Heuristic Search for Linear Positive Systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912904633122816 |
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| author | Ohlin, David Rantzer, Anders Tegling, Emma |
| author_facet | Ohlin, David Rantzer, Anders Tegling, Emma |
| contents | This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain class of linear systems. This is used to construct a heuristic search framework for linear {positive} systems inspired by existing methods for SSP. {We propose a heuristics-based algorithm for {efficiently} finding local solutions to the analyzed class of optimal control problems with {a given initial} state and {positive} linear dynamics.} {By leveraging the bound on optimality in each state provided by the heuristics, we also derive a novel distributed algorithm for calculating local controllers within a specified performance bound, with a distributed condition for termination.} More fundamentally, the results allow for analysis of the conditions for explicit solutions to the Bellman equation utilized by heuristic search methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heuristic Search for Linear Positive Systems Ohlin, David Rantzer, Anders Tegling, Emma Optimization and Control Systems and Control 93-10 This work considers infinite-horizon optimal control of positive linear systems applied to the case of network routing problems. We demonstrate the equivalence between Stochastic Shortest Path (SSP) problems and optimal control of a certain class of linear systems. This is used to construct a heuristic search framework for linear {positive} systems inspired by existing methods for SSP. {We propose a heuristics-based algorithm for {efficiently} finding local solutions to the analyzed class of optimal control problems with {a given initial} state and {positive} linear dynamics.} {By leveraging the bound on optimality in each state provided by the heuristics, we also derive a novel distributed algorithm for calculating local controllers within a specified performance bound, with a distributed condition for termination.} More fundamentally, the results allow for analysis of the conditions for explicit solutions to the Bellman equation utilized by heuristic search methods. |
| title | Heuristic Search for Linear Positive Systems |
| topic | Optimization and Control Systems and Control 93-10 |
| url | https://arxiv.org/abs/2410.17220 |