hyperbolic conservation laws with relaxation the effect of relaxation is important in many physical situations it is present in the kinetic theory of gases elasticity with memory gas flow with thermo non equilibrium water waves etc the governing equations often take the form of hyperbolic conservation laws with lower order terms in this article we present and analyze a simple model of hyperbolic conservation laws with relaxation effects dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified stability criteria for diffusion waves expansion waves and traveling waves are found and justified nonlinearly time asymptotic expansion and the energy method are used in the analysis for dissipative waves the expansion is similar in spirit to the chapman enskog expansion in the kinetic theory for shock waves however a different approach is needed

nonlinear stability of rarefaction waves for a viscoelastic material with memory in this paper we will discuss the stability of rarefaction waves for a viscoelastic material with memory the rarefaction waves for which the sta bility is tested are not themselves solutions to the integrodifferential equations 1 1 governing the viscoelastic material they are solutions to a related equi librium system of conservation laws given by 1 11 we shall show that if the forcing term and the past history are small and if the initial data are close to the rarefaction waves the solutions to 1 1 will approach the rarefaction waves in sup norm as the time goes to infinity j oo with the initial data u x 0 v x 0 u0 x v0 x xer l2 lim uo x v0 x u v x oo

sampled data based consensus of continuous time multi agent systems with time varying topology this technical note studies consensus problems of multiple agents with continuous time second order dynamics where each agent can obtain its positions and velocities relative to its neighbors only at sampling instants it is assumed that the sampling period of each agent is independent of the others and the interaction topology among agents is time varying where the associated direct graphs may not have spanning trees if the union graph of all direct graphs has a spanning tree then there exist controller gains and sampling periods such that consensus is reached moreover two approaches are presented to design such controller gains and sampling periods simulations are performed to validate the theoretical results

maximum allowable loss probability for consensus of multi agent systems over random weighted lossy networks this note studies the consensus seeking problem for a team of general linear dynamical agents that communicate via a weighted random lossy network linear state feedback consensus protocols are applied and both the weights and feedback gain are treated as control parameters in the protocol it is shown that the weights and the link loss probabilities of a network have non negligible effects on the consensus seeking ability of multi agent systems firstly a weight condition characterized by the eigenvalues of the weighted laplacian matrix is given for systems over ideal communication networks without packet losses secondly based on stochastic stability analysis a maximum allowable loss probability bound is proposed for systems over random lossy networks as long as the link loss probabilities of the network are less than this bound and the mean topology has spanning trees there exist linear protocols solving the mean square consensus problem of the system

quantized consensus and averaging on gossip digraphs we study distributed consensus problems of multi agent systems on directed networks and subject to quantized information flow for the communication among component agents particular attention is given to the gossip type which models their asynchronous behavior for quantization effect each agent s state is abstracted to be an integer the central question investigated is how to design distributed algorithms and what connectivity of networks that together lead to consensus this investigation is carried out for both general consensus and average consensus for each case a class of algorithms is proposed under which a necessary and sufficient graphical condition is derived to guarantee the corresponding consensus in particular the obtained graphical condition ensuring average consensus is weaker than those in the literature for either real valued or quantized states in the sense that it does not require symmetric or balanced network topologies

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

existence of the entropy solution for a viscoelastic model in this paper we consider the cauchy problem for a viscoelastic model with relaxationut x 0 f u t 1 f u 0with discontinuous large initial data where 0 0 are constants when the system is nonstrictly hyperbolic under the additional assumptionv0x l the system is reduced to an inhomogeneous scalar balance law by employing the special form of the system itself after introducing a definition of entropy solutions to the system we prove the existence uniqueness and continuous dependence of the global entropy solution for the system when the system is strictly hyperbolic some special entropy pairs of the lax type are constructed in which the progression terms are functions of a single variable and the necessary estimates for the major terms are obtained by using the theory of singular perturbation of the ordinary differential equations the special entropy pairs are used to prove the existence of the global entropy solutions for the corresponding cauchy problem by applying the method of compensated compactness

transient three dimensional rayleigh and stoneley signal effects in thermoelastic solids a transient 3d study of surface rayleigh and interface stoneley signals in fully coupled thermolastic solids begins by obtaining analytical expressions for the zeroes of the corresponding rayleigh stoneley functions that arise in the integral transforms of the solutions the expressions locate the zeroes as functions of the temporal transform variable in a complex plane defined by a scalar resultant of spatial transform variables expressions for the change in surface temperature caused by the rayleigh signal are then derived for cases of normal traction surface loading by using long time asymptotic results the expressions can be obtained analytically and they show that rayleigh stoneley signal induced thermal effects can be important the long time asymptotic results also show that rayleigh stoneley zeroes reduce to the thermally modified inverses of the classical non thermal rayleigh stoneley wave speeds this result agrees with 2d predictions that can be made on the basis of low frequency asymptotic harmonic wave studies the long time results are not restrictive because time is scaled by a small i e o 10 4 m thermoelastic characteristic length

well posedness of the global entropy solution to the cauchy problem of a hyperbolic conservation laws with relaxation in this paper we prove that the cauchy problem to a hyperbolic conservation laws with relaxation with singular initial data admits a unique global entropy solution in the sense of definition 1 1 compared with former results in this direction the main ingredient of this paper lies in the fact that it contains a uniqueness result and we do not ask f u to satisfy any convex monotonic conditions and the regularity assumption we imposed on f u is weaker c 2003 elsevier inc all rights reserved

exponential consensus of general linear multi agent systems under directed dynamic topology this paper aims to investigate the consensus control of generic linear multi agent systems mass under directed dynamic topology nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which are widely used for multiple integrator agents is explored to deal with the convergence analysis of generic linear mass it is finally shown that the exponential consensus can be reached under very relaxed conditions i e the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough moreover a least convergence rate and a bound for the unstable mode of the individual agent system both of which are independent of the switching mode can be explicitly specified

network topology and communication data rate for consensusability of discrete time multi agent systems this paper investigates the joint effect of agent dynamic network topology and communication data rate on consensusability of linear discrete time multi agent systems neglecting the finite communication data rate constraint and under undirected graphs a necessary and sufficient condition for consensusability under a common control protocol is given which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability the result is established by solving a discrete time simultaneous stabilization problem a lower bound of the optimal convergence rate to consensus which is shown to be tight for some special cases is provided as well moreover a necessary and sufficient condition for formationability of multi agent systems is obtained as a special case the discrete time second order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence the effects of undirected graphs on consensability formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph laplacian matrix an extension to directed graphs is also made the consensus problem under a finite communication data rate is finally investigated

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

transient thermal effects in edge dislocation generation near a crack edge abstract a transient 2 d study of edge dislocation generation near a crack in a fully coupled thermoelastic solid loaded by sv wave diffraction is considered exact solutions to the mixed boundary initial value problem in the integral transform space are obtained and inversions valid for short times performed the solution behavior indicates that the generation process requires only a short time period and that thermal effects might be important in particular a thermally sensitive dislocation takes longer to be emitted from the crack edge region than one described in a non thermal analysis but on the other hand does not arrest moreover in contrast to the simple relaxation effect seen in non thermal analyses dislocation generation here causes oscillations in the dynamic stress intensity factor finally the average temperature gradient across the dislocation cut is large enough to suggest that generation may be a potential source of local material disorder

zero relaxation and dissipation limits for hyperbolic conservation laws we are interested in hyperbolic systems of conservation laws with relaxation and dissipation particularly the zero relaxation limit such a limit is of interest in several physical situations including gas flow near thermo equilibrium kinetic theory with small mean free path and viscoelasticity with vanishing memory in this article we study hyperbolic systems of two conservation laws with relaxation for the stable case where the equilibrium speed is subcharacteristic with respect to the frozen speeds we illustrate for a model in viscoelasticity that no oscillation develops for the nonlinear system in the zero relaxation limit for the marginally stable case where the equilibrium speed may equal one of the frozen speeds we show for a model in phase transitions that no oscillation arises when the dissipation is present and goes to zero more slowly than the relaxation our analysis includes the construction of suitable entropy pairs to derive energy estimates we need such energy estimates not only for the compactness properties but also for the deviation from the equilibrium of the solutions for the relaxation systems the theory of compensated compactness is then applied to study the oscillation in the zero relaxation limit 1993 john wiley sons inc

a sufficient condition for convergence of sampled data consensus for double integrator dynamics with nonuniform and time varying communication delays this technical note investigates a discrete time second order consensus algorithm for networks of agents with nonuniform and time varying communication delays under dynamically changing communication topologies in a sampled data setting some new proof techniques are proposed to perform the convergence analysis it is finally shown that under certain assumptions upon the velocity damping gain and the sampling period consensus is achieved for arbitrary bounded time varying communication delays if the union of the associated digraphs of the interaction matrices in the presence of delays has a directed spanning tree frequently enough

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

state agreement for continuous time coupled nonlinear systems two related problems are treated in continuous time first the state agreement problem is studied for coupled nonlinear differential equations the vector fields can switch within a finite family associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems generalizing the work of moreau under the assumption that the vector fields satisfy a certain subtangentiality condition it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time the proof uses nonsmooth analysis second the rendezvous problem for kinematic point mass mobile robots is studied when the robots fields of view have a fixed radius the circumcenter control law of ando e ieee trans robotics automation 15 1999 pp 818 828 is shown to solve the problem the rendezvous problem is a kind of state agreement problem but the interaction structure is state dependent

response of welded thermoelastic solids to the rapid motion of thermomechanical sources parallel to the interface abstract the analysis of rapidly moving thermomechanical surface sources is extended to the study of buried thermomechanical sources that move parallel to the interface of two welded dissimilar thermoelastic half spaces at a constant subcritical speed the sources are manifest as body force line loads in the coupled equations of thermoelasticity and a 2 d steady state situation is treated exact integral transform solutions are obtained and expressions for the displacements and temperature changes are generated by analytical inversion of robust asymptotic versions of the transforms these expressions show that thermoelastic coupling effects increase with source speed and that the thermal source is always manifest in combination with a component of the mechanical source i e an effective thermal source term exists the expressions also exhibit component functions that are in effect hybrids of functions that are seen in purely thermal and isothermal elastic solutions the critical source speed is defined as the minimum of the two asymptotic thermoelastic rayleigh speeds in the half spaces and when it exists the asymptotic thermoelastic stoneley speed exact expressions for these speeds are given and used to present some typical values

synchronization and convergence of linear dynamics in random directed networks recently methods in stochastic control are used to study the synchronization properties of a nonautonomous discrete time linear system x k 1 g k x k where the matrices g k are derived from a random graph process the purpose of this note is to extend this analysis to directed graphs and more general random graph processes rather than using lyapunov type methods we use results from the theory of inhomogeneous markov chains in our analysis these results have been used successfully in deterministic consensus problems and we show that they are useful for these problems as well sufficient conditions are derived that depend on the types of graphs that have nonvanishing probabilities for instance if a scrambling graph occurs with nonzero probability then the system synchronizes

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper