partial synchronization from symmetry towards stability abstract in this paper we study the existence and stability of linear invariant manifolds in a network of coupled identical dynamical systems symmetry under permutation of different units of the network is helpful to construct explicit formulae for linear invariant manifolds of the network in order to classify them and to examine their stability through lyapunov s direct method

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

distributed l 2 gain output feedback control of homogeneous and heterogeneous systems the importance of static output feedback opfb design for aircraft control process control and elsewhere has been well documented since the 1960s since full state measurements are not usually available in practical systems this problem is compounded in the case of multi agent systems mas where each agent has its own state variable and measured outputs therefore this paper addresses the l 2 gain opfb synchronization of linear mas subject to external disturbances both homogeneous and heterogeneous mas are considered for homogeneous mas it is shown that the l 2 gain static opfb synchronization problem of mas can be cast into the l 2 gain static opfb problem for a set of decoupled systems that depend on the graph topology a modified riccati equation is introduced which gives the opfb gain and the coupling gain of the proposed static opfb control protocol for heterogeneous mas it is shown that the l 2 gain synchronization problem can be cast into the l 2 gain static opfb problem of a set of decoupled systems plus a coupling condition on their dynamic compensators that depends on the graph topology a certain novel gain matrix is introduced in the dynamics of the control protocol to improve the performance

core of ideals in integral domains abstract this paper uses objects and techniques from multiplicative ideal theory to develop explicit formulas for the core of ideals in various classes of integral domains not necessarily noetherian we also investigate the existence of minimal reductions originally established by rees and sally for local noetherian rings all results are illustrated by original examples in noetherian and non noetherian settings where we explicitly compute the core and validate some open questions recently raised in the literature

integrally closed modules over two dimensional regular local rings this paper is based on work of rees on integral closures of modules and initiates the study of integrally closed modules over two dimensional regular local rings in analogy with the classical theory of complete ideals of zariski the main results can be regarded as generalizations of zariski s product theorem they assert that the tensor product mod torsion of integrally closed modules is integrally closed that the symmetric algebra mod torsion of an integrally closed module is a normal domain and that the first fitting ideal of an integrally closed module is an integrally closed ideal a construction of indecomposable integrally closed modules is also given the primary technical tool is a study of the buchsbaum rim multiplicity

a comparison of two methods for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium abstract a comparison is made of two methods for solving the inverse scattering problem for acoustic waves in an inhomogeneous absorbing medium these methods were recently introduced by colton kirsch and monk and are based on considering a weighted average of the far field data instead of the far field data itself the comparison is based on numerical examples for the special case of spherically stratified media

brief paper decentralised static output feedback stabilisation and synchronisation of networks in this paper global stabilisation of a complex network is attained by applying local decentralised output feedback control to a minimum number of nodes of the network the stabilisation of the network is treated as a rank constrained problem strict positive realness conditions on the node level dynamics allow nonlinearities uncertainties which satisfy the sector conditions to be considered a network of chua oscillators with 75 nodes is considered to demonstrate the efficacy of the approach

randomized optimal consensus of multi agent systems in this paper we formulate and solve a randomized optimal consensus problem for multi agent systems with stochastically time varying interconnection topology the considered multi agent system with a simple randomized iterating rule achieves an almost sure consensus meanwhile solving the optimization problem min z r email protected i 1 nf i z in which the optimal solution set of objective function f i can only be observed by agent i itself at each time step simply determined by a bernoulli trial each agent independently and randomly chooses either taking an average among its neighbor set or projecting onto the optimal solution set of its own optimization component both directed and bidirectional communication graphs are studied connectivity conditions are proposed to guarantee an optimal consensus almost surely with proper convexity and intersection assumptions the convergence analysis is carried out using convex analysis we compare the randomized algorithm with the deterministic one via a numerical example the results illustrate that a group of autonomous agents can reach an optimal opinion by each node simply making a randomized trade off between following its neighbors or sticking to its own opinion at each time step

brief paper on the v stability of complex dynamical networks this paper introduces the concept of lyapunov v stability for complex dynamical networks under the new framework each dynamical node is associated with a passivity degree which indicates to what extent an effort is required for stabilizing the node from this approach the network stability problem is converted to measuring the negative definiteness of one simple matrix that characterizes the topology of the network pinning control is then suggested and investigated based on the new v stability formulation as an illustrative example a network with different node dynamics and non uniform coupling strengths is simulated to verify the analytic results moreover a comparison study for three different kinds of networks is provided to further illustrate the novelty and efficacy of the proposed v stability criterion and stabilization scheme

stabilizability conditions of multivariable uncertain systems via output feedback control a stabilizability condition is established for stabilizing multivariable uncertain dynamical systems with matched uncertainties by linear static output feedback control it is shown that under the assumptions of minimum phase and nonsingular high frequency gain for the nominal plant stabilization with linear static output feedback control is achievable a necessary and sufficient condition is also obtained for the existence of constant output feedback which makes the closed loop system strictly positive real

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

on the solvability of the constrained lyapunov problem this paper considers system theoretic conditions for the solvability of the so called constrained lyapunov problem for nonsquare systems these problems commonly appear in the control systems literature both a static output feedback problem and an observer problem are considered the basis for the work described in this paper is a new canonical form that simplifies the analysis and deals with the equality constraint in a simple way

pinning control of scale free dynamical networks abstract recently it has been demonstrated that many large complex networks display a scale free feature that is their connectivity distributions have the power law form in the present work control of a scale free dynamical network by applying local feedback injections to a fraction of network nodes is investigated the specifically and randomly pinning schemes are considered the specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme the method is applied to an array of chua s oscillators as an example

h consensus of second order multi agent systems with asymmetric delays abstract this paper is concerned with the problem of consensus in the h sense for second order continuous time multi agent systems with multiple asymmetric time varying delays by using a model transformation approach and matrix theory we establish several conditions in terms of linear matrix inequalities such that consensus of multi agent systems can be achieved in the h sense the feasibility of the consensus conditions is also analyzed as an application we consider the case of intermittent measurement between agents numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

a criterion for exponential consensus of time varying non monotone nonlinear networks in this technical note we present new results on exponential consensus for continuous time nonlinear time varying networks a key feature in the following is that the monotonicity property is not required unlike most of existing literature on the subject moreover we give an estimate of the exponential rate of convergence towards the agreement manifold finally representative example and counterexample are given

the multi agent rendezvous problem part 2 the asynchronous case this paper is concerned with the collective behavior of a group of n 1 mobile autonomous agents labelled 1 through n which can all move in the plane each agent is able to continuously track the positions of all other agents currently within its sensing region where by an agent s sensing region we mean a closed disk of positive radius r centered at the agent s current position the multi agent rendezvous problem is to devise local control strategies one for each agent which without any active communication between agents cause all members of the group to eventually rendezvous at a single unspecified location this paper describes a family of unsynchronized strategies for solving the problem correctness is established appealing to the concept of analytic synchronization

reconstruction of a spherically symmetric speed of sound consider the inverse acoustic scattering problem for a spherically symmetric inhomogeneity of compact support that arises among other places in nondestructive testing define the corresponding homogeneous and inhomogeneous interior transmission problems see e g d colton and p monk quart j mech math 41 1988 pp 97 125 here the authors study the subset of transmission eigenvalues corresponding to spherically symmetric eigenfunctions of the homogeneous interior transmission problem it is shown in mclaughlin and polyakov j differential equations to appear that these eigenvalues are the zeros of an average of the scattering amplitude and a uniqueness theorem for the inverse acoustic scattering problem is presented where these eigenvalues are the given data in the present paper an algorithm for finding the solution of the inverse acoustic scattering problem from this subset of transmission eigenvalues is developed and implemented the method given here completely determines the sound

multifrequency inverse problem for the reduced wave equation with sparse data the inverse problem for the reduced wave equation u k2n2 x u 0 is considered where the quantity to be determined is the value of n x in a compact domain d in r3 the data consists of a finite set of measurements of the scattered field produced by different incident fields the measurements are made at various points exterior to d and at possibly different frequencies the mathematical problem involves solving a system of nonlinear functional equations conditions are developed which indicate when the measured body is close to a particular comparison body a linearized perturbation is valid a new higher order nonlinear iterative procedure is developed for the full nonlinear problem which reduces to the usual solution in the linearized region the method is illustrated by computational results for the one dimensional case

a newton like method for solving rank constrained linear matrix inequalities this paper presents a newton like algorithm for solving systems of rank constrained linear matrix inequalities though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases numerical experiments including application to an output feedback stabilization problem show the effectiveness of the algorithm

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

persistent excitation in adaptive systems the importance of the concept of persistent excitation pe in adaptive identification and control has been recognized for some time recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems there is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control hence there is a real need for a deeper understanding of the concept the paper is written with three objectives the first which is tutorial in nature is to provide a general framework for the discussion of persistent excitation and to collect results in the area which are scattered throughout the adaptive literature the second objective is to present some new results related to the uniform asymptotic stability u a s and robustness of adaptive systems and the relation of pe to the stability properties of a class of non linear systems the final objective is to di

multifrequency inverse problem for the reduced wave equation resolution cell and stability the multifrequency inverse problem associated with the reduced wave equation u k2n2 x u 0 x r3 is examined for the case where the data set is sparse the resolution cell or solution set is examined in detail and is shown to be an infinite dimensional manifold the concept of stability is introduced it is shown that the intrinsic condition of structural stability to the inverse process selects out a preferred set of solutions from the solution set the structural stability of various iterative schemes used in the inverse process are examined

static output feedback stabilization of interconnected systems abstract this paper is concerned with the celebrated static output feedback control problem sofp subject to linear constraints on control input k e g bounds on control magnitude zeros in some elements of k etc these constraints typically arise in the control of resource limited systems interconnected to each other where the local control for each system makes use of its own and neighboring systems outputs only and its magnitude is bounded this control problem can be approached by a spectral norm minimization technique q snm whose preliminary version was previously introduced with little mathematical justification but shown to be promising for the regular sofp without control constraints this paper mathematically justifies q snm by showing its explicit relationship with spectral radius and extends q snm to accommodate various linear control constraints this paper also discusses the practical application of q snm to vehicle formation control which demonstrates the merit of q snm

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

the core of a module over a two dimensional regular local ring abstract this paper explicitly determines the core of a torsion free integrally closed module over a two dimensional regular local ring it is analogous to a result of huneke and swanson which determines the core of an integrally closed ideal the main result asserts that the core of a finitely generated torsion free integrally closed module over a two dimensional regular local ring is the product of the module and a certain fitting ideal of the module the technical tools used are quadratic transforms and buchsbaum rim multiplicity

symmetric powers of complete modules over a two dimensional regular local ring this is the published version also available here http dx doi org 10 1090 s0002 9947 97 01819 9 first published in trans amer math soc in 1997 published by the american mathematical society

connection graph stability method for synchronized coupled chaotic systems this paper elucidates the relation between network dynamics and graph theory a new general method to determine global stability of total synchronization in networks with different topologies is proposed this method combines the lyapunov function approach with graph theoretical reasoning in this context the main step is to establish a bound on the total length of all paths passing through an edge on the network connection graph in particular the method is applied to the study of synchronization in rings of 2k nearest neighbor coupled oscillators a rigorous bound is given for the minimum coupling strength sufficient for global synchronization of all oscillators this bound is explicitly linked with the average path length of the coupling graph contrary to the master stability function approach developed by pecora and carroll the connection graph stability method leads to global stability of synchronization and it permits not only constant but also time dependent interaction coefficients in a companion paper blinking model and synchronization in small world networks with a time varying coupling see this issue this method is extended to the blinking model of small world networks where in addition to the fixed 2 k nearest neighbor interactions all the remaining links are rapidly switched on and off independently of each other

a layered analysis of consensus this paper introduces a simple notion of layering as a tool for analyzing well behaved runs of a given model of distributed computation using layering a model independent analysis of the consensus problem is performed and then applied to proving lower bounds and impossibility results for consensus in a number of familiar and less familiar models the proofs are simpler and more direct than existing ones and they expose a unified structure to the difficulty of reaching consensus in particular the proofs for the classical synchronous and asynchronous models now follow the same outline a new notion of connectivity among states in runs of a consensus protocol called potence connectivity is introduced this notion is more general than previous notions of connectivity used for this purpose and plays a key role in the uniform analysis of consensus

blinking model and synchronization in small world networks with a time varying coupling the paper proposes a new type of small world networks of cells with chaotic behavior this network consists of a regular lattice of cells with constant 2k nearest neighbor couplings and time dependent on off couplings between any other pair of cells in each time interval of duration such a coupling is switched on with probability p and the corresponding switching random variables are independent for different links and for different times at each moment the coupling structure corresponds to a small world graph but the shortcuts change from time interval to time interval which is a good model for many real world dynamical networks it is to be distinguished from networks that have randomly chosen shortcuts fixed in time here we apply the connection graph stability method developed in the companion paper connection graph stability method for synchronized coupled chaotic systems see this issue to the study of global synchronization in this network with the time varying coupling structure in the case where the on off switching is fast with respect to the characteristic synchronization time of the network the synchronization thresholds are explicitly linked with the average path length of the coupling graph and with the probability p of shortcut switchings in this blinking model we prove that for the blinking model a few random shortcut additions significantly lower the synchronization threshold together with the effective characteristic path length short interactions between cells as in the blinking model are important in practice to cite prominent examples computers networked over the internet interact by sending packets of information and neurons in our brain interact by sending short pulses called spikes the rare interaction between arbitrary nodes in the network greatly facilitates synchronization without loading the network much in this respect we believe that it is more efficient than a structure of fixed random connections

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