Value iteration for (switched) homogeneous systems
Name
Rinehart.IEEE09.Value.Iteration.pdf
Size
199.44 KB
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Adobe PDF
Checksum (MD5)
eb5b4705b44160aeffc9899d9067c2d5
Author(s)
Dahleh, Munther A.
Kolmanovsky, Ilya V.
Rinehart, Michael David
Date Issued
June 2009
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers
Citation
Rinehart, M., M. Dahleh, and I. Kolmanovsky. “Value Iteration for (Switched) Homogeneous Systems.” Automatic Control, IEEE Transactions on 54.6 (2009): 1290-1294. ©2009 IEEE.
Version
Final published version
Abstract
In this note, we prove that dynamic programming value iteration converges uniformly for discrete-time homogeneous systems and continuous-time switched homogeneous systems. For discrete-time homogeneous systems, rather than discounting the cost function (which exponentially decreases the weights of the cost of future actions), we show that such systems satisfy approximate dynamic programming conditions recently developed by Rantzer, which provides a uniform bound on the convergence rate of value iteration over a compact set. For continuous-time switched homogeneous system, we present a transformation that generates an equivalent discrete-time homogeneous system with an additional ldquosamplingrdquo input for which discrete-time value iteration is compatible, and we further show that the inclusion of homogeneous switching costs results in a continuous value function.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/TAC.2009.2013055
