arXiv subjects

Yinzhuang Yi

Publications and source records attributed to Yinzhuang Yi.

7 recordsLinked to original sources

arXiv2026

Constrained Variational Inference via Safe Particle Flow

We propose a control barrier function (CBF) formulation for enforcing equality and inequality constraints in variational inference. The key idea is to define a barrier functional on the space of probability density functions that encode the desired constraints imposed on the variational density. By leveraging the Liouville equation, we establish a connection between the time derivative of the variational density and the particle drift, which enables the systematic construction of corresponding CBFs associated to the particle drift. Enforcing these CBFs gives rise to the safe particle flow and ensures that the variational density satisfies the original constraints imposed by the barrier functional. This formulation provides a principled and computationally tractable solution to constrained variational inference, with theoretical guarantees of constraint satisfaction. The effectiveness of the method is demonstrated through numerical simulations.

math.OC↗

arXiv2026

Variational Formulation of Particle Flow

This paper provides a formulation of the log-homotopy particle flow from the perspective of variational inference. We show that the transient density used to derive the particle flow follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density. When considering a parametric family of variational densities, the function space Fisher-Rao gradient flow simplifies to the natural gradient flow of the variational density parameters. By adopting a Gaussian variational density, we derive a Gaussian approximated Fisher-Rao particle flow and show that, under linear Gaussian assumptions, it reduces to the Exact Daum and Huang particle flow. Additionally, we introduce a Gaussian mixture approximated Fisher-Rao particle flow to enhance the expressive power of our model through a multi-modal variational density. Simulations on low- and high-dimensional estimation problems illustrate our results.

stat.ML↗

arXiv2025

EAST: Environment Aware Safe Tracking using Planning and Control Co-Design

This paper considers the problem of autonomous mobile robot navigation in unknown environments with moving obstacles. We propose a new method to achieve environment-aware safe tracking (EAST) of robot motion plans that integrates an obstacle clearance cost for path planning, a convex reachable set for robot motion prediction, and safety constraints for dynamic obstacle avoidance. EAST adapts the motion of the robot according to the locally sensed environment geometry and dynamics, leading to fast motion in wide open areas and cautious behavior in narrow passages or near moving obstacles. Our control design uses a reference governor, a virtual dynamical system that guides the robot's motion and decouples the path tracking and safety objectives. While reference governor methods have been used for safe tracking control in static environments, our key contribution is an extension to dynamic environments using convex optimization with control barrier function (CBF) constraints. Thus, our work establishes a connection between reference governor techniques and CBF techniques for safe control in dynamic environments. We validate our approach in simulated and real-world environments, featuring complex obstacle configurations and natural dynamic obstacle motion.

cs.RO↗

arXiv2025

Sensor-Based Distributionally Robust Control for Safe Robot Navigation in Dynamic Environments

We introduce a novel method for mobile robot navigation in dynamic, unknown environments, leveraging onboard sensing and distributionally robust optimization to impose probabilistic safety constraints. Our method introduces a distributionally robust control barrier function (DR-CBF) that directly integrates noisy sensor measurements and state estimates to define safety constraints. This approach is applicable to a wide range of control-affine dynamics, generalizable to robots with complex geometries, and capable of operating at real-time control frequencies. Coupled with a control Lyapunov function (CLF) for path following, the proposed CLF-DR-CBF control synthesis method achieves safe, robust, and efficient navigation in challenging environments. We demonstrate the effectiveness and robustness of our approach for safe autonomous navigation under uncertainty in simulations and real-world experiments with differential-drive robots.

cs.RO↗

arXiv2024

Distributionally Robust Lyapunov Function Search Under Uncertainty

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.

math.OC↗

arXiv2023

Safe and Stable Control Synthesis for Uncertain System Models via Distributionally Robust Optimization

This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF), respectively. To take model uncertainty into account, robust and chance formulations of the constraints are commonly considered. However, this requires known error bounds or a known distribution for the model uncertainty, and the resulting formulations may suffer from over-conservatism or over-confidence. In this paper, we assume that only a finite set of model parametric uncertainty samples is available and formulate a distributionally robust chance-constrained program (DRCCP) for control synthesis with CBF safety and CLF stability guarantees. To facilitate efficient computation of control inputs during online execution, we present a reformulation of the DRCCP as a second-order cone program (SOCP). Our formulation is evaluated in an adaptive cruise control example in comparison to 1) a baseline CLF-CBF quadratic programming approach, 2) a robust approach that assumes known error bounds of the system uncertainty, and 3) a chance-constrained approach that assumes a known Gaussian Process distribution of the uncertainty.

math.OC↗

arXiv2022

Control Synthesis for Stability and Safety by Differential Complementarity Problem

This paper develops a novel control synthesis method for safe stabilization of control-affine systems as a Differential Complementarity Problem (DCP). Our design uses a control Lyapunov function (CLF) and a control barrier function (CBF) to define complementarity constraints in the DCP formulation to certify stability and safety, respectively. The CLF-CBF-DCP controller imposes stability as a soft constraint, which is automatically relaxed when the safety constraint is active, without the need for parameter tuning or optimization. We study the closed-loop system behavior with the CLF-CBF-DCP controller and identify conditions on the existence of local equilibria. Although in certain cases the controller yields undesirable local equilibria, those can be confined to a small subset of the safe set boundary by proper choice of the control parameters. Then, our method can avoid undesirable equilibria that CLF-CBF quadratic programming techniques encounter.

math.OC↗