What is the most suitable Lyapunov function?

P Zhou, X Hu, Z Zhu, J Ma - Chaos, Solitons & Fractals, 2021 - Elsevier
Lyapunov function provides feasible estimation and prediction of nonlinear system stability,
and useful guidance for adaptive control in chaos and synchronization approach. In case of …

Energy function for some maps and nonlinear oscillators

J Ma - Applied Mathematics and Computation, 2024 - Elsevier
Continuous dynamical systems with different nonlinear terms can show rich dynamical
characteristic, which can be presented and verified in nonlinear oscillators. Reliable …

Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control

C Dawson, S Gao, C Fan - IEEE Transactions on Robotics, 2023 - ieeexplore.ieee.org
Learning-enabled control systems have demonstrated impressive empirical performance on
challenging control problems in robotics, but this performance comes at the cost of reduced …

Safe model-based reinforcement learning with stability guarantees

F Berkenkamp, M Turchetta… - Advances in neural …, 2017 - proceedings.neurips.cc
Reinforcement learning is a powerful paradigm for learning optimal policies from
experimental data. However, to find optimal policies, most reinforcement learning algorithms …

Safe nonlinear control using robust neural lyapunov-barrier functions

C Dawson, Z Qin, S Gao, C Fan - Conference on Robot …, 2022 - proceedings.mlr.press
Safety and stability are common requirements for robotic control systems; however,
designing safe, stable controllers remains difficult for nonlinear and uncertain models. We …

Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods

C Dawson, S Gao, C Fan - arXiv preprint arXiv:2202.11762, 2022 - arxiv.org
Learning-enabled control systems have demonstrated impressive empirical performance on
challenging control problems in robotics, but this performance comes at the cost of reduced …

Formal synthesis of Lyapunov neural networks

A Abate, D Ahmed, M Giacobbe… - IEEE Control Systems …, 2020 - ieeexplore.ieee.org
We propose an automatic and formally sound method for synthesising Lyapunov functions
for the asymptotic stability of autonomous non-linear systems. Traditional methods are either …

Safe learning of regions of attraction for uncertain, nonlinear systems with gaussian processes

F Berkenkamp, R Moriconi… - 2016 IEEE 55th …, 2016 - ieeexplore.ieee.org
Control theory can provide useful insights into the properties of controlled, dynamic systems.
One important property of nonlinear systems is the region of attraction (ROA), a safe subset …

Learning safe, generalizable perception-based hybrid control with certificates

C Dawson, B Lowenkamp, D Goff… - IEEE Robotics and …, 2022 - ieeexplore.ieee.org
Many robotic tasks require high-dimensional sensors such as cameras and Lidar to navigate
complex environments, but developing certifiably safe feedback controllers around these …

Lyapunov-Net: A deep neural network architecture for Lyapunov function approximation

N Gaby, F Zhang, X Ye - 2022 IEEE 61st Conference on …, 2022 - ieeexplore.ieee.org
We develop a versatile deep neural network architecture, called Lyapunov-Net, to
approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net …