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Found 9 papers, 1 papers with code
Compositionally Verifiable Vector Neural Lyapunov Functions for Stability Analysis of Interconnected Nonlinear Systems
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of dimensionality.
LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction
In this paper, we describe a lightweight Python framework that provides integrated learning and verification of neural Lyapunov functions for stability analysis.
Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification
We provide a theoretical analysis of both algorithms in terms of convergence of neural approximations towards the true optimal solutions in a general setting.
Stochastic Control Barrier Functions with Bayesian Inference for Unknown Stochastic Differential Equations
Control barrier functions are widely used to synthesize safety-critical controls.
Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions.
Robustly Complete Finite-State Abstractions for Control Synthesis of Stochastic Systems
The essential step of abstraction-based control synthesis for nonlinear systems to satisfy a given specification is to obtain a finite-state abstraction of the original systems.
Data-Driven Learning of Safety-Critical Control with Stochastic Control Barrier Functions
More specifically, we propose a data-driven stochastic control barrier function (DDSCBF) framework and use supervised learning to learn the unknown stochastic dynamics via the DDSCBF scheme.
Safety-Critical Control of Stochastic Systems using Stochastic Control Barrier Functions
We propose a notion of stochastic control barrier functions (SCBFs)and show that SCBFs can significantly reduce the control efforts, especially in the presence of noise, compared to stochastic reciprocal control barrier functions (SRCBFs), and offer a less conservative estimation of safety probability, compared to stochastic zeroing control barrier functions (SZCBFs).
Smooth Converse Lyapunov-Barrier Theorems for Asymptotic Stability with Safety Constraints and Reach-Avoid-Stay Specifications
While the converse Lyapunov-barrier theorems are not constructive, as with classical converse Lyapunov theorems, we believe that the unified necessary and sufficient conditions with a single Lyapunov-barrier function are of theoretical interest and can hopefully shed some light on computational approaches.
