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A Compositional Approach to Stochastic Optimal Control with Co-safe Temporal Logic Specifications

Horowitz, Matanya B. and Wolff, Eric M. and Murray, Richard M. (2014) A Compositional Approach to Stochastic Optimal Control with Co-safe Temporal Logic Specifications. In: 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE , Piscataway, NJ, pp. 1466-1473. ISBN 978-1-4799-6934-0. http://resolver.caltech.edu/CaltechAUTHORS:20150402-125326775

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Abstract

We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/IROS.2014.6942750 DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6942750PublisherArticle
ORCID:
AuthorORCID
Murray, Richard M.0000-0002-5785-7481
Additional Information:© 2014 IEEE. The authors thank the anonymous reviewers for their helpful comments. The first and second authors were supported by NSF GRFP and NDSEG fellowships, respectively. Additional support was provided by the Boeing Corporation.
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
National Defense Science and Engineering Graduate (NDSEG) FellowshipUNSPECIFIED
Boeing CorporationUNSPECIFIED
Record Number:CaltechAUTHORS:20150402-125326775
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150402-125326775
Official Citation:Horowitz, M.B.; Wolff, E.M.; Murray, R.M., "A compositional approach to stochastic optimal control with co-safe temporal logic specifications," Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on , vol., no., pp.1466,1473, 14-18 Sept. 2014 doi: 10.1109/IROS.2014.6942750 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6942750&isnumber=6942370
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56308
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Apr 2015 20:47
Last Modified:02 Apr 2015 20:47

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