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 …
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 …
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
Learning-enabled control systems have demonstrated impressive empirical performance on
challenging control problems in robotics, but this performance comes at the cost of reduced …
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 …
experimental data. However, to find optimal policies, most reinforcement learning algorithms …
Safe nonlinear control using robust neural lyapunov-barrier functions
Safety and stability are common requirements for robotic control systems; however,
designing safe, stable controllers remains difficult for nonlinear and uncertain models. We …
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
Learning-enabled control systems have demonstrated impressive empirical performance on
challenging control problems in robotics, but this performance comes at the cost of reduced …
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 …
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 …
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 …
complex environments, but developing certifiably safe feedback controllers around these …
Lyapunov-Net: A deep neural network architecture for Lyapunov function approximation
We develop a versatile deep neural network architecture, called Lyapunov-Net, to
approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net …
approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net …