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Semidefinite Relaxations for Stochastic Optimal Control Policies

Horowitz, Matanya B. and Burdick, Joel W. (2014) Semidefinite Relaxations for Stochastic Optimal Control Policies. In: 2014 American Control Conference. IEEE , Piscataway, NJ, pp. 3006-3012. ISBN 978-1-4799-3272-6.

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Recent results in the study of the Hamilton Jacobi Bellman (HJB) equation have led to the discovery of a formulation of the value function as a linear Partial Differential Equation (PDE) for stochastic nonlinear systems with a mild constraint on their disturbances. This has yielded promising directions for research in the planning and control of nonlinear systems. This work proposes a new method obtaining approximate solutions to these linear stochastic optimal control (SOC) problems. A candidate polynomial with variable coefficients is proposed as the solution to the SOC problem. A Sum of Squares (SOS) relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function.

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Additional Information:© 2014 AACC. The authors would like to thank Venkat Chandrasakaran for guidance and suggestions. This work was partially supported by DARPA, through the ARM-S and DRC programs, as well as the Robotics Technology Consortium Alliance (RCTA).
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Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Robotics Technology Consortium Alliance (RTCA)UNSPECIFIED
Record Number:CaltechAUTHORS:20150320-095302633
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Official Citation:Horowitz, M.B.; Burdick, J.W., "Semidefinite relaxations for stochastic optimal control policies," American Control Conference (ACC), 2014 , vol., no., pp.3006,3012, 4-6 June 2014 doi: 10.1109/ACC.2014.6859382 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55945
Deposited By: Tony Diaz
Deposited On:20 Mar 2015 19:29
Last Modified:03 Oct 2019 08:10

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