arXiv subjects

Kenji Kashima

Publications and source records attributed to Kenji Kashima.

At least 19 recordsLinked to original sources

arXiv2026

Attack-Aware Intrusion Risk Monitoring for Aerial Surveillance via Probabilistic Signal Temporal Logic

This paper considers online intrusion-risk assessment and graded warning for unmanned aerial vehicles under bounded measurement attacks. To address this problem, we develop a monitoring framework that combines trusted state estimation, attack-aware risk assessment, and probabilistic signal temporal logic (PrSTL). Trusted observations support recursive state estimation, while potentially attacked observations inform integrity testing and intrusion-risk assessment. The key contribution is a confidence-set construction that combines normalized innovation statistics with physical attack bounds to characterize admissible measurement biases. The resulting family of bias-corrected Gaussian posteriors yields an upper bound on the probability of occupying a no-fly zone or its surrounding safety margin. Confidence guarantees and finite-cover numerical certificates quantify the reliability of this risk envelope, which is evaluated with or without an integrity alarm. The PrSTL monitor analyzes the resulting risk sequence to distinguish ordered, persistent, and repeated risk and produces graded warnings with explicit robustness margins and supporting windows. We validate the monitor in flight experiments with a Crazyflie quadrotor tracked by a Vicon motion capture system. Controlled comparisons quantify the contributions of individual monitoring components. Prescribed risk profiles verify the temporal semantics and illustrate how distinct risk patterns produce different warning levels.

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arXiv2026

Control Realization of Schrödinger Bridges over Discrete-Time Nonlinear Systems via Maximum-Entropy Distribution Steering

This paper shows how a Schrodinger bridge (SB) structure emerges from maximum-entropy (MaxEnt) distribution steering of discrete-time nonlinear systems. We also establish that the resulting bridge can be realized by an optimal control policy. We consider general state and input costs, non-Gaussian endpoint distributions, and input constraints. Assuming the existence of a feasible policy with finite objective value, we show that the state-path measure under a MaxEnt optimal control policy is the unique SB. The reference measure of this SB is induced by an optimal policy of the corresponding terminal-unconstrained problem. Moreover, we give an equivalent characterization of the optimal state-path measure using a killed reference and its normalized Feynman--Kac measure, thereby interpreting the state cost as killing. We then characterize the finite-cost feasibility by the existence of an endpoint coupling having finite Kullback--Leibler divergence from the reference endpoint distribution. For compactly supported marginals with bounded target density, we derive reachability-based sufficient conditions guaranteeing this feasibility. We further provide specializations to fully actuated control-affine and reachable linear systems.

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arXiv2026

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

This paper proposes a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. Control inputs and risk allocation are jointly optimized under general, possibly non-Gaussian, uncertainties through sufficient deterministic conditions for probabilistic constraint satisfaction. A decreasing risk regularizer ensures existence and full use of the allowable risk. Under the stated regularity assumptions, the joint solution is unique and locally Lipschitz-continuous, supporting stable numerical optimization. The formulation is extended to learning-based exactly linearizable (EL) models through monotone state and input transformations. A hybrid powertrain example compares deterministic control, equal risk allocation, and optimized risk allocation with and without regularization in terms of charge sustaining, constraint violations, closed-loop cost, and solver time.

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arXiv2026

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

We consider a mutual information (MI) regularized optimal density control of a discrete-time linear system. MI optimal control has been utilized for exploration in reinforcement learning and privacy protection in control. 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 investigate its convergence properties. In addition, we reveal a relationship between the MI optimal density control problem and a so-called generalized Schrödinger bridge problem associated with the discrete-time linear system. Based on the results of MI optimal density control and this relationship, we also investigate alternating optimization for the Schrödinger bridge problem and its convergence properties.

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arXiv2026

Tsallis Entropy Regularization for Linear Quadratic Regulator and Kullback-Leibler Control

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. The aim of this paper is to show that formulations based on Tsallis entropy, which is a one-parameter extension of Shannon entropy, retain many of the structural and computational advantages of Shannon-entropy-based approaches while offering additional benefits. In particular, we derive a closed-form solution for the linear quadratic regulator and an efficient computational method for the Kullback-Leibler control problem. We also demonstrate its usefulness in balancing between exploration and sparsity of the obtained control law.

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arXiv2026

On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems

Mutual information regularization has recently been studied in reinforcement learning (RL) as an extension of entropy regularization, in which not only the policy but also the reference distribution (prior) is optimized, and has also been used for privacy preserving policy design. To obtain theoretical insight into how this joint optimization affects policy stochasticity, we study a model-based linear-quadratic setting that preserves this key structure while permitting an explicit analysis. Specifically, we consider a mutual information optimal control problem (MIOCP) for stochastic discrete-time linear systems with quadratic costs and Gaussian policies and priors. We first review alternating optimization of the policy and the prior with a technical extension. We then establish the existence of an optimal solution, characterize its covariance matrices, and derive sufficient conditions under which the optimal policy is either a stochastic feedback policy or a deterministic open-loop policy. We further interpret this characterization in terms of the state information disclosed through the control input. We also analyze the limiting behavior of alternating optimization under the sufficient conditions. The validity of the theoretical results is demonstrated through numerical experiments.

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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

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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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

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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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

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

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

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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arXiv2025

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 $μ$s in a standard laptop, not only ensures stability with considering sampled-data implementation but also effectively enhances control performance.

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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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arXiv2025

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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