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

on the a_ infty conditions for general bases we discuss several characterizations of the a infty class of weights in the setting of general bases although they are equivalent for the usual muckenhoupt weights we show that they can give rise to different classes of weights for other bases we also obtain new characterizations for the usual a infty weights

on global leader following consensus of identical linear dynamic systems subject to actuator saturation abstract this paper studies the leader following consensus problem for a group of agents with identical linear systems subject to control input saturation we focus on two classes of linear systems neutrally stable systems and double integrator systems for neurally stable systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with proper choices of relative potential functions global consensus can also be achieved over a switching communication topology for double integrator systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with the help of a simple saturation function in the local feedback laws global consensus can also be achieved over a switching communication topology simulation results illustrate the theoretical results

ls μ averaging domains abstract in this paper we first introduce l s averaging domains which are generalizations of l s averaging domains introduced by s g staples we characterize l s averaging domains using the quasihyperbolic metric as applications we prove norm inequalities for conjugate a harmonic tensors in l s averaging domains which can be considered as generalizations of the hardy and littlewood theorem for conjugate harmonic functions finally we give applications to quasiconformal and quasiregular mappings

fractional integrals on weighted hardy spaces abstract in this paper applying the atomic decomposition and molecular characterization of the real weighted hardy spaces h w p r n we give the weighted boundedness of the homogeneous fractional integral operator t from h w p p r n to l q w q r n and from h w p p r n to h w q q r n

boundedness properties in a family of weighted morrey spaces with emphasis on power weights abstract we define a scale of weighted morrey spaces which contains different versions of weighted spaces appearing in the literature this allows us to obtain weighted estimates for operators in a unified way in general we obtain results for weights of the form x w x with w a p and nonnegative we study particularly some properties of power weighted spaces and in the case of the hardy littlewood maximal operator our results for such spaces are sharp by using extrapolation techniques the results are given in abstract form in such a way that they are automatically obtained for many operators

distributed continuous time optimization nonuniform gradient gains finite time convergence and convex constraint set in this paper a distributed optimization problem with general differentiable convex objective functions is studied for continuous time multi agent systems with single integrator dynamics the objective is for multiple agents to cooperatively optimize a team objective function formed by a sum of local objective functions with only local interaction and information while explicitly taking into account nonuniform gradient gains finite time convergence and a common convex constraint set first a distributed nonsmooth algorithm is introduced for a special class of convex objective functions that have a quadratic like form it is shown that all agents reach a consensus in finite time while minimizing the team objective function asymptotically second a distributed algorithm is presented for general differentiable convex objective functions in which the interaction gains of each agent can be self adjusted based on local states a corresponding condition is then given to guarantee that all agents reach a consensus in finite time while minimizing the team objective function asymptotically third a distributed optimization algorithm with state dependent gradient gains is given for general differentiable convex objective functions it is shown that the distributed continuous time optimization problem can be solved even though the gradient gains are not identical fourth a distributed tracking algorithm combined with a distributed estimation algorithm is given for general differentiable convex objective functions it is shown that all agents reach a consensus while minimizing the team objective function in finite time fifth as an extension of the previous results a distributed constrained optimization algorithm with nonuniform gradient gains and a distributed constrained finite time optimization algorithm are given it is shown that both algorithms can be used to solve a distributed continuous time optimization problem with a common convex constraint set numerical examples are included to illustrate the obtained theoretical results

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

sobolev inequalities for products of powers we derive weighted sobolev inequalities of the form if lllq ciivfiilp f e co ri 1 p q oo for classes of weight functions u v which include v s that are a finite product of certain power weights times an ap function

constrained consensus in unbalanced networks with communication delays in this note a constrained consensus problem is studied for multi agent systems in unbalanced networks in the presence of communication delays here each agent needs to lie in a closed convex constraint set while reaching a consensus the communication graphs are directed dynamically changing and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length the analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary to tackle the loss of symmetry caused by unbalanced graphs and communication delays a novel approach is proposed the idea is to estimate the distance from each agent to the intersection set of all agents constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction it is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system it is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded finally a numerical example is included to illustrate the obtained theoretical results

fractional integrals on weighted and spaces we characterize the pairs of doubling weights u v on rn such that iiwiihj ch hj 0 0 is the fractional integral operator we also consider the behavior of an associated maximal function applications of the results to sobolev inequalities in weighted lp spaces are given 1 introduction and notation in this paper we will characterize the pairs of doubling weights it v on rn such that pafwm 0 is the fractional integral operator we shall also give applications of these results to sobolev inequalities in weighted lp spaces a weight function u is said to belong to ds p 1 if u tq 1 and every cube q c rn where u q denotes the u measure of q and tq is the cube with the same center as q but with t times the edgelength we write dx j idu analogously u g rdv v 0 if u tq ctnuu q for every t 1 and every cube q it is not hard to see that if u g d then u g rdv for some v 0 we write u rhr r 1 if 1 1 r 1 rprr u x t dx i x dx 0 and e s then we denote as usual f x t f 0t x where t x t n x t and n f x sup f y t vfithta x y t yern t 0 x y 0

cumulants for random matrices as convolutions on the symmetric group in this paper we show that free cumulants can be naturally seen as the limiting value of cumulants of matrices we define these objects as functions on the symmetric group by some convolution relations involving the generalized moments we state that some characteristic properties of the free cumulants already hold for these cumulants

the structure of the reverse holder classes in this paper we study the structure of the class of functions rhs which satisfy the reverse holder inequality with exponent s i to do so we introduce a new operator the minimal operator which is analogous to the hardy littlewood maximal operator and a new class of functions rhcc which plays the same role for rhs that the class ax does for the ap classes

global consensus for discrete time multi agent systems with input saturation constraints in this paper we consider the global consensus problem for discrete time multi agent systems with input saturation constraints under fixed undirected topologies we first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents we then focus on two special cases where the agent model is either neutrally stable or a double integrator for the neutrally stable case any linear protocol of a particular form which solves the consensus problem for the case without input saturation constraints also solves the global consensus problem for the case with input saturation constraints for the double integrator case we show that a subset of linear protocols which solve the consensus problem for the case without saturation constraints also solve the global consensus problem for the case with input saturation constraints the results are illustrated by numerical simulations

distributed multi agent optimization subject to nonidentical constraints and communication delays in this paper we study a distributed optimization problem using a subgradient projection algorithm for multi agent systems subject to nonidentical constraints and communication delays under local communication here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions each of which is known to only one agent first we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs instead the agents optimize a weighted sum of the local objective functions then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length furthermore we consider the case of communication delays where the delays are mutually independent it is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded finally numerical examples are included to show the obtained theoretical results

a characterization of two weight norm inequalities for fractional and poisson integrals caracterisation de deux inegalites de normes ponderees pour les integrales fractionnaires et de poisson applications aux operateurs differentiels elliptiques degeneres

distributed h constrained consensus problem abstract this paper is concerned with the distributed h constrained consensus problem for multi agent systems the objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired h performance index in the presence of external disturbances a nonlinear distributed algorithm is adopted to solve this constrained consensus problem to measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set a nonlinear function is constructed as the h output function by analyzing the convexity of the convex set a sufficient condition is given to solve the constrained consensus problem with the desired h performance finally a numerical simulation example is provided to show the effectiveness of our theoretical results

consensus of a class of second order multi agent systems with time delay and jointly connected topologies this technical note investigates consensus problems of a class of second order continuous time multi agent systems with time delay and jointly connected topologies we first introduce a neighbor based linear protocol with time delay then we derive a sufficient condition in terms of linear matrix inequalities lmis for average consensus of the system furthermore we discuss the case where the time delay affects only the information that is being transmitted and show that consensus can be reached with arbitrary bounded time delay finally simulation results are provided to demonstrate the effectiveness of our theoretical results

lyapunov based approach to multiagent systems with switching jointly connected interconnection this note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies neighbor based rules are adopted to realize local control strategies for these continuous time autonomous agents described by double integrators although the interagent connection structures vary over time and related graphs may not be connected a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed lyapunov based approach and related space decomposition technique

reaching an optimal consensus dynamical systems that compute intersections of convex sets in this paper multi agent systems minimizing a sum of objective functions where each component is only known to a particular node is considered for continuous time dynamics with time varying interconnection topologies assuming that each node can observe a convex solution set of its optimization component and the intersection of all such sets is nonempty the considered optimization problem is converted to an intersection computation problem by a simple distributed control rule the considered multi agent system with continuous time dynamics achieves not only a consensus but also an optimal agreement within the optimal solution set of the overall optimization objective directed and bidirectional communications are studied respectively and connectivity conditions are given to ensure a global optimal consensus in this way the corresponding intersection computation problem is solved by the proposed decentralized continuous time algorithm we establish several important properties of the distance functions with respect to the global optimal solution set and a class of invariant sets with the help of convex and non smooth analysis

higher order commutators for vector valued calderon zygmund operators weighted norm estimates for higher order commutators are obtained the proof that remain valid in the vector valued case are obtained as an application of some extrapolation results the vector valued version of the commutator theorem is applied to the carleson operator u m d banach spaces approximate identities and maximal operators

weighted norm inequalities for potential operators on donne des conditions suffisantes pour que des inegalites de la forme g x y f y d y 9 d x 1 9 c f y p d y 1 p soient vraies pour des fonctions mesurables f on determine la dependance de la constante c par rapport aux mesures

boundedness of singular integral operators with variable kernels abstract let k be a generalized calderon zygmund kernel defined on r n r n 0 the singular integral operator with variable kernel given by t f x p v r n k x x y f y d y is studied we show that if the kernel k x y satisfies the l q hormander condition with respect to x and y variables respectively then t is bounded on l w p if we add an extra dini type condition on k then we may show the h w p l w p boundedness of t