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Control a state-dependent dynamic graph to a pre-specified structure

Fei Chen, Zengqiang Chen, Zhongxin Liu, Zhuzhi Yuan (2009)

Kybernetika

Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states....

Control systems on semi-simple Lie groups and their homogeneous spaces

Velimir Jurdjevic, Ivan Kupka (1981)

Annales de l'institut Fourier

In the present paper, we consider the class of control systems which are induced by the action of a semi-simple Lie group on a manifold, and we give a sufficient condition which insures that such a system can be steered from any initial state to any final state by an admissible control. The class of systems considered contains, in particular, essentially all the bilinear systems. Our condition is semi-algebraic but unlike the celebrated Kalman criterion for linear systems, it is not necessary. In...

Controllability of three-dimensional Navier–Stokes equations and applications

Armen Shirikyan (2005/2006)

Séminaire Équations aux dérivées partielles

We formulate two results on controllability properties of the 3D Navier–Stokes (NS) system. They concern the approximate controllability and exact controllability in finite-dimensional projections of the problem in question. As a consequence, we obtain the existence of a strong solution of the Cauchy problem for the 3D NS system with an arbitrary initial function and a large class of right-hand sides. We also discuss some qualitative properties of admissible weak solutions for randomly forced NS...

Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti, Jean-Claude Vivalda (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...

Controller design for bush-type 1-d wave networks∗

Yaxuan Zhang, Genqi Xu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...

Controller design for bush-type 1-d wave networks

Yaxuan Zhang, Genqi Xu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...

Controller design for bush-type 1-d wave networks∗

Yaxuan Zhang, Genqi Xu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram’s...

Controlling Nanoparticles Formation in Molten Metallic Bilayers by Pulsed-Laser Interference Heating

M. Khenner, S. Yadavali, R. Kalyanaraman (2012)

Mathematical Modelling of Natural Phenomena

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer,...

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2001)

ESAIM: Control, Optimisation and Calculus of Variations

It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...

Convergence and uniqueness problems for Dirichlet forms on fractals

Roberto Peirone (2000)

Bollettino dell'Unione Matematica Italiana

M 1 è un particolare operatore di minimizzazione per forme di Dirichlet definite su un sottoinsieme finito di un frattale K che è, in un certo senso, una sorta di frontiera di K . Viene talvolta chiamato mappa di rinormalizzazione ed è stato usato per definire su K un analogo del funzionale u ↦ ∫ grad ⁢ u 2 e un moto Browniano. In questo lavoro si provano alcuni risultati sull'unicità dell'autoforma (rispetto a M 1 ), e sulla convergenza dell'iterata di M 1 rinormalizzata. Questi risultati sono collegati con l'unicità...

Currently displaying 261 – 280 of 352