arXiv subjects

Kenji Kashima

Publications and source records attributed to Kenji Kashima.

At least 19 recordsLinked to original sources

arXiv2026

Constrained minmax density transportation for linear parabolic PDEs: a numerical optimal control perspective

This article introduces a numerical optimal control framework for minmax constrained density control for a class of noisy linear parabolic partial differential equations (PDEs), in particular the noisy heat equation. The goal is to transport an initial density to a target density while minimizing a specified cost with respect to control actions and maximizing it with respect to disturbances, all within a fixed time horizon while satisfying given convex path constraints. To address this, the spatial derivatives in the PDE are discretized using finite-difference approximations, transforming the problem into a system of ordinary differential equations in time. The admissible space of control and disturbance trajectories is then finitely parametrized, and the resulting optimal control problem is formulated as a convex semi-infinite program (SIP) under mild assumptions. By leveraging new numerical tools from convex SIP theory, we establish guarantees for exact solutions that account for constraint satisfaction under an infinite family of disturbance realizations, and we establish an optimization-based computationally efficient algorithm to recover these solutions. Comprehensive numerical examples to demonstrate and validate our findings are included.

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arXiv2026

Mutual Information Optimal Density Control of Linear Systems and Generalized Schr\"{o}dinger Bridges with Reference Refinement

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 Schr\"{o}dinger bridge problem associated with the discrete-time linear system.

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arXiv2026

Unbalanced Optimal Transport and Density Control for Discrete-Time Linear Systems

This article studies unbalanced optimal transport (UOT) and its dynamical extension, unbalanced density control (UDC), for a class of constrained discrete-time linear systems. UOT compares measures with unequal total mass by balancing transport cost and fidelity to reference measures, while UDC incorporates system dynamics and constraints into this framework. Focusing on Gaussian references and discrete-time linear systems, we show that both problems admit globally optimal convex formulations, analogous to covariance steering. A numerical experiment is provided to illustrate our approach.

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arXiv2026

Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions

In this article, we study unbalanced optimal transport (UOT) and establish a control-theoretic dynamical extension, which we call the unbalanced density control (UDC), for a class of Gaussian reference measures. In the static setting, we consider UOT with quadratic transport cost and Kullback--Leibler penalties on the marginals relative to prescribed Gaussian measures. We show that the infinite-dimensional variational problem admits an exact Gaussian reduction, yielding a finite-dimensional optimization over masses, means, and covariances, together with a closed-form expression for the optimal transported mass. We then formulate UDC for discrete-time linear systems, where the initial and terminal state measures are imposed softly through KL penalties and the intermediate evolution is governed by controlled linear dynamics with quadratic control cost. For this problem, we prove that any feasible solution can be replaced, without loss of optimality, by a Gaussian initial measure and an affine-Gaussian control policy. This leads to an exact finite-dimensional reformulation and, after a standard covariance-steering lifting, to an SDP-based optimization for fixed mass, again coupled with a closed-form mass update. We further establish existence of optimal solutions and identify a sufficient condition under which the affine-Gaussian UDC policy is deterministic. These results provide globally optimal solution methods for both Gaussian UOT and Gaussian UDC. Finally, we illustrate our results with several numerical examples.

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arXiv2026

Convex Chance-Constrained Stochastic Control under Uncertain Specifications with Application to Learning-Based Hybrid Powertrain Control

This paper presents a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. By jointly optimizing control inputs and risk allocation under general (possibly non-Gaussian) uncertainties, the proposed method guarantees probabilistic constraint satisfaction while ensuring strict convexity, leading to uniqueness and continuity of the optimal solution. The formulation is further extended to nonlinear model-based control using exactly linearizable models identified through machine learning. The effectiveness of the proposed approach is demonstrated through model predictive control applied to a hybrid powertrain system.

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arXiv2026

Robust maximum hands-off optimal control: existence, maximum principle, and $L^{0}$-$L^1$ equivalence

This work advances the maximum hands-off sparse control framework by developing a robust counterpart for constrained linear systems with parametric uncertainties. The resulting optimal control problem minimizes an $L^{0}$ objective subject to an uncountable, compact family of constraints, and is therefore a nonconvex, nonsmooth robust optimization problem. To address this, we replace the $L^{0}$ objective with its convex $L^{1}$ surrogate and, using a nonsmooth variant of the robust Pontryagin maximum principle, show that the $L^{0}$ and $L^{1}$ formulations have identical sets of optimal solutions -- we call this the robust hands-off principle. Building on this equivalence, we propose an algorithmic framework -- drawing on numerically viable techniques from the semi-infinite robust optimization literature -- to solve the resulting problems. An illustrative example is provided to demonstrate the effectiveness of the approach.

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arXiv2025

Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control

Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.

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arXiv2025

Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance

We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-convex program and show that it can be efficiently and tractably solved using the DC algorithm. Numerical results validate our approach through various data-driven schemes.

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arXiv2025

On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems

In recent years, mutual information optimal control has been proposed as an extension of maximum entropy optimal control. Both approaches introduce regularization terms to render the policy stochastic, and it is important to theoretically clarify the relationship between the temperature parameter (i.e., the coefficient of the regularization term) and the stochasticity of the policy. Unlike in maximum entropy optimal control, this relationship remains unexplored in mutual information optimal control. In this paper, we investigate this relationship for a mutual information optimal control problem (MIOCP) of discrete-time linear systems. After extending the result of a previous study of the MIOCP, we establish the existence of an optimal policy of the MIOCP, and then derive the respective conditions on the temperature parameter under which the optimal policy becomes stochastic and deterministic. Furthermore, we also derive the respective conditions on the temperature parameter under which the policy obtained by an alternating optimization algorithm becomes stochastic and deterministic. The validity of the theoretical results is demonstrated through numerical experiments.

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arXiv2025

Mutual Information Optimal Control of Discrete-Time Linear Systems

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.

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arXiv2025

Dynamical models for distributed social power perception in Friedkin-Johnsen influence networks

Social power quantifies the ability of individuals to influence others and plays a central role in social influence networks. Yet, computing social power typically requires global knowledge and significant computational or storage capability, especially in large-scale networks with stubborn individuals. In this paper, we propose a distributed perception mechanism based on the Friedkin-Johnsen opinion dynamics that enables individuals to estimate their true social power through local interactions. The mechanism starts from independent initial perceptions and relies only on local information: each individual only needs to know its neighbors' stubbornness and the influence weights they accord. We provide rigorous dynamical system analysis that characterizes equilibria, invariant sets, and convergence. Conditions are established for convergence to the true social power in both the static setting with fixed influence weights and the reflected-appraisal setting where influence weights coevolve with perceptions. The proposed mechanism remains reliable under extreme initial perceptions, disconnected influence networks, reflected-appraisal coupling, and variations in timescales. Numerical examples illustrate our results.

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arXiv2025

Formation Shape Control using the Gromov-Wasserstein Metric

This article introduces a formation shape control algorithm, in the optimal control framework, for steering an initial population of agents to a desired configuration via employing the Gromov-Wasserstein distance. The underlying dynamical system is assumed to be a constrained linear system and the objective function is a sum of quadratic control-dependent stage cost and a Gromov-Wasserstein terminal cost. The inclusion of the Gromov-Wasserstein cost transforms the resulting optimal control problem into a well-known NP-hard problem, making it both numerically demanding and difficult to solve with high accuracy. Towards that end, we employ a recent semi-definite relaxation-driven technique to tackle the Gromov-Wasserstein distance. A numerical example is provided to illustrate our results.

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arXiv2024

Risk-sensitive control as inference with R\'enyi divergence

This paper introduces the risk-sensitive control as inference (RCaI) that extends CaI by using R\'{e}nyi divergence variational inference. RCaI is shown to be equivalent to log-probability regularized risk-sensitive control, which is an extension of the maximum entropy (MaxEnt) control. We also prove that the risk-sensitive optimal policy can be obtained by solving a soft Bellman equation, which reveals several equivalences between RCaI, MaxEnt control, the optimal posterior for CaI, and linearly-solvable control. Moreover, based on RCaI, we derive the risk-sensitive reinforcement learning (RL) methods: the policy gradient and the soft actor-critic. As the risk-sensitivity parameter vanishes, we recover the risk-neutral CaI and RL, which means that RCaI is a unifying framework. Furthermore, we give another risk-sensitive generalization of the MaxEnt control using R\'{e}nyi entropy regularization. We show that in both of our extensions, the optimal policies have the same structure even though the derivations are very different.

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arXiv2024

Tsallis Entropy Regularization for Linearly Solvable MDP and Linear Quadratic Regulator

Shannon entropy regularization is widely adopted in optimal control due to its ability to promote exploration and enhance robustness, e.g., maximum entropy reinforcement learning known as Soft Actor-Critic. In this paper, Tsallis entropy, which is a one-parameter extension of Shannon entropy, is used for the regularization of linearly solvable MDP and linear quadratic regulators. We derive the solution for these problems and demonstrate its usefulness in balancing between exploration and sparsity of the obtained control law.

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arXiv2024

Imitation-regularized Optimal Transport on Networks: Provable Robustness and Application to Logistics Planning

Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph structures has been investigated to enhance the robustness of transport on such networks. In this study, we propose an imitation-regularized OT (I-OT) that mathematically incorporates prior knowledge into the robustness of OT. This method is expected to enhance interpretability by integrating human insights into robustness and to accelerate practical applications. Furthermore, we mathematically verify the robustness of I-OT and discuss how these robustness properties relate to real-world applications. The effectiveness of this method is validated through a logistics simulation using automotive parts data.

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arXiv2024

Minimum energy density steering of linear systems with Gromov-Wasserstein terminal cost

In this paper, we newly formulate and solve the optimal density control problem with Gromov-Wasserstein (GW) terminal cost in discrete-time linear Gaussian systems. Differently from the Wasserstein or Kullback-Leibler distances employed in the existing works, the GW distance quantifies the difference in shapes of the distribution, which is invariant under translation and rotation. Consequently, our formulation allows us to find small energy inputs that achieve the desired shape of the terminal distribution, which has practical applications, e.g., robotic swarms. We demonstrate that the problem can be reduced to a Difference of Convex (DC) programming, which is efficiently solvable through the DC algorithm. Through numerical experiments, we confirm that the state distribution reaches the terminal distribution that can be realized with the minimum control energy among those having the specified shape.

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arXiv2024

Sampled-Data Primal-Dual Gradient Dynamics in Model Predictive Control

Model Predictive Control (MPC) is a versatile approach capable of accommodating diverse control requirements that holds significant promise for a broad spectrum of industrial applications. Noteworthy challenges associated with MPC include the substantial computational burden, which is sometimes considered excessive even for linear systems. Recently, a rapid computation method that guides the input toward convergence with the optimal control problem solution by employing primal-dual gradient (PDG) dynamics as a controller has been proposed for linear MPCs. However, stability has been ensured under the assumption that the controller is a continuous-time system, leading to potential instability when the controller undergoes discretization and is implemented as a sampled-data system. In this paper, we propose a discrete-time dynamical controller, incorporating specific modifications to the PDG approach, and present stability conditions relevant to the resulting sampled-data system. Additionally, we introduce an extension designed to enhance control performance, that was traded off in the original. Numerical examples substantiate that our proposed method, which can be executed in only 1 $\mu$s in a standard laptop, not only ensures stability with considering sampled-data implementation but also effectively enhances control performance.

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arXiv2023

Learning Exactly Linearizable Deep Dynamics Models

Research on control using models based on machine-learning methods has now shifted to the practical engineering stage. Achieving high performance and theoretically guaranteeing the safety of the system is critical for such applications. In this paper, we propose a learning method for exactly linearizable dynamical models that can easily apply various control theories to ensure stability, reliability, etc., and to provide a high degree of freedom of expression. As an example, we present a design that combines simple linear control and control barrier functions. The proposed model is employed for the real-time control of an automotive engine, and the results demonstrate good predictive performance and stable control under constraints.

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