arXiv subjects

Hiroyasu Tsukamoto

Publications and source records attributed to Hiroyasu Tsukamoto.

At least 19 recordsLinked to original sources

arXiv2026

Conformal Koopman for Embedded Nonlinear Control with Statistical Robustness: Theory and Real-World Validation

We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers distribution-free probabilistic bounds on the state tracking error under Koopman modeling uncertainty. Conformal prediction is employed here to rigorously derive a bound on the state-dependent modeling uncertainty throughout the trajectory, ensuring safety and robustness without assuming a specific error prediction structure or distribution. Unlike prior approaches that merely combine conformal prediction with Koopman-based control in an open-loop setting, our method establishes a closed-loop control architecture with formal guarantees that explicitly account for both forward and inverse modeling errors. Also, by expressing the tracking error bound in terms of the control parameters and the modeling errors, our framework offers a quantitative means to formally enhance the performance of arbitrary Koopman-based control. We validate our method both in numerical simulations with the Dubins car and in real-world experiments with a highly nonlinear flapping-wing drone. The results demonstrate that our method indeed provides formal safety guarantees while maintaining accurate tracking performance under Koopman modeling uncertainty.

cs.RO↗

arXiv2026

Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview

Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results in a necessary and sufficient characterization of incremental exponential stability of multiple solution trajectories with respect to each other. By using a squared differential length as a Lyapunov-like function, its nonlinear stability analysis boils down to finding a suitable contraction metric that satisfies a stability condition expressed as a linear matrix inequality, indicating that many parallels can be drawn between well-known linear systems theory and contraction theory for nonlinear systems. Furthermore, contraction theory takes advantage of a superior robustness property of exponential stability used in conjunction with the comparison lemma. This yields much-needed safety and stability guarantees for neural network-based control and estimation schemes, without resorting to a more involved method of using uniform asymptotic stability for input-to-state stability. Such distinctive features permit the systematic construction of a contraction metric via convex optimization, thereby obtaining an explicit exponential bound on the distance between a time-varying target trajectory and solution trajectories perturbed externally due to disturbances and learning errors. The objective of this paper is, therefore, to present a tutorial overview of contraction theory and its advantages in nonlinear stability analysis of deterministic and stochastic systems, with an emphasis on deriving formal robustness and stability guarantees for various learning-based and data-driven automatic control methods. In particular, we provide a detailed review of techniques for finding contraction metrics and associated control and estimation laws using deep neural networks.

cs.LG↗

arXiv2026

Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems

This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework employs conformal inference to generate coverage-based confidence sets for the closed-loop dynamics around arbitrary reference trajectories, by constructing a joint nonconformity score to quantify both the validity of contraction (i.e., incremental stability) conditions and the impact of external stochastic disturbance on the closed-loop dynamics, without any distributional assumptions. Via appropriate constraint tightening, chance constraints can be reformulated into tractable, statistically valid deterministic constraints on the reference trajectories. This enables a formal pathway to leverage and validate learning-based motion planners and controllers, such as those with neural contraction metrics, in safety-critical real-world applications. Notably, our statistical guarantees are non-diverging and can be computed with finite samples of the underlying uncertainty, without overly conservative structural priors. We demonstrate our approach in motion planning problems for designing safe, dynamically feasible trajectories in both numerical simulation and hardware experiments.

eess.SY↗

arXiv2026

SCoUT: Scalable Communication via Utility-Guided Temporal Grouping in Multi-Agent Reinforcement Learning

Communication can improve coordination in partially observed multi-agent reinforcement learning (MARL), but learning \emph{when} and \emph{who} to communicate with requires choosing among many possible sender-recipient pairs, and the effect of any single message on future reward is hard to isolate. We introduce \textbf{SCoUT} (\textbf{S}calable \textbf{Co}mmunication via \textbf{U}tility-guided \textbf{T}emporal grouping), which addresses both these challenges via temporal and agent abstraction within traditional MARL. During training, SCoUT resamples \textit{soft} agent groups every $K$ environment steps (macro-steps) via Gumbel-Softmax; these groups are latent clusters that induce an affinity used as a differentiable prior over recipients. Using the same assignments, a group-aware critic predicts values for each agent group and maps them to per-agent baselines through the same soft assignments, reducing critic complexity and variance. Each agent is trained with a three-headed policy: environment action, send decision, and recipient selection. To obtain precise communication learning signals, we derive counterfactual communication advantages by analytically removing each sender's contribution from the recipient's aggregated messages. This counterfactual computation enables precise credit assignment for both send and recipient-selection decisions. At execution time, all centralized training components are discarded and only the per-agent policy is run, preserving decentralized execution. Project website, videos and code: \hyperlink{https://scout-comm.github.io/}{https://scout-comm.github.io/}

cs.MA↗

arXiv2025

Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects

Interstellar objects (ISOs) are likely representatives of primitive materials invaluable in understanding exoplanetary star systems. Due to their poorly constrained orbits with generally high inclinations and relative velocities, however, exploring ISOs with conventional human-in-the-loop approaches is significantly challenging. This paper presents Neural-Rendezvous -- a deep learning-based guidance and control framework for encountering fast-moving objects, including ISOs, robustly, accurately, and autonomously in real time. It uses pointwise minimum norm tracking control on top of a guidance policy modeled by a spectrally-normalized deep neural network, where its hyperparameters are tuned with a loss function directly penalizing the MPC state trajectory tracking error. We show that Neural-Rendezvous provides a high probability exponential bound on the expected spacecraft delivery error, the proof of which leverages stochastic incremental stability analysis. In particular, it is used to construct a non-negative function with a supermartingale property, explicitly accounting for the ISO state uncertainty and the local nature of nonlinear state estimation guarantees. In numerical simulations, Neural-Rendezvous is demonstrated to satisfy the expected error bound for 100 ISO candidates. This performance is also empirically validated using our spacecraft simulator and in high-conflict and distributed UAV swarm reconfiguration with up to 20 UAVs.

cs.RO↗

arXiv2025

Conformal Contraction for Robust Nonlinear Control with Distribution-Free Uncertainty Quantification

We present a novel robust control framework for continuous-time, perturbed nonlinear dynamical systems with uncertainty that depends nonlinearly on both the state and control inputs. Unlike conventional approaches that impose structural assumptions on the uncertainty, our framework enhances contraction-based robust control with data-driven uncertainty prediction, remaining agnostic to the models of the uncertainty and predictor. We statistically quantify how reliably the contraction conditions are satisfied under dynamics with uncertainty via conformal prediction, thereby obtaining a distribution-free and finite-time probabilistic guarantee for exponential boundedness of the trajectory tracking error. We further propose the probabilistically robust control invariant (PRCI) tube for distributionally robust motion planning, within which the perturbed system trajectories are guaranteed to stay with a finite probability, without explicit knowledge of the uncertainty model. Numerical simulations validate the effectiveness of the proposed robust control framework and the performance of the PRCI tube.

math.OC↗

arXiv2025

Statistical Guarantees in Data-Driven Nonlinear Control: Conformal Robustness for Stability and Safety

We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal robustness, which robustifies the Lyapunov and zeroing barrier certificates of data-driven dynamical systems against model prediction uncertainties using conformal prediction. It quantifies these uncertainties by leveraging rank statistics of prediction scores over system trajectories, without assuming any specific underlying structure of the prediction model or distribution of the uncertainties. With the quantified uncertainty information, we further construct the conformally robust control Lyapunov function (CR-CLF) and control barrier function (CR-CBF), data-driven counterparts of the CLF and CBF, for fully data-driven control with statistical guarantees of finite-horizon exponential stability and safety. The performance of the proposed concept is validated in numerical simulations with four benchmark nonlinear control problems.

eess.SY↗

arXiv2025

Contraction-Aware Reinforcement Learning for Nonlinear Control with Statistical Robustness

Control contraction metrics (CCMs)-defined by Riemannian metrics under which a closed-loop system is incrementally exponentially stable-offer a constructive framework for synthesizing contracting policies in nonlinear path-tracking problems. However, while the synthesized policies ensure pointwise satisfaction of the CCM conditions, they may not ensure long-term optimality (i.e., minimizing cumulative trajectory-level tracking error) over both transient and steady-state regimes. Furthermore, the myopic nature of these policies could also make them more susceptible to learning biases when approximate dynamics are used to formulate CCMs. To address these issues, we propose to integrate CCMs into reinforcement learning (RL). CCMs provide dynamics-informed feedback for learning a policy that has a stability guarantee-i.e., is contraction-aware-while RL provides a framework for minimizing cumulative tracking error under approximate dynamics. Given a pretrained dynamics model, our algorithm, contraction-aware RL (CARL), simultaneously learns to generate CCMs and optimize a policy for rewards defined by those CCMs. We demonstrate that CARL enhances path-tracking performance and is robust to errors in approximated dynamics compared to relevant baselines in both simulated and real-world robot experiments. We also provide theoretical rationale for integrating CCMs into RL. Our code is available at https://github.com/Mgineer117/CARL, and a video of our real-world robot experiments can be found at https://youtu.be/sOJ4hulbop0.

cs.LG↗

arXiv2024

Information-Optimal Multi-Spacecraft Positioning for Interstellar Object Exploration

Interstellar objects (ISOs), astronomical objects not gravitationally bound to the sun, could present valuable opportunities to advance our understanding of the universe's formation and composition. In response to the unpredictable nature of their discoveries that inherently come with large and rapidly changing uncertainty in their state, this paper proposes a novel multi-spacecraft framework for locally maximizing information to be gained through ISO encounters with formal probabilistic guarantees. Given some approximated control and estimation policies for fully autonomous spacecraft operations, we first construct an ellipsoid around its terminal position, where the ISO would be located with a finite probability. The large state uncertainty of the ISO is formally handled here through the hierarchical property in stochastically contracting nonlinear systems. We then propose a method to find the terminal positions of the multiple spacecraft optimally distributed around the ellipsoid, which locally maximizes the information we can get from all the points of interest (POIs). This utilizes a probabilistic information cost function that accounts for spacecraft positions, camera specifications, and ISO position uncertainty, where the information is defined as visual data collected by cameras. Numerical simulations demonstrate the efficacy of this approach using synthetic ISO candidates generated from quasi-realistic empirical populations. Our method allows each spacecraft to optimally select its terminal state and determine the ideal number of POIs to investigate, potentially enhancing the ability to study these rare and fleeting interstellar visitors while minimizing resource utilization.

eess.SY↗

arXiv2024

Interstellar Object Accessibility and Mission Design

Interstellar objects (ISOs) represent a compelling and under-explored category of celestial bodies, providing physical laboratories to understand the formation of our solar system and probe the composition and properties of material formed in exoplanetary systems. In this work, we investigate existing approaches to designing successful flyby missions to ISOs, including a deep learning-driven guidance and control algorithm for ISOs traveling at velocities over 60 km/s. We have generated spacecraft trajectories to a series of synthetic representative ISOs, simulating a ground campaign to observe the target and resolve its state, thereby determining the cruise and close approach delta-Vs required for the encounter. We discuss the accessibility of and mission design to ISOs with varying characteristics, with special focuses on 1) state covariance estimation throughout the cruise, 2) handoffs from traditional navigation approaches to novel autonomous navigation for fast flyby regimes, and 3) overall recommendations about preparing for the future in situ exploration of these targets. The lessons learned also apply to the fast flyby of other small bodies, e.g., long-period comets and potentially hazardous asteroids, which also require tactical responses with similar characteristics.

astro-ph.EP↗

arXiv2024

Robust Optimal Network Topology Switching for Zero Dynamics Attacks

The intrinsic, sampling, and enforced zero dynamics attacks (ZDAs) are among the most detrimental stealthy attacks in robotics, aerospace, and cyber-physical systems. They exploit internal dynamics, discretization, redundancy/asynchronous actuation and sensing, to construct disruptive attacks that are completely stealthy in the measurement. They work even when the systems are both controllable and observable. This paper presents a novel framework to robustly and optimally detect and mitigate ZDAs for networked linear control systems. We utilize controllability, observability, robustness, and sensitivity metrics written explicitly in terms of the system topology, thereby proposing a robust and optimal switching topology formulation for resilient ZDA detection and mitigation. Our main contribution is the reformulation of this problem into an equivalent rank-constrained optimization problem (i.e., optimization with a convex objective function subject to convex constraints and rank constraints), which can be solved using convex rank minimization approaches. The effectiveness of our method is demonstrated using networked double integrators subject to ZDAs.

eess.SY↗

arXiv2024

Regret-Optimal Defense Against Stealthy Adversaries: A System Level Approach

Modern control designs in robotics, aerospace, and cyber-physical systems rely heavily on real-world data obtained through system outputs. However, these outputs can be compromised by system faults and malicious attacks, distorting critical system information needed for secure and reliable operation. In this paper, we introduce a novel regret-optimal control framework for designing controllers that make a linear system robust against stealthy attacks, including both sensor and actuator attacks. Specifically, we present (a) a convex optimization-based system metric to quantify the regret under the worst-case stealthy attack (the difference between actual performance and optimal performance with hindsight of the attack), which adapts and improves upon the $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ norms in the presence of stealthy adversaries, (b) an optimization problem for minimizing the regret of (a) in system-level parameterization, enabling localized and distributed implementation in large-scale systems, and (c) a rank-constrained optimization problem equivalent to the optimization of (b), which can be solved using convex rank minimization methods. We also present numerical simulations that demonstrate the effectiveness of our proposed framework.

eess.SY↗

arXiv2023

CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systems

The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the analytical form of our CaRT safety filter formally ensures safe maneuvers of nonlinear multi-agent systems, optimally with minimal deviation from the learning-based policy. Second, in off-nominal settings, the analytical form of our CaRT robust filter optimally tracks the certified safe trajectory, generated by the previous layer in the hierarchy, the CaRT safety filter. We show using contraction theory that CaRT guarantees safety and the exponential boundedness of the trajectory tracking error, even under the presence of deterministic and stochastic disturbance. Also, the hierarchical nature of CaRT enables enhancing its robustness for safety just by its superior tracking to the certified safe trajectory, thereby making it suitable for off-nominal scenarios with large disturbances. This is a major distinction from conventional safety function-driven approaches, where the robustness originates from the stability of a safe set, which could pull the system over-conservatively to the interior of the safe set. Our log-barrier formulation in CaRT allows for its distributed implementation in multi-agent settings. We demonstrate the effectiveness of CaRT in several examples of nonlinear motion planning and control problems, including optimal, multi-spacecraft reconfiguration.

cs.RO↗

arXiv2021

Learning-based Adaptive Control using Contraction Theory

Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametrization, called adaptive Neural Contraction Metric (aNCM). The aNCM approximates real-time optimization for computing a differential Lyapunov function and a corresponding stabilizing adaptive control law by using a Deep Neural Network (DNN). The use of DNNs permits real-time implementation of the control law and broad applicability to a variety of nonlinear systems with parametric and nonparametric uncertainties. We show using contraction theory that the aNCM ensures exponential boundedness of the distance between the target and controlled trajectories in the presence of parametric uncertainties of the model, learning errors caused by aNCM approximation, and external disturbances. Its superiority to the existing robust and adaptive control methods is demonstrated using a cart-pole balancing model.

cs.LG↗

arXiv2021

A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability

This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient condition for incremental exponential stability of non-autonomous nonlinear system trajectories. Its innovation lies in providing formal robustness guarantees for learning-based control frameworks, utilizing contraction theory as an analytical tool to study the nonlinear stability of learned systems via convex optimization. In particular, we rigorously show in this paper that, by regarding modeling errors of the learning schemes as external disturbances, the NCM control is capable of obtaining an explicit bound on the distance between a time-varying target trajectory and perturbed solution trajectories, which exponentially decreases with time even under the presence of deterministic and stochastic perturbation. These useful features permit simultaneous synthesis of a contraction metric and associated control law by a neural network, thereby enabling real-time computable and probably robust learning-based control for general control-affine nonlinear systems.

cs.LG↗

arXiv2021

Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach

This paper presents Learning-based Autonomous Guidance with RObustness and Stability guarantees (LAG-ROS), which provides machine learning-based nonlinear motion planners with formal robustness and stability guarantees, by designing a differential Lyapunov function using contraction theory. LAG-ROS utilizes a neural network to model a robust tracking controller independently of a target trajectory, for which we show that the Euclidean distance between the target and controlled trajectories is exponentially bounded linearly in the learning error, even under the existence of bounded external disturbances. We also present a convex optimization approach that minimizes the steady-state bound of the tracking error to construct the robust control law for neural network training. In numerical simulations, it is demonstrated that the proposed method indeed possesses superior properties of robustness and nonlinear stability resulting from contraction theory, whilst retaining the computational efficiency of existing learning-based motion planners.

cs.RO↗

arXiv2021

Neural Stochastic Contraction Metrics for Learning-based Control and Estimation

We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The NSCM framework allows autonomous agents to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic neural contraction metric, as illustrated in simulation results.

cs.LG↗

arXiv2020

Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is non-convex, its equivalent convex formulation is proposed utilizing state-dependent coefficient parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L2-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H-infinity, and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.

eess.SY↗