Related papers: Jacobian-Free Variational Method for Constructing …
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori…
This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this…
One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of…
We consider autonomous Hamiltonian systems and present an algorithm to compute at the same time partially hyperbolic invariant tori (whiskered tori), as well as high-order expansions of their stable and unstable manifolds. Such whiskered…
This paper introduces an innovative method for ensuring global stability in a broad array of nonlinear systems. The novel approach enhances the traditional analysis based on Jacobian matrices by incorporating the Taylor series boundary…
This paper develops a computational method for studying stable/unstable manifolds attached to periodic orbits of differential equations. The method uses high order Chebyshev-Taylor series approximations in conjunction with the…
A methodology to generate sparse Galerkin models of chaotic/unsteady fluid flows containing a minimal number of active triadic interactions is proposed. The key idea is to find an appropriate set of basis functions for the projection…
Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise…
Engineered systems naturally experience large disturbances that can disrupt desired operation because the system may fail to recover to a stable equilibrium point. It is valuable to determine the mechanism of instability when the system is…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
In this paper, we develop a computationally-efficient approach to minimum-time trajectory optimization using input-output data-based models, to produce an end-to-end data-to-control solution to time-optimal planning/control of dynamic…
The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic"…
In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the…
Conjunction analysis and maneuver planning for spacecraft collision avoidance remains a manual and time-consuming process, typically involving repeated forward simulations of hand-designed maneuvers. With the growing density of satellites…
We initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the…