probabilistic-cbf-subgaussian

name: probabilistic-cbf-subgaussian description: Probabilistic Control Barrier Functions for safety-critical systems with state estimation uncertainty using sub-Gaussian concentration. Provides finite-sample safety certificates via particle-based CVaR estimation. Use for spacecraft proximity operations, safety-critical control under uncertainty, and formal safety guarantees with probabilistic constraints.

Probabilistic Control Barrier Functions with Sub-Gaussian Concentration

This skill implements a particle-based probabilistic Control Barrier Function (CBF) framework for safety-critical systems with state estimation uncertainty, exploiting sub-Gaussian structure for tight probabilistic guarantees.

Overview

Safety-critical control systems must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. This framework overcomes the trade-off between tightness of probabilistic guarantees and computational tractability.

Key Features:

• Sub-Gaussian structure exploitation
• Particle-based CVaR estimation
• Finite-sample safety certificates
• Explicit tail bounds for Gaussian uncertainties

When to Use This Skill

• Safety-critical systems with estimation uncertainty
• Spacecraft proximity operations
• Autonomous vehicles with noisy sensors
• Robotic systems requiring formal safety guarantees

Mathematical Framework

Sub-Gaussian Structure

Gaussian uncertainties propagating through Lipschitz-continuous control-affine dynamics preserve sub-Gaussianity of the barrier function increment:

Barrier Function Increment: h(x_{t+1}) - h(x_t)
  ↓
Sub-Gaussian Distribution
  ↓
Explicit Tail Bounds
  ↓
Probabilistic Safety Certificates

Particle-Based CVaR

• Estimation: Particle-based Conditional Value at Risk (CVaR) estimates
• Error Bounds: Finite-sample bounds on approximation error
• Ground Truth: Connection to true probabilistic constraints

Key Results

Theoretical Guarantees

Computational Tractability

The framework yields a tractable optimization problem formulation with finite-sample safety certificates, enabling real-time implementation.

Implementation Guide

System Requirements

• Control-affine dynamics
• Lipschitz-continuous barrier function
• Gaussian uncertainty model
• Particle filter for state estimation

Algorithm Steps

1. Initialize particle distribution
2. Propagate particles through dynamics
3. Compute barrier function increments
4. Estimate CVaR using particles
5. Apply safety constraints to control
6. Execute safe control action

Parameters

Validation

Numerical experiments demonstrate:

• Tight yet provably valid probabilistic safety guarantees
• Comparison with existing approaches
• Trade-off between conservatism and performance

References

Paper: Probabilistic Control Barrier Functions for Systems with State Estimation Uncertainty using Sub-Gaussian Concentration

• Authors: Kazuya Echigo, David E. J. van Wijk, Pol Mestres, Ersin Daş, Joel W. Burdick
• arXiv: 2604.08831
• Date: 2026-04-10
• Categories: eess.SY

Related Skills

• control-barrier-functions: General CBF methodologies
• safety-critical-control: Safety-critical control systems
• stochastic-control: Stochastic control frameworks

Activation Keywords

• probabilistic-cbf-subgaussian
• probabilistic cbf subgaussian
• probabilistic cbf subgaussian

Tools Used

• read - 读取技能文档
• write - 创建输出
• exec - 执行相关命令

Instructions for Agents

1. 理解技能的核心方法论
2. 根据用户问题提供针对性回答
3. 遵循最佳实践

Examples

Example 1: 基本查询

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