arXiv subjects

Kaito Ito

Publications and source records attributed to Kaito Ito.

14 recordsLinked to original sources

arXiv2026

Distribution Steering via Sliced Optimal Transport Control

Distribution steering seeks feedback laws that drive the state law of a dynamical system between prescribed initial and terminal distributions. Optimal transport provides a natural geometric approach, but its implementation generally requires a transport map or coupling in the full state space. Sliced optimal transport avoids this full-dimensional construction through one-dimensional projections. Yet, the resulting projected maps specify only directional displacements and do not by themselves prescribe a realizable feedback law. To this end, we develop a finite-horizon control framework based on sliced optimal transport. At each sampling instant, a projected optimal transport map defines a directional terminal condition, whose minimum-energy realization yields a randomized single-direction controller. Averaging over projection directions gives a deterministic sliced feedback. For the single-integrator dynamics, the averaged feedback makes the sliced Wasserstein distance to the target non-increasing. For Gaussian endpoint laws, it is affine, preserves Gaussianity, and steers the mean and covariance to their prescribed terminal values. We further identify a law-dependent gain that yields linear decay of the sliced Wasserstein distance together with an explicit characterization of the control energy. We also prove that the randomized controller converges to the averaged sliced flow as the sampling period vanishes. Finally, we extend the construction to linear dynamical systems. Reachability-normalized coordinates allow instantaneous realization of the sliced velocity for uniformly fully actuated systems, while local controllability Gramians provide exact finite-step realization for general controllable systems. Numerical examples illustrate the resulting distributional flows.

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arXiv2026

Distribution Control of Stochastic Oscillators via Periodic Feedforward and Population-Level Feedback

We address the problem of steering the phase distribution of oscillators all receiving the same control input to a given target distribution. In a large population limit, the distribution of oscillators can be described by a probability density. Thus, we formulate the problem as distribution control over a Fokker--Planck equation. In particular, we consider the case where oscillators are subject to stochastic noise, for which the theoretical understanding is still lacking. First, we characterize the asymptotic reachability of the phase distribution under periodic feedforward control via the Fourier coefficients of the target density and the phase sensitivity function of oscillators. This enables us to design a periodic input that makes the stationary distribution of oscillators closest to the target by solving a convex optimization problem. Next, we devise a distribution controller combining periodic and population-level feedback control, where the feedback component is designed to accelerate the convergence of the distribution of oscillators. We exhibit some convergence results for the proposed method, including a result that holds even under measurement errors in the phase distribution. The effectiveness of the proposed method is demonstrated by a numerical example.

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arXiv2026

Sliced Wasserstein Steering between Gaussian Measures

Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in practice often reveals only linear views of the state -- camera silhouettes, LiDAR beams, tomographic slices. We develop a sliced feedback controller for distribution steering: the evolving law is projected onto one-dimensional directions on the sphere, the optimal one-dimensional velocity is synthesized in each projection, and these velocities are averaged to produce a feedback control in the ambient space. The construction reduces to the Benamou--Brenier problem in one dimension. In addition, it is invariant under orthogonal transforms, nonexpansive under projections, and well posed on $\mathcal{P}_2(\mathbb{R}^n)$. Computation proceeds by sampling directions on the sphere and solving independent one-dimensional subproblems, yielding a scalable method aligned with partial observations. In the Gaussian setting, we show that the developed sliced controller steers the law to the prescribed target. Furthermore, we derive an identity relating the energy consumption incurred by the controller to the sliced Wasserstein distance.

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arXiv2026

Optimal Centered Active Excitation in Linear System Identification

We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.

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arXiv2025

Online Control of Linear Systems under Unbounded Noise

This paper investigates the problem of controlling a linear system under possibly unbounded stochastic noise with unknown convex cost functions, known as an online control problem. In contrast to the existing work, which assumes the boundedness of noise, we show that an $ \tilde{O}(\sqrt{T}) $ high-probability regret can be achieved under unbounded noise, where $ T $ denotes the time horizon. Notably, the noise is only required to have a finite fourth moment. Moreover, when the costs are strongly convex and the noise is sub-Gaussian, we establish an $ O({\rm poly} (\log T)) $ regret bound.

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arXiv2024

Maximum Entropy Density Control of Discrete-Time Linear Systems with Quadratic Cost

This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy density control problem. Specifically, the running cost is given by quadratic forms of the state and the control input, and the initial and target distributions are Gaussian. We first reveal that our problem boils down to solving two Riccati difference equations coupled through their boundary values. Based on them, we give the closed-form expression of the unique optimal policy. Next, we show that the optimal density control of a backward system can be obtained simultaneously with the forward-time optimal policy. The backward solution gives another expression of the forward solution. Finally, by considering the limit where the entropy regularization vanishes, we derive the unregularized density control in closed form.

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arXiv2024

Risk-sensitive control as inference with Rényi divergence

This paper introduces the risk-sensitive control as inference (RCaI) that extends CaI by using Rényi 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 Rényi 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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arXiv2023

Entropic Model Predictive Optimal Transport for Underactuated Linear Systems

This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform efficient dynamical transport of agents. However, the proposed method requires the invertibility of input matrices, which severely limits its applicability. To resolve this issue, we extend the method to (possibly underactuated) controllable linear systems. In addition, we ensure the convergence properties of the method for general controllable linear systems. The effectiveness of the proposed method is demonstrated by a numerical example.

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arXiv2023

Maximum entropy optimal density control of discrete-time linear systems and Schrödinger bridges

We consider an entropy-regularized version of optimal density control of deterministic discrete-time linear systems. Entropy regularization, or a maximum entropy (MaxEnt) method for optimal control has attracted much attention especially in reinforcement learning due to its many advantages such as a natural exploration strategy. Despite the merits, high-entropy control policies induced by the regularization introduce probabilistic uncertainty into systems, which severely limits the applicability of MaxEnt optimal control to safety-critical systems. To remedy this situation, we impose a Gaussian density constraint at a specified time on the MaxEnt optimal control to directly control state uncertainty. Specifically, we derive the explicit form of the MaxEnt optimal density control. In addition, we also consider the case where density constraints are replaced by fixed point constraints. Then, we characterize the associated state process as a pinned process, which is a generalization of the Brownian bridge to linear systems. Finally, we reveal that the MaxEnt optimal density control gives the so-called Schrödinger bridge associated to a discrete-time linear system.

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arXiv2023

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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arXiv2022

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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arXiv2022

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.

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arXiv2021

Sparse optimal stochastic control

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the $L^0$ optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with $L^1$ optimal control problem and show an equivalence theorem.

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arXiv2021

Bayesian Differential Privacy for Linear Dynamical Systems

Differential privacy is a privacy measure based on the difficulty of discriminating between similar input data. In differential privacy analysis, similar data usually implies that their distance does not exceed a predetermined threshold. It, consequently, does not take into account the difficulty of distinguishing data sets that are far apart, which often contain highly private information. This problem has been pointed out in the research on differential privacy for static data, and Bayesian differential privacy has been proposed, which provides a privacy protection level even for outlier data by utilizing the prior distribution of the data. In this study, we introduce this Bayesian differential privacy to dynamical systems, and provide privacy guarantees for distant input data pairs and reveal its fundamental property. For example, we design a mechanism that satisfies the desired level of privacy protection, which characterizes the trade-off between privacy and information utility.

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