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.
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.
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:
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
| Property | Result |
|---|---|
| Sub-Gaussian Preservation | Gaussian + Lipschitz → Sub-Gaussian |
| Tail Bounds | Explicit bounds on barrier increment |
| Finite-Sample Bounds | Error bounds for particle-based CVaR |
| Safety Certificates | Provable probabilistic safety guarantees |
The framework yields a tractable optimization problem formulation with finite-sample safety certificates, enabling real-time implementation.
| Parameter | Description | Typical Range |
|---|---|---|
| N_particles | Number of particles | 100-10000 |
| α | CVaR confidence level | 0.95-0.99 |
| h(x) | Barrier function | Problem-specific |
Numerical experiments demonstrate:
Paper: Probabilistic Control Barrier Functions for Systems with State Estimation Uncertainty using Sub-Gaussian Concentration
control-barrier-functions: General CBF methodologiessafety-critical-control: Safety-critical control systemsstochastic-control: Stochastic control frameworksexecreadwriteUser: 请帮我应用此技能
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