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Linear Hamilton Jacobi Bellman Equations in high dimensions

Horowitz, Matanya B. and Damle, Anil and Burdick, Joel W. (2014) Linear Hamilton Jacobi Bellman Equations in high dimensions. In: 53rd IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 5880-5887. ISBN 978-1-4673-6090-6. (Unpublished)

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The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent results in the structure of the HJB, and its reduction to a linear Partial Differential Equation (PDE), with methods based on low rank tensor representations, known as a separated representations, to address the curse of dimensionality. The result is an algorithm to solve optimal control problems which scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finite-horizon, average cost, and first-exit settings. The method is demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with system dimension two, six, and twelve respectively.

Item Type:Book Section
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Additional Information:© 2014 IEEE. Anil Damle is supported by NSF Fellowship DGE-1147470.
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1147470
Record Number:CaltechAUTHORS:20190410-120647917
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Official Citation:M. B. Horowitz, A. Damle and J. W. Burdick, "Linear Hamilton Jacobi Bellman Equations in high dimensions," 53rd IEEE Conference on Decision and Control, Los Angeles, CA, 2014, pp. 5880-5887. doi: 10.1109/CDC.2014.7040310
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94637
Deposited By: George Porter
Deposited On:10 Apr 2019 19:58
Last Modified:03 Oct 2019 21:05

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