On Exact Solutions to the Linear Bellman Equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912438320889856 |
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| author | Ohlin, David Pates, Richard Arcak, Murat |
| author_facet | Ohlin, David Pates, Richard Arcak, Murat |
| contents | This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the class of Linearly Solvable MDP is reformulated as a continuous-state optimal control problem. It is shown that this class naturally satisfies the conditions for explicit solution of the Bellman equation, motivating the extension of previous results to semilinear dynamics to account for input nonlinearities. The applicability of the given conditions is illustrated in scenarios with linear and quadratic cost, corresponding to the Stochastic Shortest Path and Linear-Quadratic Regulator problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Exact Solutions to the Linear Bellman Equation Ohlin, David Pates, Richard Arcak, Murat Optimization and Control Systems and Control 93-10 This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the class of Linearly Solvable MDP is reformulated as a continuous-state optimal control problem. It is shown that this class naturally satisfies the conditions for explicit solution of the Bellman equation, motivating the extension of previous results to semilinear dynamics to account for input nonlinearities. The applicability of the given conditions is illustrated in scenarios with linear and quadratic cost, corresponding to the Stochastic Shortest Path and Linear-Quadratic Regulator problems. |
| title | On Exact Solutions to the Linear Bellman Equation |
| topic | Optimization and Control Systems and Control 93-10 |
| url | https://arxiv.org/abs/2506.15527 |