Year: 2025
Type: article
Abstract: 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.
Source: IEEE Control Systems Letters
Authors: David Ohlin, Richard Pates, Murat Arcak
Institutions: Lund University, University of California, Berkeley
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4411640016