Results 61 to 70 of about 19,301 (215)

An approximating method for the stabilizing solution of the Hamilton-Jacobi equation for integrable systems using Hamiltonian perturbation theory [PDF]

, 2006
In this report, a method for approximating the stabilizing solution of the Hamilton-Jacobi equation for integrable systems is proposed using symplectic geometry and a Hamiltonian perturbation technique.
Sakamoto, N., Schaft, A.J. van der
core   +6 more sources

Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics
Mohamed E. M. Alngar, Khaled A. Gepreel, Reham M. A. Shohib, Yakup Yildirim   +3 more
wiley   +1 more source

Constructive factorization of LPDO in two variables

, 2005
We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left.
A. Loewy, D. Grigoriev, E. A. Kartashova, E. Beke, E. Landau, J. Apel, M. Bronstein, R. Beals, S. P. Tsarev   +8 more
core   +1 more source

Quaternionic-valued ordinary differential equations. The Riccati equation

Journal of Differential Equations, 2009
The paper uses Poincaré's operator and finite-dimensional fixed point theory to obtain existence and multiplicity results for the T-periodic solutions \(q(t)\) of quaternionic-valued equations of the form \[ \dot q = qa(t)q + b(t)q + qd(t) + c(t), \] where \(a, b, c : \mathbb R \to \mathbb H\) are T-periodic continuous quaternionic-valued functions ...
openaire   +2 more sources

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Numerical solution of differential algebraic riccati equations

Linear Algebra and its Applications, 1990
The numerical solution of the matrix differential algebraic Riccati equation (DARE) arising from singular or descriptor control problems is studied. The solvability of such equations under different conditions is discussed. Numerical methods for the solution of the DAREs are applied to these equations after a transformation of the DARE to a form where ...
Kunkel, P., Mehrmann, V.
openaire   +1 more source

HyLPD Digital Twin Control for UAV Stability in High‐Wind Conditions

Optimal Control Applications and Methods, EarlyView.
This work introduces a novel HyLPD, a hybrid control framework combining Linear Quadratic Regulator (LQR) for baseline stability and Deep Deterministic Policy Gradient (DDPG) for adaptive compensation, tailored for UAVs under high‐wind conditions.
Cara Rose, Robert McMurray, Muhammad Usman Hadi   +2 more
wiley   +1 more source

Optimal Homogeneous ℒp$$ {\boldsymbol{\mathcal{L}}}_{\boldsymbol{p}} $$‐Gain Controller

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Nonlinear ℋ∞$$ {\mathscr{H}}_{\infty } $$‐controllers are designed for arbitrarily weighted, continuous homogeneous systems with a focus on systems affine in the control input. Based on the homogeneous ℒp$$ {\mathcal{L}}_p $$‐norm, the input–output behavior is quantified in terms of the homogeneous ℒp$$ {\mathcal{L}}_p $$‐gain as a ...
Daipeng Zhang, Benjamin Calmbach, Jaime A. Moreno, Johann Reger   +3 more
wiley   +1 more source

A Multiagent Transfer Function Neuroapproach to Solve Fuzzy Riccati Differential Equations

Journal of Applied Mathematics, 2014
A numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach for neural networks (NN). This proposed new approach provides different degrees of polynomial subspaces for each of the transfer function ...
Mohammad Shazri Shahrir, N. Kumaresan, Kuru Ratnavelu, M. Z. M. Kamali   +3 more
doaj   +1 more source

On one oscillatory criterion for the second order linear ordinary differential equations [PDF]

Opuscula Mathematica, 2016
The Riccati equation method is used to establish an oscillatory criterion for second order linear ordinary differential equations. An oscillatory condition is obtained for the generalized Hill's equation.
Gevorg Avagovich Grigorian
doaj   +1 more source