7 papers · 1 filter
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…
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…
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…
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…
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…
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…