L10-StochOptControl

# L10-StochOptControl

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Unformatted text preview: nt not an index) with x ∈ Rn to be invertible. Look at the treatment of controllability by Zabczyk [9] (or in the other sources provided) and prove that this holds.” Output: A precis of the proof in a page. 8 C Read about, and be able to explain, the Ott, Grebogi, and Yorke algorithm for stabilizing chaotic dynamics (you’ll ﬁnd an account of it in ref. [7]). Output: A precis of the method in a page or less. 9 C Please convince yourself of the proof of Bode’s Integral Formula - you’ll ﬁnd it provided in [6]. Output: A precis of the proof in a page. 10 C Be able to derive the optimal control and cost-to-go of Linear Quadratic Gaussian control [1]. Output: A precis of the proof in half a page. Read [12] you do not need to understand fully. Output: Read it. Nick Jones Elements of Stochastic Optimal Control: ICDNS Noisy dynamics We now consider Gaussian perturbations to our dynamical system. dx = f (x , u , t )dt + d ξ These can be distinct for diﬀerent state variables and element of d ξ can be correlated between them: < d ξi d ξj >= νij (t , x , u )dt (though uncorrelated in time). Note that the control and noise need not be independent. Nick Jones Elements of Stochastic Optimal Control: ICDNS Expected cost and optimal cost-to-go dx = f (x , u , t )dt + d ξ T C (x0 , u (0 → T )) = W (xT ) + dt w (x , u , t ) 0 Any particular control u (0 → T ) (with i.c. x0 ) thus speciﬁes an ensemble of trajectories w...
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## This document was uploaded on 03/01/2014 for the course EE 208 at Imperial College.

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