3,520 research outputs found
Port-Hamiltonian systems: an introductory survey
The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis
In this paper, we extend the eigenvalue method of the algebraic Riccati
equation to the differential Riccati equation (DRE) in contraction analysis.
One of the main results is showing that solutions to the DRE can be expressed
as functions of nonlinear eigenvectors of the differential Hamiltonian matrix.
Moreover, under an assumption for the differential Hamiltonian matrix, real
symmetricity, regularity, and positive semidefiniteness of solutions are
characterized by nonlinear eigenvalues and eigenvectors
A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression
Many machine learning problems can be formulated as predicting labels for a
pair of objects. Problems of that kind are often referred to as pairwise
learning, dyadic prediction or network inference problems. During the last
decade kernel methods have played a dominant role in pairwise learning. They
still obtain a state-of-the-art predictive performance, but a theoretical
analysis of their behavior has been underexplored in the machine learning
literature.
In this work we review and unify existing kernel-based algorithms that are
commonly used in different pairwise learning settings, ranging from matrix
filtering to zero-shot learning. To this end, we focus on closed-form efficient
instantiations of Kronecker kernel ridge regression. We show that independent
task kernel ridge regression, two-step kernel ridge regression and a linear
matrix filter arise naturally as a special case of Kronecker kernel ridge
regression, implying that all these methods implicitly minimize a squared loss.
In addition, we analyze universality, consistency and spectral filtering
properties. Our theoretical results provide valuable insights in assessing the
advantages and limitations of existing pairwise learning methods.Comment: arXiv admin note: text overlap with arXiv:1606.0427
Conservation laws and open systems on higher-dimensional networks
We discuss a framework for defining physical open systems on higher-dimensional complexes. We start with the formalization of the dynamics of open electrical circuits and the Kirchhoff behavior of the underlying open graph or 1-complex. It is discussed how the graph can be closed to an ordinary graph, and how this defines a Dirac structure on the extended graph. Then it is shown how this formalism can be extended to arbitrary k-complexes, which is illustrated by a discrete formulation of heat transfer on a two-dimensional spatial domain.
Group analysis of differential equations and generalized functions
We present an extension of the methods of classical Lie group analysis of
differential equations to equations involving generalized functions (in
particular: distributions). A suitable framework for such a generalization is
provided by Colombeau's theory of algebras of generalized functions. We show
that under some mild conditions on the differential equations, symmetries of
classical solutions remain symmetries for generalized solutions. Moreover, we
introduce a generalization of the infinitesimal methods of group analysis that
allows to compute symmetries of linear and nonlinear differential equations
containing generalized function terms. Thereby, the group generators and group
actions may be given by generalized functions themselves.Comment: 27 pages, LaTe
COORDINATION OF LEADER-FOLLOWER MULTI-AGENT SYSTEM WITH TIME-VARYING OBJECTIVE FUNCTION
This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system in the case of complete information exchange. Using Lyapunov methods, the stability and boundedness of the agents\u27 trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results. Then, we extend these results for multi-agent systems with limited information exchange and switching communication topology. The first steps of the realization of an experimental framework have been made with the ultimate goal of verifying the simulation results in practice
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