28 citations · 74 across the 24 of their papers we have counts for
24 papers
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…
Generalizing Dynamics Modeling More Easily from Representation Perspective
Yiming Wang, Zhengnan Zhang, Genghe Zhang +7
Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently,…
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…
Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández +1
Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physi…
Towards Learning and Verifying Maximal Lyapunov-Barrier Functions with a Zubov PDE Formulation
Yiming Meng, Jun Liu
Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specif…
Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems
Yun Su, Hans De Sterck, Jun Liu
Leveraging a stochastic extension of Zubov's equation, we develop a physics-informed neural network (PINN) approach for learning a neural Lyapunov function that captures the larges…
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…
Stability of Jordan Recurrent Neural Network Estimator
Avneet Kaur, Ruikun Zhou, Jun Liu +1
State estimation refers to determining the states of a dynamical system that starts from a noisy initial condition and evolves under process noise, based on noisy measurements and…
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…
Resolvent-Type Data-Driven Learning of Generators for Unknown Continuous-Time Dynamical Systems
Yiming Meng, Ruikun Zhou, Melkior Ornik +1
A semigroup characterization, or equivalently, a characterization by the generator, is a classical technique used to describe continuous-time nonlinear dynamical systems. In the re…
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…
Koopman-Based Learning of Infinitesimal Generators without Operator Logarithm
Yiming Meng, Ruikun Zhou, Melkior Ornik +1
The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variab…
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…
Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification
Jun Liu, Yiming Meng, Maxwell Fitzsimmons +1
We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE…
Learning Regions of Attraction in Unknown Dynamical Systems via Zubov-Koopman Lifting: Regularities and Convergence
Yiming Meng, Ruikun Zhou, Jun Liu
The estimation for the region of attraction (ROA) of an asymptotically stable equilibrium point is crucial in the analysis of nonlinear systems. There has been a recent surge of in…
Harmonic Control Lyapunov Barrier Functions for Constrained Optimal Control with Reach-Avoid Specifications
Amartya Mukherjee, Ruikun Zhou, Haocheng Chang +1
This paper introduces harmonic control Lyapunov barrier functions (harmonic CLBF) that aid in constrained control problems such as reach-avoid problems. Harmonic CLBFs exploit the…
A Generalized Nyquist-Shannon Sampling Theorem Using the Koopman Operator
Zhexuan Zeng, Jun Liu, Ye Yuan
In the field of signal processing, the sampling theorem plays a fundamental role for signal reconstruction as it bridges the gap between analog and digital signals. Following the c…
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…