Mutual Information Optimal Control of Discrete-Time Linear Systems
This work addresses control theory challenges by introducing a novel optimization framework for linear systems, though it appears incremental as it builds upon existing maximum entropy methods.
The authors tackled the problem of mutual information optimal control for discrete-time linear systems by extending maximum entropy optimal control to simultaneously optimize policy and prior, deriving optimal Gaussian policies and priors analytically and proposing an alternating minimization algorithm validated through numerical experiments.
In this paper, we formulate a mutual information optimal control problem (MIOCP) for discrete-time linear systems. This problem can be regarded as an extension of a maximum entropy optimal control problem (MEOCP). Differently from the MEOCP where the prior is fixed to the uniform distribution, the MIOCP optimizes the policy and prior simultaneously. As analytical results, under the policy and prior classes consisting of Gaussian distributions, we derive the optimal policy and prior of the MIOCP with the prior and policy fixed, respectively. Using the results, we propose an alternating minimization algorithm for the MIOCP. Through numerical experiments, we discuss how our proposed algorithm works.