1,184 research outputs found
Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices
We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite
lattices. We also show that the breathers are well approximated by the ground
state of the nonlinear Schroedinger equation. The result is obtained by
exploiting the relation between the Klein Gordon lattice and the discrete Non
Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt
decomposition and continuum approximation techniques introduced in [7],
actually using its main result as an important lemma
Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems
A robust controller is developed for uncertain, second-order nonlinear
systems subject to simultaneous unknown, time-varying state delays and known,
time-varying input delays in addition to additive, sufficiently smooth
disturbances. An integral term composed of previous control values facilitates
a delay-free open-loop error system and the development of the feedback control
structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals
guarantees uniformly ultimately bounded tracking under the assumption that the
delays are bounded and slowly varying
Exponential stability of linear continuous time difference systems with multiple delays
"Some recent results on exponential stability of linear continuous time difference systems with discrete and distributed delay terms are extended to the case of multiple delays. New sufficient conditions for the exponential stability and exponential estimates for the solutions by using Lyapunov–Krasovskii functionals are derived. Special attention is paid to the case of systems with commensurate discrete and distributed delays.
Recommended from our members
On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper
Global attractors for gradient flows in metric spaces
We develop the long-time analysis for gradient flow equations in metric
spaces. In particular, we consider two notions of solutions for metric gradient
flows, namely energy and generalized solutions. While the former concept
coincides with the notion of curves of maximal slope, we introduce the latter
to include limits of time-incremental approximations constructed via the
Minimizing Movements approach.
For both notions of solutions we prove the existence of the global attractor.
Since the evolutionary problems we consider may lack uniqueness, we rely on the
theory of generalized semiflows introduced by J.M. Ball. The notions of
generalized and energy solutions are quite flexible and can be used to address
gradient flows in a variety of contexts, ranging from Banach spaces to
Wasserstein spaces of probability measures.
We present applications of our abstract results by proving the existence of
the global attractor for the energy solutions both of abstract doubly nonlinear
evolution equations in reflexive Banach spaces, and of a class of evolution
equations in Wasserstein spaces, as well as for the generalized solutions of
some phase-change evolutions driven by mean curvature
Spatial Hamiltonian identities for nonlocally coupled systems
We consider a broad class of systems of nonlinear integro-differential
equations posed on the real line that arise as Euler-Lagrange equations to
energies involving nonlinear nonlocal interactions. Although these equations
are not readily cast as dynamical systems, we develop a calculus that yields a
natural Hamiltonian formalism. In particular, we formulate Noether's theorem in
this context, identify a degenerate symplectic structure, and derive
Hamiltonian differential equations on finite-dimensional center manifolds when
those exist. Our formalism yields new natural conserved quantities. For
Euler-Lagrange equations arising as traveling-wave equations in gradient flows,
we identify Lyapunov functions. We provide several applications to
pattern-forming systems including neural field and phase separation problems.Comment: 39 pages, 1 figur
Effects of Delay on the Functionality of Large-scale Networks
Networked systems are common across engineering and the physical sciences. Examples include the Internet, coordinated motion of multi-agent systems, synchronization phenomena in nature etc. Their robust functionality is important to ensure smooth operation in the presence of uncertainty and unmodelled dynamics. Many such networked systems can be viewed under a unified optimization framework and several approaches to assess their nominal behaviour have been developed. In this paper, we consider what effect multiple, non-commensurate (heterogeneous) communication delays can have on the functionality of large-scale networked systems with nonlinear dynamics. We show that for some networked systems, the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions; whereas in other cases the loop gains have to be compensated for by the delay size, in order to render functionality delay-independent for arbitrary network sizes. Consensus reaching in multi-agent systems and stability of network congestion control for the Internet are used as examples. The differences and similarities of the two cases are explained in detail, and the application of the methodology to other technological and physical networks is discussed
- …