Results 1 to 10 of about 83,795 (307)

Applied Lyapunov Stability for Some Nonlinear Stochastic Differential Equations

Tikrit Journal of Pure Science, 2023
In this paper, we applied and explain the stability to some linear and  non-linear stochastic differential equations by using the Lyapunov direct second method, after finding the  stochastic differential equation which obtained by applying the (Ito ...
Nibal Sabah Abdurahman , Abdulghafoor Jasim  Salim   +1 more
doaj   +1 more source

Stable On-the-Fly Learning for Dynamic Neural Networks With Delayed Inputs

IEEE Access
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids.
Viktor Chertopolokhov, Arthur Mukhamedov, Grigory Bugriy, Vladislav Kibkalo, Vyacheslav Ionkin, Vera Tolchennikova, Isaac Chairez   +6 more
doaj   +1 more source

Stabilization of Nonlinear Control-Affine Systems With Multiple State Constraints

IEEE Access, 2020
This paper considers the synthesis of stabilizing controllers for nonlinear control-affine systems under multiple state constraints. A new control Lyapunov-barrier function approach is introduced for solving the considered problem.
Jia-Yao Jhang, Jenq-Lang Wu, Chee-Fai Yung   +2 more
doaj   +1 more source

Augmented Neural Lyapunov Control

IEEE Access, 2023
Machine learning-based methodologies have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example.
Davide Grande, Andrea Peruffo, Enrico Anderlini, Georgios Salavasidis   +3 more
doaj   +1 more source

Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems [PDF]

, 2012
This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor.
Eyink, Ginelli, Jameson, Krakos, Lea, Qiqi Wang, Ruelle, Ruelle, Thepaut, Venditti, Wang, Wolfe   +11 more
core   +2 more sources

Stability and Control of Power Systems using Vector Lyapunov Functions and Sum-of-Squares Methods

, 2015
Recently sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power systems, using an ...
Anghel, Marian, Kundu, Soumya
core   +1 more source

Direct methods for matrix Sylvester and Lyapunov equations

Journal of Applied Mathematics, 2003
We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels-Stewart method for A1X+XA2+D=0 and Hammarling's method for AX+XAT+BBT=0 with A stable.
Danny C. Sorensen, Yunkai Zhou
doaj   +1 more source

Torque Saturation in Bipedal Robotic Walking Through Control Lyapunov Function-Based Quadratic Programs

IEEE Access, 2015
This paper presents a novel method to address the actuator saturation for nonlinear hybrid systems by directly incorporating user-defined input bounds in a controller design. In particular, we consider the application of bipedal walking and show that our
Kevin Galloway, Koushil Sreenath, Aaron D. Ames, Jessy W. Grizzle   +3 more
doaj   +1 more source

Systematic Analysis and Design of Control Systems Based on Lyapunov’s Direct Method

Algorithms, 2023
This paper deals with systematic approaches for the analysis of stability properties and controller design for nonlinear dynamical systems. Numerical methods based on sum-of-squares decomposition or algebraic methods based on quantifier elimination are ...
Rick Voßwinkel, Klaus Röbenack
doaj   +1 more source

Symplectic Calculation of Lyapunov Exponents

, 1994
The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to develop a new method
Habib, Salman, Ryne, Robert D.
core   +1 more source