global target aggregation and state agreement of nonlinear multi agent systems with switching topologies in this paper we discuss coordination problems of a group of autonomous agents including the target aggregation to a convex set and the state agreement the aggregation of the whole agent group consisting of leaders informed agents and followers to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval t for any time t and then the state agreement problem is studied in a similar way an approach based on set stability and limit set analysis is given to study the multi agent convergence problems with the help of graph theory and convex analysis coordination conditions are obtained in some important cases and the results show that simple local rules can make the networked agents with first order nonlinear individual dynamics achieve desired collective behaviors

finite time consensus for controlled dynamical systems in network abstractthe key challenges in networked dynamical systems are the component heterogeneities nonlinearities and the high dimension of the formulated vector of state variables in this paper the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift for each model structure that defines homogeneous and heterogeneous multi system behaviour we derive protocols leading to finite time consensus for each model evolving in networks forming a homogeneous or heterogeneous multi system protocols integrating sufficient conditions are derived leading to finite time consensus likewise for the networking topology we make use of fixed directed and undirected graphs to prove our approaches finite time stability theory and lyapunov methods are considered as illustrative examples the homogeneous multi unicycle kinematics and the homogeneous heterogeneous multi second order dynamics in networks are studied

adaptive finite time bipartite consensus for second order multi agent systems with antagonistic interactions abstract this paper is concerned with the adaptive finite time bipartite consensus problems for networked second order multi agent systems with antagonistic interactions and unknown external disturbances a signed undirected graph is used to describe the interactions among agents for the leaderless case continuous nonlinear distributed protocols with adaptive update laws are given which can not only guarantee the bipartite steady state errors of any two agents converge to a small region in finite time but also eliminate the chattering problem then the proposed algorithm is extended to solve the adaptive finite time bipartite consensus tracking problem for leader follower case by designing distributed finite time estimator simulation example is included to show the effectiveness of the presented methods

adaptive finite time consensus in multi agent networks abstract this paper is concerned with the finite time consensus problem of distributed agents having non identical unknown nonlinear dynamics to a leader agent that also has unknown nonlinear control input signal by parameterization of unknown nonlinear dynamics a lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite time consensus control protocol in undirected networks homogeneous lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous theoretical analysis shows that leader following consensus can be achieved in finite time meanwhile finite time parameter convergence can be also guaranteed under the proposed control scheme an example is given to validate the theoretical results

finite time coordination in multiagent systems using sliding mode control approach abstract finite time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time in this paper we use the notion of finite time stability to apply it to the problem of coordinated motion in multiagent systems specifically we consider a group of agents described by fully actuated euler lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady state distances between the neighboring agents in finite time we use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph laplacian matrix furthermore using sliding mode control approach we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state sliding mode control is known to drive the system states to the sliding surface in finite time the key feature of our approach is in the design of non smooth sliding surfaces such that while on the sliding surface the error states converge to the origin in finite time thus ensuring finite time coordination among the agents in the network in addition we discuss the case of switching communication topologies in multiagent systems finally we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents

rank one drinfeld modules on elliptic curves the sgn normalized rank one drinfeld modules 0 associated with all elliptic curves e over fq for 4 q 13 are computed in explicit form such 0 for q 4 were computed previously these computations verify a conjecture of dorman on the norm of j q aq l and also suggest some interesting new properties of 0 we prove dorman s conjecture in the ramified case we also prove the formula deg n a q hk 1 q where n a is the norm of a and hk is the class number of k fq e we describe a remarkable conjectural property of the trace of a in even characteristic that holds in all the examples in his recent paper 1 on the factorization of norms of j invariants of ranktwo drinfeld modules with complex multiplications d dorman conjectured that such norms are monic elements of fq x dorman computed the jinvariants in several examples and found his conjecture valid in all of them for this purpose he used the rank one examples from 6 the first extensive computational test of the conjecture was carried out by one of us dummit who computed the rank one drinfeld modules associated with all elliptic curves over fq with q 13 see 3 below the results of these computations may be found on the microfiche card included at the end of this issue inspired by these computations one of us hayes proved dorman s conjecture when the infinite place is ramified see 2 below in 3 we describe an algorithm for computing the rank one drinfeld modules associated with any hyperelliptic curve over fqq and we prove some basic attributes of the algorithm in 4 we prove formulas for the degrees of the norm and trace of the j invariants of drinfeld modules associated with elliptic curves these formulas were first observed computationally they suggest a number of interesting questions for elliptic curves with complex multiplications in characteristic zero in 5 we state some conjectures about the remarkable form of the trace term in characteristic two these conjectures are supported by all our computations

distributed exponential finite time coordination of multi agent systems containment control and consensus in this paper exponential finite time coordination problems of multi agent systems are investigated including containment control and consensus the theoretical basis is that a class of nonlinear systems has favourable finite time convergence characteristic for the objective of containment control the proposed protocol ensures that the boundary agents in the same strong component exponentially reach a consensus and the internal agents exponentially converge to the convex hull spanned by the boundary agents in a finite time for the objective of consensus a pinning control strategy is designed for a fraction of agents such that all the agents exponentially reach a consensus with the leader in a finite time the distinguished features of this paper lie in the following two points 1 a smaller settling time of the lyapunov function is obtained which manifests in a faster convergence rate than the traditional one and 2 the weakly connected topology considered in this paper is more general than the o

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

a nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems a new infinitesimal sufficient condition is given for uniform global asymptotic stability ugas for time varying nonlinear systems it is used to show that a certain relaxed persistency of excitation condition called uniform spl delta persistency of excitation u spl delta pe is sufficient for uniform global asymptotic stability in certain situations u spl delta pe of the right hand side of a time varying differential equation is also shown to be necessary under a uniform lipschitz condition the infinitesimal sufficient condition for ugas involves the inner products of the flow field with the gradients of a finite number of possibly sign indefinite locally lipschitz lyapunov like functions these inner products are supposed to be bounded by functions that have a certain nested or triangular negative semidefinite structure this idea is reminiscent of a previous idea of matrosov who supplemented a lyapunov function having a negative semidefinite derivative with an additional function having a derivative that is definitely nonzero where the derivative of the lyapunov function is zero for this reason we call the main result a nested matrosov theorem the utility of our results on stability analysis is illustrated through the well known case study of the nonholonomic integrator

consensus of multi agent systems based on sampled data control this article studies the consensus problem in directed networks assuming that each agent is with double integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants we propose a protocol based on sampled data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol in virtue of this equivalent characterisation we further consider two cases fixed topology and switching topology for the first case we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem for the second case we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals respectively finally simulations are provided to illustrate the effectiveness of the theoretical results

a consensus algorithm in cat 0 space and its application to distributed fusion of phylogenetic trees abstract based on convex analysis a novel consensus algorithm of dynamical points in a cat 0 space is developed in this paper in which the associated communication graph uniformly contains a directed spanning tree the proposed algorithm provides an efficient method of solving consensus problems in a general cat 0 space while having certain robustness against weak communication the application of the new algorithm to the distributed fusion of phylogenetic trees is shown with demonstrative case simulations together with a study on the algorithm s robustness and efficiency

regularization for uniform spatial resolution properties in penalized likelihood image reconstruction traditional space invariant regularization methods in tomographic image reconstruction using penalized likelihood estimators produce images with nonuniform spatial resolution properties the local point spread functions that quantify the smoothing properties of such estimators are space variant asymmetric and object dependent even for space invariant imaging systems the authors propose a new quadratic regularization scheme for tomographic imaging systems that yields increased spatial uniformity and is motivated by the least squares fitting of a parameterized local impulse response to a desired global response the authors have developed computationally efficient methods for pet systems with shift invariant geometric responses they demonstrate the increased spatial uniformity of this new method versus conventional quadratic regularization schemes in simulated pet thorax scans

discriminative feature representation to improve projection data inconsistency for low dose ct imaging in low dose computed tomography ldct imaging the data inconsistency of measured noisy projections can significantly deteriorate reconstruction images to deal with this problem we propose here a new sinogram restoration approach the sinogram discriminative feature representation s dfr method different from other sinogram restoration methods the proposed method works through a 3 d representation based feature decomposition of the projected attenuation component and the noise component using a well designed composite dictionary containing atoms with discriminative features this method can be easily implemented with good robustness in parameter setting its comparison to other competing methods through experiments on simulated and real data demonstrated that the s dfr method offers a sound alternative in ldct

consensus on complete riemannian manifolds in finite time abstract in view of the fact that prototypes of riemannian manifolds range from euclidean surfaces to lie groups operator spaces etc the paper explores common consensus schemes for connected complete riemannian manifolds after studying the restriction exponential map we introduce a local consensus protocol with switching communication topologies for the manifolds via the isometric mapping based on one of the euclidean consensus protocols equipped with the compression decompression functions we extend the local consensus protocol and put forth a global consensus algorithm for any such manifolds these consensus schemes can provide common solutions to the consensus problems arising from various nonlinear spaces or abstract spaces belonging to connected complete riemannian manifolds in particular they are simple and concise and can converge in finite time simulation on the unit sphere is provided to verify our consensus schemes and to demonstrate the usage of our proposed techniques

reduction of noise induced streak artifacts in x ray computed tomography through spline based penalized likelihood sinogram smoothing we present a statistically principled sinogram smoothing approach for x ray computed tomography ct with the intent of reducing noise induced streak artifacts these artifacts arise in ct when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements while these approaches involve loose consideration of the measurement statistics to determine smoothing levels they do not explicitly model the statistical distributions of the measurement data we present an explicitly statistical approach to sinogram smoothing in the presence of photon starved measurements it is an extension of a nonparametric sinogram smoothing approach using penalized poisson likelihood functions that we have previously developed for emission tomography because the approach explicitly models the data statistics it is naturally adaptive it will smooth more variable measurements more heavily than it does less variable measurements we find that it significantly reduces streak artifacts and noise levels without comprising image resolution

optimal finite time consensus on fixed and periodic graphs synthesis of optimal controllers achieving finite time consensus for multiagent networks described by fixed or periodic connectivity graphs is considered the solution procedure involves posing a partially nested finite horizon decentralized control problem and converting it to a static convex optimization problem by a quadratic invariance argument the dynamic feedback controller thus synthesized optimizes a transient performance measure and guarantees consensus within a minimal number of steps

finite time connectivity preserving consensus of networked nonlinear agents with unknown lipschitz terms this technical note studies finite time consensus problem for a team of networked nonlinear agents with unknown lipschitz terms under communication constraints where each agent has a limited sensing range because the induced interaction graph is typically state dependent and dynamic we propose a distributed nonlinear consensus algorithm that is capable of preserving the initial interaction patterns by using tools from nonsmooth analysis sufficient conditions are obtained such that finite time consensus can be reached an upper bound of the convergence time is derived via a two step analysis the validity of the theoretical result is shown by one simulation example

feedback stabilization and lyapunov functions given a locally defined nondifferentiable but lipschitz lyapunov function we employ it in order to construct a discontinuous feedback law which stabilizes the underlying system to any given tolerance a converse result shows that suitable lyapunov functions of this type exist under mild assumptions we also establish that the feedback in question possesses a robustness property relative to measurement error despite the fact that it may not be continuous

finite time consensus using stochastic matrices with positive diagonals we discuss the possibility of reaching consensus in finite time using only linear iterations with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure we show that finite time average consensus can always be achieved for connected undirected graphs for directed graphs we show some necessary conditions for finite time consensus including strong connectivity and the presence of a simple cycle of even length

finite time weighted average consensus with respect to a monotonic function and its application abstract the consensus state is an important and fundamental quantity for consensus problems of multi agent systems which indicates where all the dynamical agents reach in this paper weighted average consensus with respect to a monotonic function which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values is studied for a group of kinematic agents with time varying topology by constructing a continuous nonlinear distributed protocol such a consensus problem can be solved in finite time even though the time varying topology involves unconnected graphs then the distributed protocol is employed to compute the maximum likelihood estimation of unknown parameters over sensor networks compared with the existing results the estimate scheme proposed here may reduce the costs of data communication storage memory book keeping and computational overheads

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

fourier series and the special values of l functions let k be a number field with ring of integers a let x be an idele class character for k which is trivial at each infinite place the l series l s x c x b nb is defined by the sum over all non trivial ideals b of a which are prime to the conductor f of x this sum is absolutely convergent for re s 1 when x is non trivial l s x extends analytically to a neighborhood of s 1 and jc 1 x is o although this value is of great arithmetic interest truly satisfactory formulas for l 1 x have only been obtained in the cases when k q and when k is imaginary quadratic where they are due to dirichlet and kronecker respectively these number fields are precisely the one with a unique archimedean completion k in this case a is a discrete co compact subring of a locally compact field k an analogous situation exists for global function fields k over finite fields let oc be a place of k and let a denote the ring of functions which are regular outside co then a is a discrete co compact subring of the completion k which is a locally compact field if x is an idele class character for k which is trivial at cc and we define l s x as above then for x 1 the series is regular and non zero at s 1 formulas for l 1 x were obtained by galovich and rosen in the case when a is isomorphic to the ring of polynomials over a finite field and by hayes in general in this paper we will reprove all the limit formulas for l 1 x in a uniform manner using fourier analysis on the locally compact field k we shall also obtain the functional equation of l s x following the

coordination and geometric optimization via distributed dynamical systems this paper discusses dynamical systems for disk covering and sphere packing problems we present facility location functions from geometric optimization and characterize their differentiable properties we design and analyze a collection of distributed control laws that are related to nonsmooth gradient systems the resulting dynamical systems promise to be of use in coordination problems for networked robots in this setting the distributed control laws correspond to local interactions between the robots the technical approach relies on concepts from computational geometry nonsmooth analysis and the dynamical system approach to algorithms

distributed average tracking of multiple time varying reference signals with bounded derivatives we present a distributed discontinuous control algorithm for a team of agents to track the average of multiple time varying reference signals with bounded derivatives we use tools from nonsmooth analysis to analyze the stability of the system for time invariant undirected connected network topologies we prove that the states of all agents will converge to the average of the time varying reference signals with bounded derivatives in finite time provided that the control gain is properly chosen the validity of this result is also established for scenarios with switching undirected connected network topologies for time invariant directed network topologies with a directed spanning tree we show that all agents will still reach a consensus in finite time but the convergent value is generally not the average of the time varying reference signals with bounded derivatives simulation examples are presented to show the validity of the above results

electronic noise modeling in statistical iterative reconstruction we consider electronic noise modeling in tomographic image reconstruction when the measured signal is the sum of a gaussian distributed electronic noise component and another random variable whose log likelihood function satisfies a certain linearity condition examples of such likelihood functions include the poisson distribution and an exponential dispersion ed model that can approximate the signal statistics in integration mode x ray detectors we formulate the image reconstruction problem as a maximum likelihood estimation problem using an expectation maximization approach we demonstrate that a reconstruction algorithm can be obtained following a simple substitution rule from the one previously derived without electronic noise considerations to illustrate the applicability of the substitution rule we present examples of a fully iterative reconstruction algorithm and a sinogram smoothing algorithm both in transmission ct reconstruction when the measured signal contains additive electronic noise our simulation studies show the potential usefulness of accurate electronic noise modeling in low dose ct applications

finite time consensus with disturbance rejection by discontinuous local interactions in directed graphs in this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous time first order integrator dynamics affected by bounded disturbances the topology of the network is described by a directed graph the proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time an upper bound to the convergence time is explicitly derived in the technical note simulation results referring to a network of coupled kuramoto like oscillators are illustrated to corroborate the theoretical analysis

distributed average tracking for reference signals with bounded accelerations in this technical note the distributed average tracking dat problem for reference signals with bounded accelerations is considered a sliding mode surface is designed such that trajectories on the surface will achieve dat a discontinuous control algorithm is then proposed to guarantee that the surface can be reached in finite time it is shown that if the switching network topology is connected at all time then dat can be solved by properly choosing a gain parameter of the algorithm

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

nonsingular fixed time consensus tracking for second order multi agent networks this paper investigates the fixed time consensus tracking problem for second order multi agent systems in networks with directed topology global well defined nonlinear consensus protocols are constructed with the aid of a newly designed sliding surface for each double integrator agent dynamics in particular the proposed framework eliminates the singularity and the settling time is assignable for any initial conditions this makes it possible for network consensus problems to design and estimate the convergence time off line finally simulation is included to demonstrate the performance of the new protocols

min max time consensus tracking with communication guarantee in this paper a collection of double integrator agents with bounded inputs is considered communication is possible between any two agents only if the inter agent distance is less than a fixed threshold a special node referred to as the leader generates an unknown reference trajectory to which all the other agents are required to converge in the shortest possible time assuming the initial communication graph to be connected a directed spanning tree rooted at the leader is identified using a local algorithm the dynamics of any two agents connected by an edge in the selected tree are modeled as a time optimal pursuit evasion game while maintaining the inter agent communication link using the corresponding feedback saddle point strategies local min max time control laws for each pair of agents are formulated for the selected tree the proposed collection of local min max time control strategies is shown to be the communication preserving global min max time strategy

revisiting normalized gradient descent fast evasion of saddle points the paper considers normalized gradient descent ngd a natural modification of classical gradient descent gd in optimization problems it is shown that contrary to gd ngd escapes saddle points quickly a serious shortcoming of gd in nonconvex problems is that it can take arbitrarily long to escape from the neighborhood of a saddle point in practice this issue can significantly slow the convergence of gd particularly in high dimensional nonconvex problems the paper focuses on continuous time dynamics it is shown that 1 ngd almost never converges to saddle points and 2 the time required for ngd to escape from a ball of radius r about a saddle point x is at most 5 sqrt kappa r where kappa is the condition number of the hessian of f at x as a simple application of these results a global convergence time bound is established for ngd under mild assumptions

consensus in directed networks of agents with nonlinear dynamics this technical note studies the consensus problem for cooperative agents with nonlinear dynamics in a directed network both local and global consensus are defined and investigated techniques for studying the synchronization in such complex networks are exploited to establish various sufficient conditions for reaching consensus the local consensus problem is first studied via a combination of the tools of complex analysis local consensus manifold approach and lyapunov methods a generalized algebraic connectivity is then proposed to study the global consensus problem in strongly connected networks and also in a broad class of networks containing spanning trees for which ideas from algebraic graph theory matrix theory and lyapunov methods are utilized

decentralized formation control of mobile agents a unified framework abstract this paper studies the formation control problem for systems consisting of multiple mobile agents that are described by first order differential equations and second order differential equations respectively the following issues are investigated bounded input disturbance and time delay in derivation of the main results a blend of graph theoretic and system theoretic tools is employed where local potential functions and lasalle s invariant principle play central roles finally numerical examples which support the analytical results very well are also included

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

on the stabilization in finite time of locally controllable systems by means of continuous time varying feedback law it is proven that if for any positive time t there exists an open loop control u a t depending continuously on the initial data a vanishing for a 0 and steering a small neighborhood of 0 into 0 in time t then the control system can be locally stabilized in small time by means of continuous time varying feedback law provided that the dimension of the state space is at least 4 and the strong accessibility rank condition holds

penalized weighted least squares approach to sinogram noise reduction and image reconstruction for low dose x ray computed tomography reconstructing low dose x ray computed tomography ct images is a noise problem this work investigated a penalized weighted least squares pwls approach to address this problem in two dimensions where the wls considers first and second order noise moments and the penalty models signal spatial correlations three different implementations were studied for the pwls minimization one utilizes a markov random field mrf gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the pwls cost function by iterative gauss seidel algorithm another employs karhunen loeve kl transform to de correlate data signals among nearby views and minimizes the pwls adaptively to each kl component by analytical calculation where the spatial correlation among nearby bins is modeled by the same gibbs functional the third one models the spatial correlations among image pixels in image domain also by a mrf gibbs functional and minimizes the pwls by iterative successive over relaxation algorithm in these three implementations a quadratic functional regularization was chosen for the mrf model phantom experiments showed a comparable performance of these three pwls based methods in terms of suppressing noise induced streak artifacts and preserving resolution in the reconstructed images computer simulations concurred with the phantom experiments in terms of noise resolution tradeoff and detectability in low contrast environment the kl pwls implementation may have the advantage in terms of computation for high resolution dynamic low dose ct imaging

finite time distributed consensus via binary control protocols this paper investigates the finite time distributed consensus problem for multi agent systems using a binary consensus protocol and the pinning control scheme compared with other consensus algorithms which need the complete state or output information of neighbors the proposed algorithm only requires sign information of the relative state measurements that is the differences between a node s state and that of its neighbors this corresponds to only requiring a single bit quantization error relative to each neighbor this signum protocol is realistic in terms of observed behavior in animal groups where relative motion is determined not by full time signal measurements but by coarse estimates of relative heading differences between neighbors the signum protocol does not require explicit measurement of time signals from neighbors and hence has the potential to significantly reduce the requirements for both computation and sensing analysis of discontinuous dynamical systems is used including the filippov solutions and set valued lie derivative based on the second order information on the evolution of lyapunov functions the conditions that guarantee the finite time consensus for the systems are identified numerical examples are given to illustrate the theoretical results

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

finite time distributed linear equation solver for solutions with minimum l_1 norm this paper proposes a continuous time distributed algorithm for multiagent networks to achieve a solution with the minimum l 1 norm to underdetermined linear equations the proposed algorithm comes from a combination of the filippov set valued map with the projection consensus flow given the underlying network is undirected and fixed it is shown that the proposed algorithm drives all agents individual states to converge in finite time to a common value which is the minimum l 1 norm solution

finite time convergent gradient flows with applications to network consensus this paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function extending recent results on nonsmooth stability analysis we characterize their asymptotic convergence properties and identify conditions that guarantee finite time convergence we discuss the application of the results to consensus problems in multi agent systems and show how the proposed nonsmooth gradient flows achieve consensus in finite time

fixed time consensus tracking for multiagent systems with high order integrator dynamics this paper addresses the fixed time leader follower consensus problem for high order integrator multiagent systems subject to matched external disturbances a new cascade control structure based on a fixed time distributed observer is developed to achieve the fixed time consensus tracking control a simulation example is included to show the efficacy and the performance of the proposed control structure with respect to different initial conditions

distributed control of angle constrained cyclic formations using bearing only measurements abstract this paper studies distributed control of multi vehicle formations with angle constraints using bearing only measurements it is assumed that each vehicle can only measure the local bearings of their neighbors and there are no wireless communications among the vehicles the desired formation is a cyclic one whose underlying information flow is described by an undirected cycle graph we propose a distributed bearing only formation control law that ensures local exponential or finite time stability collision avoidance between any vehicles can be locally guaranteed in the absence of inter vehicle distance measurements

fixed time stable gradient flows applications to continuous time optimization this paper proposes novel gradient flow schemes that yield convergence to the optimal point of a convex optimization problem within a fixed time from any given initial condition for unconstrained optimization constrained optimization and min max problems it is shown that the solution of the modified gradient flow dynamics exists and is unique under certain regularity conditions on the objective function while fixed time convergence to the optimal point is shown via lyapunov based analysis the application of the modified gradient flow to unconstrained optimization problems is studied under the assumption of gradient dominance a relaxation of strong convexity then a modified newton s method is presented that exhibits fixed time convergence under some mild conditions on the objective function building upon this method a novel technique for solving convex optimization problems with linear equality constraints that yields convergence to the optimal point in fixed time is developed finally the general min max problem is considered and a modified scheme to obtain the optimal solution of saddle point dynamics in fixed time is developed

cooperative optimal control for lipschitz nonlinear systems over generally directed topologies abstract this paper studies the cooperative optimal control for multi agent systems mass with lipschitz nonlinearities over general digraphs the leader following consensus model consisting of multiple followers and one leader is constructed distributed optimal control protocols using the linear quadratic regulator approach are designed under the proposed protocols the performance index of the mas is optimized by solving the algebraic riccati equation are the weighting matrices of performance index rely on the lipschitz nonlinearities leading to optimal performance simulation studies are finally reported to illustrate the effectiveness of presented protocols

implicit lyapunov krasovski functionals for stability analysis and control design of time delay systems the method of implicit lyapunov krasovski functional ilkf for stability analysis of time delay systems is introduced theorems on lyapunov asymptotic hyper exponential finite time and fixed time stability analysis using ilkf are presented the hyper exponential stabilization algorithm for a time delay system is presented the theoretical result is supported by numerical simulation

penalized likelihood estimators and noise analysis for randoms precorrected pet transmission scans this paper analyzes and compares image reconstruction methods based on practical approximations to the exact log likelihood of randoms precorrected positron emission tomography pet measurements the methods apply to both emission and transmission tomography however in this paper the authors focus on transmission tomography the results of experimental pet transmission scans and variance approximations demonstrate that the shifted poisson sp method avoids the systematic bias of the conventional data weighted least squares wls method and leads to significantly lower variance than conventional statistical methods based on the log likelihood of the ordinary poisson of model the authors develop covariance approximations to analyze the propagation of noise from attenuation maps into emission images via the attenuation correction factors acf s empirical pixel and region variances from real transmission data agree closely with the analytical predictions both the approximations and the empirical results show that the performance differences between the op model and sp model are even larger when considering noise propagation from the transmission images into the final emission images than the differences in the attenuation maps themselves

distributed finite time tracking of multiple non identical second order nonlinear systems with settling time estimation this paper investigates the distributed finite time consensus tracking problem for a group of autonomous agents modeled by multiple non identical second order nonlinear systems first a class of distributed finite time protocols are proposed based on the relative position and relative velocity measurements by providing a topology dependent lyapunov function it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded then a new class of observer based algorithms are designed to solve the finite time consensus tracking problem without using relative velocity measurements the main contribution of this paper is that by computing the value of the lyapunov function at the initial point the finite settling time can be theoretically estimated for second order multi agent systems with the proposed control protocols finally the effectiveness of the analytical results is illustrated by an application in low earth orbit spacecraft formation flying

a finite time particle swarm optimization algorithm for odor source localization abstract this paper is concerned with a finite time particle swarm optimization algorithm for odor source localization first a continuous time finite time particle swarm optimization fpso algorithm is developed based on the continuous time model of the particle swarm optimization pso algorithm since the introduction of a nonlinear damping item the proposed continuous time fpso algorithm can converge over a finite time interval furthermore in order to enhance its exploration capability a tuning parameter is introduced into the proposed continuous time fpso algorithm the algorithm s finite time convergence is analyzed by using the lyapunov approach second the discrete time fpso algorithm is obtained by using a given dicretization scheme the corresponding convergence condition is derived by using a linear matrix inequality lmi approach finally the features and performance of the proposed fpso algorithm are illustrated by using two ill posed functions and twenty five benchmark functions respectively in numerical simulation results the problem of odor source localization is presented to validate the effectiveness of the proposed fpso algorithm

stickelberger ideals and divisor class numbers let k k be a finite abelian extension of function fields with galois group g using the stickelberger elements associated to k k studied by j tate p deligne and d hayes we construct an ideal i in the integral group ring mathbb z g relative to the extension k k whose elements annihilate the group of divisor classes of degree zero of k and whose rank is equal to the degree of the extension when k k is a wide or narrow ray class extension we compute the index of i in mathbb z g which is equal to the divisor class number of k up to a trivial factor

finite time formation control for linear multi agent systems a motion planning approach abstract this paper investigates the problem of finite time formation control for multi agent systems with general linear dynamics first of all the considered formation problem is converted into the motion planning problem where the systems are steered from initial positions to the desired terminal configurations then by using pontryagin maximum principle an optimal formation control law is developed for multi agent systems based on some invertible conditions with the designed control law the multi agent systems can achieve the desired formation in finite time where the formation configurations and the settling time can be specified in advance according to task requirements meanwhile a performance index is guaranteed to be optimal further it is proved that the formation problem concerned is solved if and only if the linear systems are controllable finally a possible application of the proposed control law to spacecraft formation flying with circular and near circular reference orbit is illustrated

local noise weighted filtering for emphysema scoring of low dose ct images computed tomography ct has become the new reference standard for quantification of emphysema the most popular measure of emphysema derived from ct is the pixel index pi which expresses the fraction of the lung volume with abnormally low intensity values as pi is calculated from a single fixed threshold on intensity this measure is strongly influenced by noise this effect shows up clearly when comparing the pi score of a high dose scan to the pi score of a low dose i e noisy scan of the same subject in this paper the noise variance nova filter is presented a general framework for iterative nonlinear filtering which uses an estimate of the spatially dependent noise variance in an image the nova filter iteratively estimates the local image noise and filters the image for the specific purpose of emphysema quantification of low dose ct images a dedicated noniterative nova filter is constructed by using prior knowledge of the data to obtain a good estimate of the spatially dependent noise in an image the performance of the nova filter is assessed by comparing characteristics of pairs of high dose and low dose scans the compared characteristics are the pi scores for different thresholds and the size distributions of emphysema bullae after filtering the pi scores of high dose and low dose images agree to within 2 3 points the reproducibility of the high dose bullae size distribution is also strongly improved nova filtering of a ct image of typically 400 spl times 512 spl times 512 voxels takes only a couple of minutes which makes it suitable for routine use in clinical practice

consensus dynamics with arbitrary sign preserving nonlinearities abstract this paper studies consensus problems for multi agent systems defined on directed graphs where the consensus dynamics involves general nonlinear and discontinuous functions sufficient conditions only involving basic properties of the nonlinear functions and the topology of the underlying graph are derived for the agents to converge to consensus

nonparametric regression sinogram smoothing using a roughness penalized poisson likelihood objective function the authors develop and investigate an approach to tomographic image reconstruction in which nonparametric regression using a roughness penalized poisson likelihood objective function is used to smooth each projection independently prior to reconstruction by unapodized filtered backprojection fbp as an added generalization the roughness penalty is expressed in terms of a monotonic transform known as the link function of the projections the approach is compared to shift invariant projection filtering through the use of a hanning window as well as to a related nonparametric regression approach that makes use of an objective function based on weighted least squares wls rather than the poisson likelihood the approach is found to lead to improvements in resolution noise tradeoffs over the hanning filter as well as over the wls approach the authors also investigate the resolution and noise effects of three different link functions the identity square root and logarithm links the choice of link function is found to influence the resolution uniformity and isotropy properties of the reconstructed images in particular in the case of an idealized imaging system with intrinsically uniform and isotropic resolution the choice of a square root link function yields the desirable outcome of essentially uniform and isotropic resolution in reconstructed images with noise performance still superior to that of the hanning filter as well as that of the wls approach

nonlinear consensus via continuous sampled and aperiodic updates we consider a first order multi agent system with nonlinear control protocols performing consensus we first address the convergence properties of the continuous system then periodically sampled control inputs are treated where we derive explicit upper bounds on the sampling interval to preserve global stability moreover we design an aperiodic and event triggered updating law to reduce the control efforts even further while ensuring the closed loop stability and providing a strictly positive lower bound on the inter execution time finally the robustness of this approach with respect to additive disturbances is examined by applying 2 gain analysis

augmented likelihood image reconstruction the presence of high density objects remains an open problem in medical ct imaging data of projections passing through objects of high density such as metal implants are dominated by noise and are highly affected by beam hardening and scatter reconstructed images become less diagnostically conclusive because of pronounced artifacts that manifest as dark and bright streaks a new reconstruction algorithm is proposed with the aim to reduce these artifacts by incorporating information about shape and known attenuation coefficients of a metal implant image reconstruction is considered as a variational optimization problem the afore mentioned prior knowledge is introduced in terms of equality constraints an augmented lagrangian approach is adapted in order to minimize the associated log likelihood function for transmission ct during iterations temporally appearing artifacts are reduced with a bilateral filter and new projection values are calculated which are used later on for the reconstruction a detailed evaluation in cooperation with radiologists is performed on software and hardware phantoms as well as on clinically relevant patient data of subjects with various metal implants results show that the proposed reconstruction algorithm is able to outperform contemporary metal artifact reduction methods such as normalized metal artifact reduction

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