Value Iteration for (Switched) Homogeneous Systems
| Autor: | Munther A. Dahleh, Michael Rinehart, I.V. Kolmanovsky |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Mathematical optimization
Linear system Function (mathematics) Computer Science Applications Discrete time and continuous time Rate of convergence Control and Systems Engineering Bellman equation Homogeneous polynomial Convergence (routing) Applied mathematics Electrical and Electronic Engineering Dynamical system (definition) Mathematics |
| Zdroj: | IEEE Transactions on Automatic Control. 54:1290-1294 |
| ISSN: | 1558-2523 0018-9286 |
| DOI: | 10.1109/tac.2009.2013055 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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