on the diffusion in a lattice gas model group theoretic approach motivated by some recent results concerning the model of a noninteracting one dimensional lattice gas with an order preservation of particles where multiple occupancy of the sites is not excluded we give new symmetries and new reductions of the corresponding continuum nonlinear partial differential equation closed form analytic solutions are found

new exact solutions of heat conduction in metals we consider the way in which a solution to a class of nonlinear partial differential equationss u ut k u ux x approaches the similarity form the problem we solve is chosen for two main reasons first the equation above is of widespread use in modeling physical situations and second it provides a tractable but significant example of a free boundary problem

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

distributed adaptive consensus and output tracking of unknown linear systems on directed graphs this paper considers both the distributed consensus control and output tracking problems of a group of unknown linear subsystems using the relative output information of neighboring subsystems each system is a minimum phase siso system with relative degree one and unknown parameters and the interaction graph among the subsystems is directed for the case where the directed graph is strongly connected a distributed adaptive protocol is designed to achieve consensus for the case where there exists an arbitrary constant reference signal a distributed adaptive controller together with an internal model are presented to achieve output tracking in the sense that the subsystem outputs asymptotically follow a reference constant the proposed adaptive protocols are independent of the parameters of the subsystems only use the relative outputs of neighboring subsystems and hence are fully distributed

sampled data consensus for multi agent systems with quantised communication this paper studies the sampled data consensus problem of first order and second order multi agent systems mass with logarithmic quantised information transmission both undirected and directed communication topologies are considered under the undirected connected communication topology we adopt for each agent the standard consensus protocols based on the logarithmic quantised relative states between neighbouring agents under the directed communication topology so as to preserve the weighted average of agents states we utilise the encoding decoding strategy to transmit quantised information and estimate neighbouring agents states and then distributed control laws based on the state estimates are employed for each agent under both kinds of communication topologies we prove that for any given sampling period by designing appropriate control gains first order mass can reach consensus for any given quantiser accuracy while second order mass can reach consensus if the quantiser accuracy is smal

area stationary surfaces in the heisenberg group h1 we consider area stationary surfaces perhaps with a volume constraint in the heisenberg group h1 endowed with its carnot caratheodory distance by analyzing the first variation of area we characterize c2 area stationary surfaces as those with mean curvature zero or constant if a volume preserving condition is assumed and such that the characteristic curves meet orthogonally the singular curves moreover a minkowski type formula relating the area the mean curvature and the volume is obtained for volume preserving area stationary surfaces enclosing a given region as a consequence of the characterization of area stationary surfaces we refine the bernstein type theorem given in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 and nicola garofalo scott pauls the bernstein problem in the heisenberg group arxiv math dg 0209065 to describe all c2 entire area stationary graphs over the xy plane in a calibration argument shows that these graphs are globally area minimizing finally by using the description of the singular set in jih hsin cheng jenn fang hwang andrea malchiodi paul yang minimal surfaces in pseudohermitian geometry ann sc norm super pisa cl sci 5 4 1 2005 129 177 mr 2165405 the characterization of area stationary surfaces and the ruling property of constant mean curvature surfaces we prove our main results where we classify area stationary surfaces in with or without a volume constraint and non empty singular set in particular we deduce the following counterpart to alexandrov uniqueness theorem in euclidean space any compact connected c2 surface in area stationary under a volume constraint must be congruent to a rotationally symmetric sphere obtained as the union of all the geodesics of the same curvature joining two points as a consequence we solve the isoperimetric problem in assuming c2 smoothness of the solutions 13 completely reducible hypersurfaces in a pencil pages 672 688 j v pereira s yuzvinsky preview pdf 324 k related articles 14 modules over motivic cohomology pages 689 727 oliver rondigs paul arne ostvaer preview pdf 303 k related articles 15 the fundamental group of period domains over finite fields pages 728 741 sascha orlik preview pdf 154 k related articles articles 1 15

designing fully distributed consensus protocols for linear multi agent systems with directed graphs this technical note addresses the distributed consensus protocol design problem for multi agent systems with general linear dynamics and directed communication graphs existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the laplacian matrix associated with the communication graph which however is global information in this technical note based on only the agent dynamics and the relative states of neighboring agents a distributed adaptive consensus protocol is designed to achieve leader follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node the proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed extensions to the case with multiple leaders are further studied

consensus in time delayed multi agent systems with quantized dwell times abstract this paper investigates the effects of quantized dwell times in solving consensus problems in time delayed multi agent systems with the asynchronous property of unpredictable quantization jumps in inter agent communications the quantized dwell times can be introduced on purpose or be inherent from quantizing devices they beneficially avoid undesirable fast chattering of quantizers outputs and mathematical difficulties in convergence analysis the main result shows that the largest eigenvalue of the interaction graph laplacian well characterizes the dependence of maximum allowable time delay on quantized dwell times and quantizer parameters under the assumption of heterogeneous time varying transmission delays simulations are presented to show the effectiveness of the main result

classification of the similarity solutions of free kramers equation we obtain a complete classification of all possible nontrivial similarity solutions of the free kramers equations together with a necessary and sufficient condition for each type to be reducible to the heat equation a confluent hypergeometric solution of the free kramers equation is derived for some classes of similarity solutions

genericity results for singular curves let m be a smooth manifold and cal d m m geq 2 be the set of rank m distributions on m endowed with the whitney c infty topology we show the existence of an open set o m dense in cal d m so that every nontrivial singular curve of a distribution d of o m is of minimal order and of corank one in particular for m geq 3 every distribution of o m does not admit nontrivial rigid curves as a consequence for generic sub riemannian structures of rank greater than or equal to three there does not exist nontrivial minimizing singular curves

isoholonomic problems and some applications we study the problem of finding the shortest loops with a given holonomy we show that the solutions are the trajectories of particles in yang mills potentials theorem 4 or equivalently the projections of kaluza klein geodesics theorem 2 applications to quantum mechanics berry s phase sect 3 and the optimal control of deformable bodies sect 6 are touched upon

on the rendezvous problem for multiple nonholonomic agents in this note a decentralized feedback control strategy that drives a system of multiple nonholonomic unicycles to a rendezvous point in terms of both position and orientation is introduced the proposed nonholonomic control law is discontinuous and time invariant and using tools from nonsmooth lyapunov theory and graph theory the stability of the overall system is examined similarly to the linear case the convergence of the multi agent system relies on the connectivity of the communication graph that represents the inter agent communication topology the control law is first defined in order to guarantee connectivity maintenance for an initially connected communication graph moreover the cases of static and dynamic communication topologies are treated as corollaries of the proposed framework

non minimality of corners in subriemannian geometry we give a short solution to one of the main open problems in subriemannian geometry namely we prove that length minimizers do not have corner type singularities with this result we solve problem ii of agrachev s list and provide the first general result toward the 30 year old open problem of regularity of subriemannian geodesics

similarity solutions for fragmenting systems with continuous mass loss a linear rate equation describing fragmentation processes which includes both continuous and discrete loss of mass is reduced to a partial differential equation different types of similarity solutions are obtained by applying lie s similarity method

discontinuities and hysteresis in quantized average consensus we consider continuous time average consensus dynamics in which the agents states are communicated through uniform quantizers solutions to the resulting system are defined in the krasowskii sense and are proven to converge to conditions of practical consensus to cope with undesired chattering phenomena we introduce a hysteretic quantizer and we study the convergence properties of the resulting dynamics by a hybrid system approach

smoothness of subriemannian isometries we show that the group of isometries i e distance preserving homeomorphisms of an equiregular subriemannian manifold is a finite dimensional lie group of smooth transformations the proof is based on a new pde argument in the spirit of harmonic coordinates establishing that in an arbitrary subriemannian manifold there exists an open dense subset where all isometries are smooth

new classes of similarity solutions of the inhomogeneous nonlinear diffusion equations the lie similarity method has been used to extend the similarity solutions of the one dimensional inhomogeneous nonlinear diffusion equations we determine the lie point symmetry vector fields and calculate the similarity ansatz then we discuss the resulting nonlinear ordinary differential equations exact solutions are found and their relations to some real physical situations are discussed

brief paper stability analysis for multi agent systems using the incidence matrix quantized communication and formation control the spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi agent control problems in particular we consider the problem of state agreement with quantized communication and the problem of distance based formation control in both cases stabilizing control laws are provided when the communication graph is a tree it is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi agent control problems

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

consensus with quantized relative state measurements in this paper cooperative control of multi agent systems under limited communication between neighboring agents is investigated in particular quantized values of the relative states are used as the control parameters by taking advantage of tools from nonsmooth analysis explicit convergence results are derived for both uniform and logarithmic quantizers under static and time varying communication topologies compared with our previous work less conservative conditions that ensure global convergence are provided moreover second order dynamical systems under similar constraints are taken into account computer simulations are provided to demonstrate the validity of the derived results

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control