28 citations · 74 across the 24 of their papers we have counts for
13 papers · 1 filter
Universal Approximation of Maximal Lyapunov Functions with Anchored Neural Networks
Jun Liu
Maximal Lyapunov functions encode the entire domain of attraction of an asymptotically stable equilibrium, but preserving strict decrease under neural approximation is difficult be…
Verifiable Error Bounds for Physics-Informed Neural KKL Observers
Hannah Berin-Costain, Harry Wang, Kirsten Morris +1
This paper proposes a computable state-estimation error bound for learning-based Kazantzis--Kravaris/Luenberger (KKL) observers. Recent work learns the KKL transformation map with…
Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations
Jun Liu
Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equat…
Safe Domains of Attraction for Discrete-Time Nonlinear Systems: Characterization and Verifiable Neural Network Estimation
Mohamed Serry, Haoyu Li, Ruikun Zhou +2
Analysis of nonlinear autonomous systems typically involves estimating domains of attraction, which have been a topic of extensive research interest for decades. Despite that, accu…
Data-driven optimal control of unknown nonlinear dynamical systems using the Koopman operator
Zhexuan Zeng, Ruikun Zhou, Yiming Meng +1
Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling compu…
Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems
Ruikun Zhou, Yiming Meng, Zhexuan Zeng +1
Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vecto…
Formally Verified Physics-Informed Neural Control Lyapunov Functions
Jun Liu, Maxwell Fitzsimmons, Ruikun Zhou +1
Control Lyapunov functions are a central tool in the design and analysis of stabilizing controllers for nonlinear systems. Constructing such functions, however, remains a significa…
Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systems
Thanin Quartz, Ruikun Zhou, Hans De Sterck +1
Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning a…
LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
In this paper, we describe a lightweight Python framework that provides integrated learning and verification of neural Lyapunov functions for stability analysis. The proposed tool,…
Compositionally Verifiable Vector Neural Lyapunov Functions for Stability Analysis of Interconnected Nonlinear Systems
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stabi…
Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification
Yiming Meng, Ruikun Zhou, Amartya Mukherjee +3
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonli…
Stochastic Control Barrier Functions with Bayesian Inference for Unknown Stochastic Differential Equations
Chuanzheng Wang, Yiming Meng, Jun Liu +1
Control barrier functions are widely used to synthesize safety-critical controls. However, the presence of Gaussian-type noise in dynamical systems can generate unbounded signals a…
On the Powerball Method for Optimization
Ye Yuan, Mu Li, Jun Liu +1
We propose a new method to accelerate the convergence of optimization algorithms. This method simply adds a power coefficient to the gradient during optimization. We ca…