arXiv subjects

Chi Ho Leung

Publications and source records attributed to Chi Ho Leung.

8 recordsLinked to original sources

arXiv2026

Bayesian Safety Guarantees for Port-Hamiltonian Systems with Learned Energy Functions

Control barrier functions for port-Hamiltonian systems inherit model uncertainty when the Hamiltonian is learned from data. We show how to propagate this uncertainty into a safety filter with independently tunable credibility budgets. To propagate this uncertainty, we employ a two-stage Bayesian approach. First, posterior prediction over the Hamiltonian yields credible bands for the energy storage, producing Bayesian barriers whose safe sets are high-probability inner approximations of the true allowable set with credibility $1 - (η_{\mathrm{ptB}})$. Independently, a drift credible ellipsoid accounts for vector field uncertainty in the CBF inequality with credibility $1 - (η_{\rm dr})$. Since energy and drift uncertainties enter through disjoint credible sets, the end-to-end safety guarantee is at least $1 - (η_{\rm dr} + η_{\mathrm{ptB}})$. Experiments on a mass-spring oscillator with a GP-learned Hamiltonian show that the proposed filter preserves safety despite limited and noisy observations.

eess.SY↗

arXiv2026

Port-Transversal Barriers: Graph-Theoretic Safety for Port-Hamiltonian Systems

Synthesizing control barrier functions (CBFs) for complex nonlinear systems remains difficult, particularly when safety constraints have high relative degree with respect to the input. In this work, we study the class of composite port-Hamiltonian systems as a network of interconnected subsystems, and this network admits a natural graph structure. We propose a novel graph-theoretic framework for the CBF synthesis problem. The framework addresses the problem of CBF construction for complex nonlinear systems by offering a relative-degree constraint induced by graph distance and a barrier reshaping rule informed by the graph topology. Furthermore, we perform a feasibility analysis of the reshaped barrier under a bounded input constraint and identify the sufficient conditions for feasibility. Lastly, the proposed framework is validated on an LC ladder network, where the CBF feasibility on a capacitor charge constraint depends on where the input enters the network.

eess.SY↗

arXiv2026

Spectral Flow Learning Theory: Finite-Sample Guarantees for Vector-Field Identification

We study the identification of continuous-time vector fields from irregularly sampled trajectories. We introduce spectral flow learning, which learns in a windowed flow space using a lag-linear label operator that aggregates lagged Koopman actions. We provide finite-sample, high-probability (FS-HP) guarantees for the class of variable-step linear multistep methods (vLMM). The FS-HP rates are constructed using spectral regularization with qualification-controlled filters for flow predictors under standard source and filter assumptions. A multistep observability inequality links flow error to vector-field error and yields two-term bounds that combine a statistical rate with an explicit discretization bias from vLMM theory. Simulations on a controlled mass-spring system corroborate the theory and clarify conditioning, step-sample tradeoffs, and practical implications.

eess.SY↗

arXiv2025

Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes

We propose the multistep port-Hamiltonian Gaussian process (MS-PHS GP) to learn physically consistent continuous-time dynamics and a posterior over the Hamiltonian from noisy, irregularly-sampled trajectories. By placing a GP prior on the Hamiltonian surface $H$ and encoding variable-step multistep integrator constraints as finite linear functionals, MS-PHS GP enables closed-form conditioning of both the vector field and the Hamiltonian surface without latent states, while enforcing energy balance and passivity by design. We state a finite-sample vector-field bound that separates the estimation and variable-step discretization terms. Lastly, we demonstrate improved vector-field recovery and well-calibrated Hamiltonian uncertainty on mass-spring, Van der Pol, and Duffing benchmarks.

cs.LG↗

arXiv2025

Online Identification of Time-Varying Systems Using Excitation Sets and Change Point Detection

In this work, we first show that the problem of parameter identification is often ill-conditioned and lacks the persistence of excitation required for the convergence of online learning schemes. To tackle these challenges, we introduce the notion of optimal and greedy excitation sets which contain data points with sufficient richness to aid in the identification task. We then present the greedy excitation set-based recursive least squares algorithm to alleviate the problem of the lack of persistent excitation, and prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. When data points are generated from time-varying parameters, online estimators tend to underfit the true parameter trajectory, and their predictability deteriorates. To tackle this problem, we propose a memory resetting scheme leveraging change point detection techniques. Finally, we illustrate the performance of the proposed algorithms via several numerical case studies to learn the (time-varying) parameters of networked epidemic dynamics, and compare it with results obtained using conventional approaches.

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arXiv2024

Collaborative Safety-Critical Formation Control with Obstacle Avoidance

This work explores a collaborative method for ensuring safety in multi-agent formation control problems. We formulate a control barrier function (CBF) based safety filter control law for a generic distributed formation controller and extend our previously developed collaborative safety framework to an obstacle avoidance problem for agents with acceleration control inputs. We then incorporate multi-obstacle collision avoidance into the collaborative safety framework. This framework includes a method for computing the maximum capability of agents to satisfy their individual safety requirements. We analyze the convergence rate of our collaborative safety algorithm, and prove the linear-time convergence of cooperating agents to a jointly feasible safe action for all agents under the special case of a tree-structured communication network with a single obstacle for each agent. We illustrate the analytical results via simulation on a mass-spring kinematics-based formation controller and demonstrate the finite-time convergence of the collaborative safety algorithm in the simple proven case, the more general case of a fully-connected system with multiple static obstacles, and with dynamic obstacles.

cs.RO↗

arXiv2024

Collaborative Safe Formation Control for Coupled Multi-Agent Systems

The safe control of multi-robot swarms is a challenging and active field of research, where common goals include maintaining group cohesion while simultaneously avoiding obstacles and inter-agent collision. Building off our previously developed theory for distributed collaborative safety-critical control for networked dynamic systems, we propose a distributed algorithm for the formation control of robot swarms given individual agent dynamics, induced formation dynamics, and local neighborhood position and velocity information within a defined sensing radius for each agent. Individual safety guarantees for each agent are obtained using rounds of communication between neighbors to restrict unsafe control actions among cooperating agents through safety conditions derived from high-order control barrier functions. We provide conditions under which a swarm is guaranteed to achieve collective safety with respect to multiple obstacles using a modified collaborative safety algorithm. We demonstrate the performance of our distributed algorithm via simulation in a simplified physics-based environment.

math.OC↗

arXiv2023

Adaptive Identification of SIS Models

Effective containment of spreading processes such as epidemics requires accurate knowledge of several key parameters that govern their dynamics. In this work, we first show that the problem of identifying the underlying parameters of epidemiological spreading processes is often ill-conditioned and lacks the persistence of excitation required for the convergence of adaptive learning schemes. To tackle this challenge, we leverage a relaxed property called initial excitation combined with a recursive least squares algorithm to design an online adaptive identifier to learn the parameters of the susceptible-infected-susceptible (SIS) epidemic model from the knowledge of its states. We prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. We illustrate the convergence of the error of the estimated epidemic parameters via several numerical case studies and compare it with results obtained using conventional approaches.

eess.SY↗