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Suboptimal stabilizing controllers for linearly solvable system

Leong, Yoke Peng and Horowitz, Matanya B. and Burdick, Joel W. (2015) Suboptimal stabilizing controllers for linearly solvable system. In: 54th IEEE Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 7157-7164. ISBN 978-1-4799-7884-7. https://resolver.caltech.edu/CaltechAUTHORS:20160217-101732457

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Abstract

This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is transformed into a linear partial differential equation for a class of systems with a particular constraint on the stochastic disturbance. It is shown that this linear partial differential equation can be relaxed to a linear differential inclusion, allowing for approximating polynomial solutions to be generated using sum of squares programming. It is shown that the resulting solutions are stochastic control Lyapunov functions with a number of compelling properties. In particular, a-priori bounds on trajectory suboptimality are shown for these approximate value functions. The result is a technique whereby approximate solutions may be computed with non-increasing error via a hierarchy of semidefinite optimization problems.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/CDC.2015.7403348 DOIArticle
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7403348&isnumber=7402066PublisherArticle
http://arxiv.org/abs/1509.07922arXivDiscussion Paper
Additional Information:© 2015 IEEE.
Record Number:CaltechAUTHORS:20160217-101732457
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160217-101732457
Official Citation:Leong, Yoke Peng; Horowitz, Matanya B.; Burdick, Joel W., "Suboptimal stabilizing controllers for linearly solvable system," in Decision and Control (CDC), 2015 IEEE 54th Annual Conference on , vol., no., pp.7157-7164, 15-18 Dec. 2015 doi: 10.1109/CDC.2015.7403348
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64530
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Feb 2016 18:39
Last Modified:03 Oct 2019 09:38

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