Value iteration for (switched) homogeneous systems
Author(s)Dahleh, Munther A.; Kolmanovsky, Ilya V.; Rinehart, Michael David
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers
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.
Final published version
INSPEC Accession Number: 10728500