L10-StochOptControl

L10-StochOptControl

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 03/01/2014 for the course EE 208 at Imperial College.

Ask a homework question - tutors are online