Mutual Information Optimal Density Control of Linear Systems and Generalized Schrödinger Bridges with Reference Refinement

2026-05-10

AI Summary

This work addresses the challenge of reconciling performance and safety in discrete-time linear systems under mutual information regularized optimal control, where the inherent stochasticity of policies may violate stringent state uncertainty constraints required in safety-critical applications. To overcome this limitation, the authors propose a Gaussian density constraint that explicitly shapes the state distribution at specified time steps and develop an alternating optimization algorithm to solve the resulting mutual information-regularized optimal density control problem. Theoretical analysis establishes an equivalence between this formulation and the generalized Schrödinger bridge problem in discrete time, enabling closed-form solutions for each substep of the algorithm. The proposed approach preserves the performance benefits of mutual information regularization while achieving precise control over state uncertainty, thereby significantly enhancing its applicability in safety-sensitive domains.

Abstract

We consider a mutual information (MI) regularized version of optimal density control of a discrete-time linear system. MI optimal control has been proposed as an extension of maximum entropy optimal control to trade off between control performance and benefits provided by stochastic inputs. MI regularization induces stochasticity in the policy, which poses challenges for applications of MI optimal control in safety-critical scenarios. To remedy this situation, we impose Gaussian density constraints at specified times to directly control state uncertainty. For this MI optimal density control problem, we propose an alternating optimization algorithm and derive the closed form of each step in the algorithm. In addition, we reveal that the alternating optimization of the MI optimal density control problem coincides with that of the so-called generalized Schrödinger bridge problem associated with the discrete-time linear system.

Problem

• Mutual Information
• Optimal Density Control
• Linear Systems
• State Uncertainty
• Gaussian Constraints

Innovation

• Mutual Information
• Optimal Density Control
• Generalized Schrödinger Bridge
• Gaussian Density Constraints
• Alternating Optimization