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Kenji Kashima

Kenji Kashima appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.OCeess.SYSystems and ControlMachine Learningquant-phRoboticscond-mat.stat-mechmath.NANumerical Analysis

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Published work

12 published item(s)

preprint2026arXiv

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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preprint2026arXiv

Mutual Information Optimal Density Control of Linear Systems and Generalized Schrödinger 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 Schrödinger bridge problem associated with the discrete-time linear system.

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preprint2026arXiv

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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preprint2023arXiv

An LMI Framework for Contraction-based Nonlinear Control Design by Derivatives of Gaussian Process Regression

Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed not on controllers but on their partial derivatives, which makes control design challenging. In this paper, we illustrate this so-called integrability problem can be solved by a non-standard use of Gaussian process regression (GPR) for parameterizing controllers and then establish an LMI framework of contraction-based control design for nonlinear discrete-time systems, as an easy-to-implement tool. Later on, we consider the case where the drift vector fields are unknown and employ GPR for functional fitting as its standard use. GPR describes learning errors in terms of probability, and thus we further discuss how to incorporate stochastic learning errors into the proposed LMI framework.

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preprint2023arXiv

Entropic Model Predictive Optimal Transport over Dynamical Systems

We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational cost. In this paper, by using entropy regularization, we propose Sinkhorn MPC, which is a dynamical transport algorithm integrating model predictive control (MPC) and the so-called Sinkhorn algorithm. The notable feature of the proposed method is that it achieves cost-effective transport in real time by performing control and transport planning simultaneously, which is illustrated in numerical examples. Moreover, under some assumption on iterations of the Sinkhorn algorithm integrated in MPC, we reveal the global convergence property for Sinkhorn MPC thanks to the entropy regularization. Furthermore, focusing on a quadratic control cost, without the aforementioned assumption we show the ultimate boundedness and the local asymptotic stability for Sinkhorn MPC.

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preprint2022arXiv

Kullback-Leibler control for discrete-time nonlinear systems on continuous spaces

Kullback-Leibler (KL) control enables efficient numerical methods for nonlinear optimal control problems. The crucial assumption of KL control is the full controllability of the transition distribution. However, this assumption is often violated when the dynamics evolves in a continuous space. Consequently, applying KL control to problems with continuous spaces requires some approximation, which leads to the lost of the optimality. To avoid such approximation, in this paper, we reformulate the KL control problem for continuous spaces so that it does not require unrealistic assumptions. The key difference between the original and reformulated KL control is that the former measures the control effort by KL divergence between controlled and uncontrolled transition distributions while the latter replaces the uncontrolled transition by a noise-driven transition. We show that the reformulated KL control admits efficient numerical algorithms like the original one without unreasonable assumptions. Specifically, the associated value function can be computed by using a Monte Carlo method based on its path integral representation.

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preprint2022arXiv

Learning Stabilizable Deep Dynamics Models

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global exponential stability using neural networks. In this paper, we propose a new method for learning the dynamics of input-affine control systems. An important feature is that a stabilizing controller and control Lyapunov function of the learned model are obtained as well. Moreover, the proposed method can also be applied to solving Hamilton-Jacobi inequalities. The usefulness of the proposed method is examined through numerical examples.

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preprint2022arXiv

Matrix Pontryagin principle approach to controllability metrics maximization under sparsity constraints

Controllability maximization problem under sparsity constraints is a node selection problem that selects inputs that are effective for control in order to minimize the energy to control for desired state. In this paper we discuss the equivalence between the sparsity constrained controllability metrics maximization problems and their convex relaxation. The proof is based on the matrix-valued Pontryagin maximum principle applied to the controllability Lyapunov differential equation.

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preprint2022arXiv

Sinkhorn MPC: Model predictive optimal transport over dynamical systems

We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over a dynamical system, which is challenging due to its high computational cost. In this paper, we propose Sinkhorn MPC, which is a dynamical transport algorithm combining model predictive control and the so-called Sinkhorn algorithm. The notable feature of the proposed method is that it achieves cost-effective transport in real time by performing control and transport planning simultaneously. In particular, for linear systems with an energy cost, we reveal the fundamental properties of Sinkhorn MPC such as ultimate boundedness and asymptotic stability.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics

Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics.

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preprint2008arXiv

Control of Quantum Systems Despite Feedback Delay

Feedback control (based on the quantum continuous measurement) of quantum systems inevitably suffers from estimation delays. In this paper we give a delay-dependent stability criterion for a wide class of nonlinear stochastic systems including quantum spin systems. We utilize a semi-algebraic problem approach to incorporate the structure of density matrices. To show the effectiveness of the result, we derive a globally stabilizing control law for a quantum spin-1/2 systems in the face of feedback delays.

0 citations0 reviewsNo code linkedOpen access
preprint2008arXiv

Effects of time delay in feedback control of linear quantum systems

We investigate feedback control of linear quantum systems subject to feedback-loop time delays. In particular, we examine the relation between the potentially achievable control performance and the time delays, and provide theoretical guidelines for the future experimental setup in two physical systems, which are typical in this research field. The evaluation criterion for the analysis is given by the optimal control performance formula, the derivation of which is from the classical control theoretic results about the input-output delay systems.

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