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

• URL: http://arxiv.org/abs/2605.09349v1
• Date: Sun, 10 May 2026 06:02:10 GMT
• Title: Mutual Information Optimal Density Control of Linear Systems and Generalized Schrödinger Bridges with Reference Refinement
• Abstract summary: We consider a mutual information (MI) regularized version of optimal density control of a discrete-time linear system.<n>MI regularization inducesity in the policy, which poses challenges for applications of MI optimal control in safety-critical scenarios.<n>We propose an alternating optimization algorithm and derive the closed form of each step in the algorithm.
• Score: 2.1485350418225244
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space [99.30250506439678]
  This work reformulates language generation as an optimal control problem.<n>It provides a unified theoretical perspective to analyze autoregressive and diffusion models.
  arXiv  Detail & Related papers  (2026-05-14T08:13:43Z)
• Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions [1.9116784879310027]
  We study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC)<n>In the static setting, we consider UOT with quadratic transport cost and Kullback--Leibler penalties on the marginals relative to prescribed Gaussian measures.<n>We prove that any feasible solution can be replaced, without loss of optimality, by a Gaussian initial measure and an affine-Gaussian control policy.
  arXiv  Detail & Related papers  (2026-05-05T19:32:03Z)
• Backscatter Device-aided Integrated Sensing and Communication: A Pareto Optimization Framework [59.30060797118097]
  Integrated sensing and communication (ISAC) systems potentially encounter significant performance degradation in densely obstructed urban non-line-of-sight scenarios.<n>This paper proposes a backscatter approximation (BD)-assisted ISAC system, which leverages passive BDs naturally distributed in environments of enhancement.
  arXiv  Detail & Related papers  (2025-07-12T17:11:06Z)
• Mutual Information Optimal Control of Discrete-Time Linear Systems [0.07366405857677226]
  We formulate a mutual information optimal control problem (MIOCP) for discrete-time linear systems.<n>This problem can be regarded as an extension of a maximum entropy optimal control problem (MEOCP)
  arXiv  Detail & Related papers  (2025-07-07T07:04:27Z)
• Krotov Type Optimization of Coherent and Incoherent Controls for Open Two-Qubit Systems [77.34726150561087]
  This work considers two-qubit open quantum systems driven by coherent and incoherent controls. Incoherent control induces time-dependent decoherence rates via time-dependent spectral density of the environment. The system evolves according to the Gorini-Kossakowski-Sudarshan-Lindblad master equation with time-dependent coefficients.
  arXiv  Detail & Related papers  (2023-08-11T13:17:19Z)
• Optimal control for state preparation in two-qubit open quantum systems driven by coherent and incoherent controls via GRAPE approach [77.34726150561087]
  We consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation. We study evolution of the von Neumann entropy, purity, and one-qubit reduced density matrices under optimized controls.
  arXiv  Detail & Related papers  (2022-11-04T15:20:18Z)
• Robustness of a universal gate set implementation in transmon systems via Chopped Random Basis optimal control [50.591267188664666]
  We numerically study the implementation of a universal two-qubit gate set, composed of CNOT, Hadamard, phase and $pi/8$ gates, for transmon-based systems. The control signals to implement such gates are obtained using the Chopped Random Basis optimal control technique, with a target gate infidelity of $10-2$.
  arXiv  Detail & Related papers  (2022-07-27T10:55:15Z)
• Maximum entropy optimal density control of discrete-time linear systems and Schr\"odinger bridges [0.087024326813104]
  We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Despite the merits, high-entropy control policies induced by the regularization introduce probabilistic uncertainty into systems. We reveal that the MaxEnt optimal density control gives the so-called Schr"odinger bridge associated to a discrete-time linear system.
  arXiv  Detail & Related papers  (2022-04-11T17:06:23Z)
• Advancing Trajectory Optimization with Approximate Inference: Exploration, Covariance Control and Adaptive Risk [29.811633555275666]
  We look at the input inference for control (i2c) algorithm, and derive three key characteristics that enable advanced trajectory optimization. An expert' linear Gaussian controller that combines the benefits of open-loop optima and closed-loop variance reduction when optimizing for nonlinear systems.
  arXiv  Detail & Related papers  (2021-03-10T19:52:31Z)
• Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics [77.34726150561087]
  We propose direct optimal control as a robust and flexible alternative to indirect control theory. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential.
  arXiv  Detail & Related papers  (2020-10-08T07:59:29Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)
• Convergence Guarantees of Policy Optimization Methods for Markovian Jump Linear Systems [3.3343656101775365]
  We show that the Gauss-Newton method converges to the optimal state feedback controller for MJLS at a linear rate if at a controller which stabilizes the closed-loop dynamics in the mean sense. We present an example to support our theory.
  arXiv  Detail & Related papers  (2020-02-10T21:13:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.