)?] = m², where m is a constant. (11.3.10) Solve this problem by using Theorem 11.3.1. (Hint: Solve for each l ER the unconstrained problem 173(8, ) = inf E** |/ (X4)2 + bu?)dr + X(X%)? x4)2 with optimal control ut. Then try to find to such that E*,* [(x 0 ) ) = m².) =