Related papers: Thomas Decomposition and Nonlinear Control Systems
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
A novel control design approach for general nonlinear systems is described in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. Extensive…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
A dynamic iteration scheme for linear infinite-dimensional port-Hamiltonian systems is proposed. The dynamic iteration is monotone in the sense that the error is decreasing, it does not require any stability condition and is in particular…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
The concept of nonlinear modes is useful for the dynamical characterization of nonlinear mechanical systems. While efficient and broadly applicable methods are now available for the computation of nonlinear modes, nonlinear modal testing is…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…
This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and thus is different from the well-known correlative sparsity…
Theoretical studies of nonequilibrium systems are complicated by the lack of a general framework. In this work we first show that a transformation introduced by Ao recently (J. Phys. A {\bf 37}, L25 (2004)) is related to previous works of…
We study the task of smoothing a circuit, i.e., ensuring that all children of a plus-gate mention the same variables. Circuits serve as the building blocks of state-of-the-art inference algorithms on discrete probabilistic graphical models…
Multi-step manipulation tasks where robots interact with their environment and must apply process forces based on the perceived situation remain challenging to learn and prone to execution errors. Accurately simulating these tasks is also…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
Control theory often takes the mathematical model of the to-be-control-led system for granted. In contrast, port-Hamiltonian systems theory bridges the gap between modelling and control for physical systems. It provides a unified framework…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…