passivity based synchronization of a class of complex dynamical networks with time varying delay this paper proposes a complex delayed dynamical network consisting of n linearly and diffusively coupled identical reaction diffusion neural networks by utilizing some inequality techniques a sufficient condition ensuring the output strict passivity is derived for the proposed network model then we reveal the relationship between output strict passivity and synchronization of the proposed network model moreover based on the obtained passivity result and the relationship between output strict passivity and synchronization a criterion for synchronization is established finally a numerical example is provided to illustrate the correctness and effectiveness of the proposed results

limit sets zero dynamics and internal models in the problem of nonlinear output regulation in this paper we lay the foundations for a nonequilibrium theory of nonlinear output regulation giving a more general nonequilibrium definition of the problem deriving necessary conditions and using these necessary conditions we present a set of sufficient conditions and a design methodology for the solution of the problem in question our analysis leads to a nonequilibrium enhancement of the internal model principle

multiplex pi control for consensus in networks of heterogeneous linear agents in this paper we propose a multiplex proportional integral approach for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances the proportional and integral actions are deployed on two different layers across the network each with its own topology sufficient conditions for convergence are derived that depend upon the structure of the network the parameters and topologies characterizing the control layers and the node dynamics the effectiveness of the theoretical results is illustrated numerically on a set of representative examples including a power network model

agreeing in networks this paper considers a problem of output agreement in heterogeneous networks with dynamics on the nodes as well as on the edges the control and disturbance signals entering the nodal dynamics are unmatched meaning that some nodes are only subject to disturbances and not to the actuating signals to further enrich our model and motivated by synchronization problems in physical networks we accommodate solvable algebraic constraints resulting in a fairly general and heterogeneous network it is shown that appropriate dynamic feedback controllers achieve output agreement on a desired vector in the presence of physical coupling and despite the influence of constant as well as time varying disturbances furthermore we address the case of an optimal steady state deployment of the control effort over the network by suitable distributed controllers as a case study the proposed results are applied to a heterogeneous microgrid

diagonal stability on cactus graphs and application to network stability analysis a square matrix e is said to be diagonally stable if there exists a diagonal matrix d 0 satisfying de etd 0 this notion has been instrumental in recent studies on stability of interconnected system models in communication and biological networks in which the subsystems satisfy passivity properties and the matrix e combines this passivity information with the interconnection structure this paper presents a necessary and sufficient condition for diagonal stability when the digraph describing the network conforms to a cactus structure which means that a pair of distinct simple circuits in the graph have at most one common vertex in the special case of a single circuit this diagonal stability test recovers the secant criterion that was recently derived for cyclic networks the paper then incorporates the new diagonal stability test in network stability analysis where the diagonal entries of the matrix d serve as weights in a lyapunov function constructed from storage functions that verify passivity properties of the components finally the paper illustrates this stability test on examples motivated by gene networks and population dynamics

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

semidefinite programming relaxations for semialgebraic problems a hierarchy of convex relaxations for semialgebraic problems is introduced for questions reducible to a finite number of polynomial equalities and inequalities it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility the main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials and some results from real algebraic geometry the techniques provide a constructive approach for finding bounded degree solutions to the positivstellensatz and are illustrated with examples from diverse application fields

synchronization of interconnected systems with applications to biochemical networks an input output approach this paper provides synchronization conditions for networks of nonlinear systems the components of the network referred to as compartments in this paper are made up of an identical interconnection of subsystems each represented as an operator in an extended l2 space and referred to as a species the compartments are in turn coupled through a diffusion like term among the respective species the synchronization conditions are provided by combining the input output properties of the subsystems with information about the structure of the network the paper also explores results for state space models as well as biochemical applications the work is motivated by cellular networks where signaling occurs both internally through interactions of species and externally through intercellular signaling the theory is illustrated by providing synchronization conditions for networks of goodwin oscillators

an input output framework for submanifold stabilization we study submanifold stabilization problems from an input output perspective where plant and controller are relations on their sets of input output signals in contrast to the classical input output approaches we consider signals whose integral p fold distance to a submanifold is finite for feedback interconnections of relations on such signals we develop a framework to show that the distance of the output of the plant to the desired submanifold remains bounded within this framework we present a small gain theorem a feedback theorem for conic relations and a feedback theorem for passive relations we connect our findings to multiplier theory and present applications to synchronization and pattern generation

brief paper diagonal stability of a class of cyclic systems and its connection with the secant criterion we consider a class of systems with a cyclic interconnection structure that arises among other examples in dynamic models for certain biochemical reactions we first show that a secant criterion for local stability derived earlier in the literature is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices we then revisit a recent generalization of this criterion to output strictly passive systems and recover the same stability condition using our diagonal stability result as a tool for constructing a lyapunov function using this procedure for lyapunov construction we exhibit classes of cyclic systems with sector nonlinearities and characterize their global stability properties

a unifying framework for robust synchronization of heterogeneous networks via integral quadratic constraints a general framework for analysing robust synchronization in large scale heterogenous networks is proposed based on the theory of integral quadratic constraints iqcs dynamic agents are represented as linear time invariant single input single output systems the agents exchange information according to a sparse dynamical interconnection operator in order to achieve synchronization where their outputs are steered to the same possibly time varying signal the main technical hindrance to applying iqcs in this context lies with the presence of the marginally stable dynamics which define the trajectory to which the agents outputs synchronize it is shown that by working with conditions defined on modified signal spaces of interest and exploiting the graph structure underlying the connections between the dynamic systems iqc methods can be applied directly to synchronization analysis without recourse to loop transformations which may obscure the inherent structural properties of the multi agent networked systems decentralized and scalable conditions for synchronization are proposed within this setting the iqc framework is demonstrated to unify and generalize some of the existing results in the literature including certain nyquist type consensus certificates for time delay systems moreover it allows the role of feedback in robustness against uncertainty to be better manifested within the context of synchronization

generalised absolute stability and sum of squares this paper introduces a general framework for analysing nonlinear systems using absolute stability theory and sum of squares programming the technique decomposes a vector field into a system with a polynomial vector field in feedback with a nonlinear memoryless term which is contained in a generalised sector inequality with polynomial bounds this decomposition can be used to model uncertainty in the nonlinearity or to bound difficult to analyse terms by simpler polynomial functions such as time varying non polynomial or higher order nonlinearities conditions for stability and regions of attraction are found using polynomial and lur e type lyapunov functions which generalise those used for the derivation of the multivariable circle and popov criteria in classical absolute stability the technique extends both absolute stability theory and the applicability of sum of squares programming the usefulness of the technique is demonstrated with illustrative examples

analysis and control of output synchronization in directed and undirected complex dynamical networks this research focuses on the problem of output synchronization in undirected and directed complex dynamical networks respectively by applying barbalat s lemma first to ensure the output synchronization several sufficient criteria are established for these network models based on some mathematical techniques such as the lyapunov functional method and matrix theory furthermore some adaptive schemes to adjust the coupling weights among network nodes are developed to achieve the output synchronization by applying the designed adaptive laws several criteria for output synchronization are deduced for the network models in addition a design procedure of the adaptive law is shown finally two simulation examples are used to show the effectiveness of the previous results

synchronization of coupled discrete time harmonic oscillators with rational frequency this technical note studies the synchronization of coupled discrete time harmonic oscillators with rational frequency under switching topology the remarkable feature of this problem is that the conditions that merely involve the connectivity structure of topology does not suffice for synchronizing the oscillators we propose a frequency dependent topology condition that indicates in what way the topology switches and introduce firmly nonexpansive mapping fnm from functional analysis under the condition the synchronization of coupled oscillators is related to an infinite product of fnms which share only one zero common fixed point by a convergence result on infinite product of a finite number of fnm we present a synchronization result for the coupled oscillators finally a simulation example is given to illustrate the effectiveness of the result

coordination of passive systems under quantized measurements in this paper we investigate a passivity approach to collective coordination and synchronization problems in the presence of quantized measurements and show that coordination tasks can be achieved in a practical sense for a large class of passive systems

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

on applicability of auxiliary system approach to detect generalized synchronization in complex network generalized synchronization is ubiquitous in nature it is well known that the auxiliary system approach has been widely used to verify the presence of generalized synchronization this approach was firstly proposed in a drive response system then extended to the bidirectionally coupled systems and complex networks however the well known generalized auxiliary system method lacks a rigorous theoretical basis for its various applications two recent counterexamples indicate us the inapplicability of this method inspired by the counterexamples we find that it is interesting to ask the following two fundamental questions i why is the generalized auxiliary system approach unworkable in the networks with bidirectional couplings ii are there any essential conditions for the applications of this approach this technical note aims at establishing a rigorous theoretical basis for the applicability of auxiliary system approach that is the generalized auxiliary system approach is effective only if there does not exist any path from nodes to their driving neighbors who drive these nodes in a network several representative examples are also given to validate our theoretical results

synchronization under space and time dependent heterogeneities we study output synchronization of nonlinear systems subject to a class of spatially and temporally varying heterogeneities we begin by addressing reaction diffusion pdes and show that an incremental passivity property in the nominal reaction dynamics is fundamental in guaranteeing spatial homogenization of trajectories our distributed control achieves homogenization by defining an internal model subsystem for each output corresponding to the respective heterogeneity we also design a similar distributed internal model control that achieves output synchronization of a network of incrementally passive nonlinear ode systems in the presence of heterogeneities we prove that our control laws effectively compensate for desynchronizing effects due to the differences between the heterogeneous inputs we illustrate our algorithms on ring oscillators and bistable systems the main contribution of the paper is a constructive and unified approach to guaranteeing homogenization under heterogeneities for both reaction diffusion pde and diffusively coupled ode systems

synchronization of diffusively coupled limit cycle oscillators we develop analytical and numerical conditions to determine whether limit cycle oscillations synchronize in diffusively coupled systems we examine two classes of systems reaction diffusion pdes with neumann boundary conditions and compartmental odes where compartments are interconnected through diffusion terms with adjacent compartments in both cases the uncoupled dynamics are governed by a nonlinear system that admits an asymptotically stable limit cycle we provide two time scale averaging methods for certifying stability of spatially homogeneous time periodic trajectories in the presence of sufficiently small or large diffusion and develop methods using the structured singular value for the case of intermediate diffusion we highlight cases where diffusion stabilizes or destabilizes such trajectories

synchronization of networks of heterogeneous agents with common nominal behavior this paper deals with the problem of synchronization in networks of heterogeneous agents with common nominal behavior the agents are modeled as possibly nonlinear perturbed versions of a common siso nominal lti operator and they are interconnected via a sparse memoryless interconnection operator coherent with the communication graph underlying the network the network is said to synchronize if the outputs of the agents tend to align along given directions the most important case being consensus or agreement the paper provides a general result based on iqcs that ensures synchronization of the network with robustness w r t uncertainties in the interconnection and in each agent s dynamics scalability issues are discussed in the scenario where the interconnection operator is a constant normal matrix yielding the generalization of the very popular linear consensus algorithm the wide range of applicability of the proposed criterion is shown by providing synchronization conditions in some important examples whenever possible graphical criteria are proposed for checking the required conditions

a high order discontinuous galerkin approach to the elasto acoustic problem abstract we address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous galerkin scheme on polygonal and polyhedral meshes the coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid elastic and fluid acoustic domains we state and prove a well posedness result for the strong formulation of the problem present a stability analysis for the semi discrete formulation and finally prove an a priori h p version error estimate for the resulting formulation in a suitable mesh dependent energy norm we also discuss the time integration scheme employed to obtain the fully discrete system the convergence results are validated by numerical experiments carried out in a two dimensional setting

passivity of nonlinear incremental systems application to pi stabilization of nonlinear rlc circuits abstract it is well known that if the linear time invariant system x a x b u y c x is passive the associated incremental system x a x b u y c x with u y the constant input and output associated to an equilibrium state x is also passive in this paper we identify a class of nonlinear passive systems of the form x f x gu y h x whose incremental model is also passive using this result we then prove that a large class of nonlinear rlc circuits with strictly convex electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear pi control

hierarchical clustering of dynamical networks using a saddle point analysis this paper studies cluster synchronization in dynamical networks a class of cooperative dynamical networks that exhibit clustering in their asymptotic behavior is analyzed the network nodes are equipped with heterogeneous dynamics and interact with a nonlinear and saturated interaction rule it is proven that cluster synchronization appears asymptotically independent of the initial conditions the clustering behavior of the dynamic network is shown to correspond to the solution of a static saddle point problem enabling a precise characterization of the clustering structure we show how the clustering structure depends on the relation between the underlying graph the node dynamics and the saturation level of the interactions this interpretation leads to deeper combinatorial insights related to clustering including a generalization of classical network partitioning problems such as the inhibiting bisection problem the min s t cut problem and hierarchical clustering analysis the theoretical results are applied for the analysis of a test case network inspired by the ieee 30 bus system

a projective quasi newton method for nonlinear optimization abstract a trust region method for nonlinear optimization problems with equality constraints is proposed in this paper this method incorporates quadratic subproblems in which orthogonal projective matrices of the jacobian of constraint functions are used to replace qr decompositions as qr decomposition does not ensure continuity but projective matrix does convergence behaviour of the new method can be discussed under more reasonable assumptions the method maintains a two step feature one movement in the range space of the jacobian whereas the other one in the null space it is proved that all accumulation points of iterates are kkt karush kuhn tucker points and the method has a one step superlinear convergence rate

passivity gains and the secant condition for stability a generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems the key is the introduction of a quantity that combines gain and phase information for each system in the cascade for linear one dimensional systems the known result is recovered exactly 2005 elsevier b v all rights reserved

an extension of karmarkar projective algorithm for convex quadratic programming we present an extension of karmarkar s linear programming algorithm for solving a more general group of optimization problems convex quadratic programs this extension is based on the iterated application of the objective augmentation and the projective transformation followed by optimization over an inscribing ellipsoid centered at the current solution it creates a sequence of interior feasible points that converge to the optimal feasible solution in o ln iterations each iteration can be computed in o ln3 arithmetic operations wheren is the number of variables andl is the number of bits in the input in this paper we emphasize its convergence property practical efficiency and relation to the ellipsoid method

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

on the performance of nonlinear dynamical systems under parameter perturbation we present a method for analysing the deviation in transient behaviour between two parameterised families of nonlinear odes as initial conditions and parameters are varied within compact sets over which stability is guaranteed this deviation is taken to be the integral over time of a user specified positive definite function of the difference between the trajectories for instance the l 2 norm we use sum of squares programming to obtain two polynomials which take as inputs the possibly differing initial conditions and parameters of the two families of odes and output upper and lower bounds to this transient deviation equality can be achieved using symbolic methods in a special case involving linear time invariant parameter dependent systems we demonstrate the utility of the proposed methods in the problems of model discrimination and location of worst case parameter perturbation for a single parameterised family of ode models

duality and network theory in passivity based cooperative control this paper presents a class of passivity based cooperative control problems that have an explicit connection to convex network optimization problems the new notion of maximal equilibrium independent passivity is introduced and it is shown that networks of systems possessing this property asymptotically approach the solutions of a dual pair of network optimization problems namely an optimal potential and an optimal flow problem this connection leads to an interpretation of the dynamic variables such as system inputs and outputs to variables in a network optimization framework such as divergences and potentials and reveals that several duality relations known in convex network optimization theory translate directly to passivity based cooperative control problems the presented results establish a strong and explicit connection between passivity based cooperative control theory on the one side and network optimization theory on the other and they provide a unifying framework for network analysis and optimal design the results are illustrated on a nonlinear traffic dynamics model that is shown to be asymptotically clustering

synchronization of networks of nonidentical euler lagrange systems with uncertain parameters and communication delays this paper addresses the problem of synchronizing networks of nonidentical nonlinear dynamical systems described by euler lagrange equations which are assumed fully actuated with their states available for measurement but with unknown parameters the only assumption made on the communication graph is that it is connected moreover the communication is subject to constant time delays which are also unknown the main result of the paper is the construction of an adaptive controller that achieves global full state synchronization i e the difference between the agents positions and velocities asymptotically converges to zero if a desired trajectory for all systems is given a slight modification to the proposed scheme achieves also full state synchronization simulations using a ten robot manipulator network are used to illustrate the performance of the proposed schemes

stabilization and synchronization for a heterogeneous multi agent system via harmonic control abstract in this paper a class of heterogeneous multi agent systems with directed cycle graphs is investigated the stabilization and synchronization problems via harmonic control are solved under some conditions and the feedback control gains are constructively designed several numerical examples are presented to demonstrate the effectiveness of the proposed method

brief paper an internal model principle is necessary and sufficient for linear output synchronization output synchronization of a network of heterogeneous linear state space models under time varying and directed interconnection structures is investigated it is shown that assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories the resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems

some results on exponential synchronization of nonlinear systems based on recent works on transverse exponential stability we establish some necessary and sufficient conditions for the existence of a locally exponential synchronizing control law we show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems on the synchronization manifold by a linear state feedback this in turn is also equivalent to the existence of a symmetric covariant tensor field which satisfies a control matrix function inequality based on this result we provide the construction of such a synchronizer via backstepping approach in some particular cases we show how global exponential synchronization may be obtained

structure and stability of the equilibrium set in potential driven flow networks abstract in this paper we address local bifurcation properties of a family of networked dynamical systems specifically those defined by a potential driven flow on a directed graph these network flows include linear consensus dynamics or kuramoto models of coupled nonlinear oscillators as particular cases as it is well known for consensus systems these networks exhibit a somehow unconventional dynamical feature namely the existence of a line of equilibria following from a well known property of the graph laplacian matrix in connected networks with positive weights negative weights which arise in different contexts e g in consensus models in signed graphs or in kuramoto models with antagonistic actors may on the one hand lead to higher dimensional manifolds of equilibria and on the other be responsible for bifurcation phenomena in this direction we prove a saddle node bifurcation theorem for a broad family of potential driven flows in networks with one or more negative weights the goal is to state the conditions in structural terms that is in terms of the expressions defining the flowrates and the graph theoretic properties of the network not only the eigenvalue requirements but also the nonlinear transversality assumptions supporting the bifurcation motivate an analysis of independent interest concerning the rank degeneracies of nodal matrices arising in the linearized dynamics this analysis is performed in terms of the contraction deletion structure of spanning trees and uses several results from matrix analysis different examples illustrate the results some linear problems including signed graphs are aimed at illustrating the analysis of nodal matrices whereas in a nonlinear framework we apply the characterization of saddle node bifurcations to networks with a sinusoidal kuramoto like flow

clustering in a network of non identical and mutually interacting agents clustering is a phenomenon that may emerge in multi agent systems through self organization groups arise consisting of agents with similar dynamic behaviour it is observed in fields ranging from

equilibrium independent dissipativity with quadratic supply rates equilibrium independent dissipativity eid is a recently introduced system property that requires a system to be dissipative with respect to any forced equilibrium configuration this paper is a detailed examination of eid with quadratic supply rates for a common class of nonlinear control affine systems we provide an algebraic characterization of eid for such systems in the spirit of the hill moylan lemma where the usual stability condition is replaced by an incremental stability condition based on this characterization we state results concerning internal stability feedback stability and absolute stability of eid systems finally we study eid for discrete time systems providing the relevant definitions and an analogous hill moylan type characterization results for both continuous time and discrete time systems are illustrated through examples on physical systems and convex optimization algorithms

asymptotic amplitudes and cauchy gains a small gain principle and an application to inhibitory biological feedback the notions of asymptotic amplitude for signals and cauchy gain for input output systems and an associated small gain principle are introduced these concepts allow the consideration of systems with multiple and possibly feedback dependent steady states a lyapunov like characterization allows the computation of gains for state space systems and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops an application in biology mapk signaling is worked out in detail

delay robustness of interconnected passive systems an integral quadratic constraint approach we consider networks of passive systems with time delays in the interconnections and present a stability analysis technique with the help of the integral quadratic constraint iqc framework unlike the classical passivity approach that fails to characterize delay robustness and the small gain approach that conservatively accounts for arbitrarily large delays the new technique gives sharp stability estimates that depend on the duration of delay since the effect of delay depends on its duration relative to the time scales of the system we make use of a roll off iqc that captures magnitude roll off at high frequencies thus providing the critical time scale information we then combine this roll off iqc with an output strict passivity iqc that incorporates gain and phase information and demonstrate the benefit of this combined iqc approach on a cyclic interconnection structure with delay finally we develop a technique to verify these iqcs for classes of nonlinear state space models and present an example from internet congestion control

certifying spatially uniform behavior in reaction diffusion pde and compartmental ode systems we present a condition that guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction diffusion pde with neumann boundary conditions this condition makes use of the jacobian matrix of the reaction terms and the second neumann eigenvalue of the laplacian operator on the given spatial domain and eliminates the global lipschitz assumptions commonly used in mathematical biology literature we then derive numerical procedures that employ linear matrix inequalities to certify this condition and illustrate these procedures on models of several biochemical reaction networks finally we present an analog of this pde result for the synchronization of a network of identical ode models coupled by diffusion terms from a systems biology perspective the main contribution of the paper is to blend analytical and numerical tools from nonlinear systems and control theory to derive a relaxed and verifiable condition for spatial uniformity of biological processes

high order discontinuous galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes abstract we propose and analyze a high order discontinuous galerkin finite element method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements we analyze the well posedness of the resulting formulation prove h p version error a priori estimates and present a dispersion analysis showing that polygonal meshes behave as classical simplicial quadrilateral grids in terms of dispersion properties the theoretical estimates are confirmed through various two dimensional numerical verifications

convergent dynamics a tribute to boris pavlovich demidovich we review and pay tribute to a result on convergent systems by the russian mathematician boris pavlovich demidovich in a sense demidovich s approach forms a prelude to a field which is now called incremental stability of dynamical systems developments on incremental stability are reviewed from a historical perspective

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

global robust distributed output consensus of multi agent nonlinear systems an internal model approach abstract this paper studies the problem of global robust distributed output consensus of heterogeneous leader follower multi agent nonlinear systems by general directed output interactions for a class of minimum phase single input single output nonlinear agents having unity relative degree it is shown that the problem is solvable by an internal model approach under certain mild conditions a lyapunov function based output feedback control law is developed by converting the global output consensus into a global distributed stabilization problem for an augmented network

a convergence proof for an affine scaling algorithm for convex quadratic programming without nondegeneracy assumptions this paper presents a theoretical result on convergence of a primal affine scaling method for convex quadratic programs it is shown that as long as the stepsize is less than a threshold value which depends on the input data only ye and tse s interior ellipsoid algorithm for convex quadratic programming is globally convergent without nondegeneracy assumptions in addition its local convergence rate is at least linear and the dual iterates have an ergodically convergent property

an affine scaling projective reduced hessian algorithm for minimum optimization with nonlinear equality and linear inequality constraints abstract in this paper we propose a nonmonotonic interior point backtracking strategy to modify the reduced projective affine scaling trust region algorithm for solving minimum optimization subject to both nonlinear equality and linear inequality constraints the general full trust region subproblem for solving the minimum optimization is decomposed to a pair of trust region subproblems in horizontal and vertical subspaces of linearize equality constraints and extended affine scaling equality constraints by qr decomposition of an affine scaling matrix and an orthonormal basis on the null subspace the horizontal subproblem in the proposed algorithm is defined by minimizing a quadratic projective reduced hessian function subject only to an ellipsoidal trust region constraint while the vertical subproblem is also defined by the least squares subproblem subject only to an ellipsoidal trust region constraint combining trust region strategy with line search technique will switch to strictly feasible interior point step generated by a component direction of the two trust region subproblems by adopting the l1 penalty function as the merit function the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions the second order correction step and a nonmonotonic criterion are used to overcome maratos effect and speed up the convergence progress in some ill conditioned cases respectively

stability of dynamical networks with non identical nodes a multiple v lyapunov function method global asymptotic stability of general dynamical networks with non identical nodes is studied by introducing multiple v lyapunov functions in such a network the coupling strength inner coupling matrix and outer coupling matrix are all allowed to be state dependent and nonlinear a stability criterion is proposed in terms of matrix norms and eigenvalues of some lower dimensional matrices based on this criterion an optimization problem is formed whose solution can be used to test global asymptotic stability we also study the problem of how to achieve global asymptotic stability by design of controllers under the scheme of multiple v lyapunov functions the control action is regarded as a re shape of outer coupling topology and the associated controllers are designed in particular a method of adding or removing a certain number of links is proposed stability analysis of coupled non identical lorenz systems and a design example are also given to illustrate the proposed method

on synchronous steady states and internal models of diffusively coupled systems we investigate the problem of synchronizing nonidentical nonlinear dynamical systems by means of generalized diffusive couplings the focus is not on the actual solution to the problem but on the derivation of necessary conditions for the existence of such a solution despite the systems possessing nonidentical models we show that for the problem to be solvable a synchronous steady state needs to exist this condition leads to the requirement that all individual system models need to embed an internal model of some common endosystem the latter condition is expressed in terms of nonlinear partial differential equations the conditions derived in this paper are related to those known from the theory of output regulation

hp version space time discontinuous galerkin methods for parabolic problems on prismatic meshes we present a new hp version space time discontinuous galerkin dg finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal polyhedral polytopic elements giving rise to prismatic space time elements a key feature of the proposed method is the use of space time elemental polynomial bases of total degree say p defined in the physical coordinate system as opposed to standard dg time stepping methods whereby spatial elemental bases are tensorized with temporal basis functions this approach leads to a fully discrete hp dg scheme using fewer degrees of freedom for each time step compared to dg time stepping schemes employing a tensorized space time basis with acceptable deterioration of the approximation properties a second key feature of the new space time dg method is the incorporation of very general spatial meshes consisting of possibly polygonal polyhedral elements with an arbitrary number of faces a priori er

meagre functions and asymptotic behaviour of dynamical systems a measurable function x j r x x a metric space is said to be c meagre if c x is non empty and for every closed set k x with k c x 1 k has 5nite lebesgue measure this concept of meagreness is shown to provide a unifying framework which facilitates a variety of characterizations extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems by way of motivation consider the initial value problem f x x 0 rn with f rn rn locally lipschitz and denote its unique solution by x t t de5ned on its maximal interval of existence i 0 let g rn r be continuous assume that x is a bounded solution of the initial value problem in which case i 0 then g x is uniformly continuous if in addition g x l1 then we may conclude by an elementary observation frequently referred to as barb alat s lemma 5 see also 18 section 21 lemma 1 that g x t 0 as t 0 since by boundedness x t approaches as t its non empty compact invariant limit set b we also conclude that b g 1 0 it follows that x t tends as t to the largest invariant subset of g 1 0 this is a short proof of theorem 1 2 of 6 the proof in 6 is based on arguments involving properties of the dow generated by the dieerential

synchronization and dynamic consensus of heterogeneous networked systems we present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs heterogeneous systems may have totally different dynamical models albeit of the same dimension or may possess equal models with different lumped parameters we show that their behavior when network interconnected is fully characterized in terms of two properties whose study may be recasted in terms of the stability analysis of two corresponding interconnected dynamical systems that evolve in orthogonal spaces on one hand we have the so called emergent dynamics and on the other the synchronization error dynamics based on this premise we introduce the concept of dynamic consensus and we present results on robust stability which assess the conditions for practical asymptotic synchronization of networked systems and characterize their collective behavior to illustrate our main theoretical findings we broach a brief case study on mutual synchronization of heterogeneous chaotic oscillators

stable synchronization of mechanical system networks in this paper we address stabilization of a network of underactuated mechanical systems with unstable dynamics the coordinating control law stabilizes the unstable dynamics with a term derived from the method of controlled lagrangians and synchronizes the dynamics across the network with potential shaping designed to couple the mechanical systems the coupled system is lagrangian with symmetry and energy methods are used to prove stability and coordinated behavior two cases of asymptotic stabilization are discussed one yields convergence to synchronized motion staying on a constant momentum surface and the other yields convergence to a relative equilibrium we illustrate the results in the case of synchronization of n carts each balancing an inverted pendulum

a dissipativity approach to safety verification for interconnected systems we propose a computational method for verifying a state space safety constraint of a network of interconnected dynamical systems satisfying a dissipativity property we construct an invariant set as the sublevel set of a lyapunov function comprised of local storage functions for each subsystem this approach requires only knowledge of a local dissipativity property for each subsystem and the static interconnection matrix for the network and we pose the safety verification as a sum of squares feasibility problem in addition to reducing the computational burden of system design we allow the safety constraint and initial conditions to depend on an unknown equilibrium thus offering increased flexibility over existing techniques

nonmonotonic projected algorithm with both trust region and line search for constrained optimization in this paper we combine a reduced hessian method with a mixed strategy using both trust region and line search techniques for constrained optimization the adopted strategy switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable by using fletcher s penalty function as a merit function the resulting algorithm possesses global convergence while maintaining a superlinear local convergence rate under some reasonable conditions a nonmonotonic criterion is suggested which does not require the merit function to reduce its value after every iteration

port hamiltonian systems on graphs in this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port hamiltonian systems on open graphs the basic idea is to associate with the incidence matrix of any directed graph a dirac structure relating the flow and effort variables associated to the edges and vertices of the graph and to formulate energy storing or energy dissipating relations between the flow and effort variables of the edges and the internal vertices this allows for state variables associated to the edges and formalizes the interconnection of networks examples from different origins such as consensus algorithms that share the same structure are shown it is shown how the identified hamiltonian structure offers systematic tools for the analysis and control of the resulting dynamics

synchronization and balancing on the n torus in this paper we study the behavior of a network of n agents each evolving on the circle we propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the possibly time varying and unidirectional communication graphs the global convergence analysis on the n torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the euclidean space

a high order discontinuous galerkin method for nonlinear sound waves abstract we propose a high order discontinuous galerkin scheme for nonlinear acoustic waves on polytopic meshes to model sound propagation with losses through homogeneous media we use westervelt s nonlinear wave equation with strong damping challenges in the numerical analysis lie in handling the nonlinearity in the model which involves the derivatives in time of the acoustic velocity potential and in preventing the equation from degenerating we rely in our approach on the banach fixed point theorem combined with a stability and convergence analysis of a linear wave equation with a variable coefficient in front of the second time derivative by doing so we derive an a priori error estimate for westervelt s equation in a suitable energy norm for the polynomial degree p 2 numerical experiments carried out in two dimensional settings illustrate the theoretical convergence results in addition we demonstrate efficiency of the method in a three dimensional domain with varying medium parameters where we use the discontinuous galerkin approach in a hybrid way

conditions on shifted passivity of port hamiltonian systems abstract in this paper we examine the shifted passivity property of port hamiltonian systems shifted passivity accounts for the fact that in many applications the desired steady state values of the input and output variables are nonzero and thus one is interested in passivity with respect to the shifted signals we consider port hamiltonian systems with strictly convex hamiltonian and derive conditions under which shifted passivity is guaranteed in case the hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix moreover we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback thus paving the path for controller design stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions the utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system

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

equilibrium independent passivity we extend the traditional notion of passivity to a forced system whose equilibrium is dependent on the control input by defining equilibrium independent passivity a system property characterized by a dissipation inequality centered at an arbitrary equilibrium point we provide a necessary input output condition which can be tested for systems of arbitrary dimension and sufficient conditions to certify this property for scalar systems an example from network stability analysis is presented which demonstrates the utility of this new definition we then proceed to numerical certification of equilibrium independent passivity using sum of squares programming finally through numerical examples we show that equilibrium independent passivity is less restrictive than incremental passivity

a trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints a trust region and affine scaling interior point method tram is proposed for a general nonlinear minimization with linear inequality constraints in 8 in the proposed approach a newton step is derived from the complementarity conditions based on this newton step a trust region subproblem is formed and the original objective function is monotonically decreased explicit sufficient decrease conditions are proposed for satisfying complementarity dual feasibility and second order optimality the objective of this paper is to establish global and local convergence properties of the proposed trust region and affine scaling interior point method it is shown that the proposed decrease conditions are sufficient for achieving complementarity dual feasibility and second order optimality respectively it is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem and a damped trust region step can achieve quadratic convergence

nonmonotonic back tracking trust region interior point algorithm for linear constrained optimization in this paper we modify the trust region interior point algorithm proposed by bonnans and pola in siam j optim 7 3 1997 717 for linear constrained optimization a mixed strategy using both trust region and line search techniques is adopted which switches to back tracking steps when a trial step produced by the trust region subproblem may be unacceptable the global convergence and local convergence rate of the improved algorithm are established under some reasonable conditions a nonmonotonic criterion is used to speed up the convergence progress in some ill conditioned cases the results of numerical experiments are reported to show the effectiveness of the proposed algorithm

analysis of interconnected oscillators by dissipativity theory this paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension oscillators are regarded as open systems that satisfy a particular dissipation inequality it is shown that this characterization has implications for the global stability analysis of limit cycle oscillations i in isolated oscillators ii in interconnections of oscillators and iii for the global synchrony analysis in interconnections of identical oscillators

practical synchronization with diffusive couplings we investigate the problem of synchronizing nonidentical or perturbed nonlinear systems in the considered setup the systems are incapable to synchronize under diffusive couplings instead assuming the quad property for each system we derive conditions under which the synchronization error can be kept arbitrarily small by a proper choice of the interconnection structure this motivates the definition of practical synchronization as an alternative synchronization notion for nonidentical or perturbed dynamical systems the presented results are intimately related to synchronization of passive systems but it is shown that the stronger quad assumption is essential in our framework the proposed concept of practical synchronization translates directly into a notion of robust synchronization beyond that the results open the way for an investigation of synchronization phenomena on unbalanced graphs leading to the concept of cluster synchronization

coordination of multi agent euler lagrange systems via energy shaping networking improves robustness in this paper the robust coordination of multi agent systems via energy shaping is studied the agents are nonidentical euler lagrange systems with uncertain parameters which are regulated with and without exchange of information between the agents by the classical energy based controller where the potential energy function is shaped such that if the parameters are known all agents converge globally to the same desired constant equilibrium under parameter uncertainty the globally asymptotically stable gas equilibrium point is shifted away from its desired value and this paper shows that adding information exchange between the agents to the decentralized control policy improves the steady state performance more precisely it proves that if the undirected communication graph is connected the equilibrium of the networked controller is always closer in a suitable metric to the desired one than that of the decentralized controller the result holds for all interconnection gains if the potential energy functions are quadratic else it is true for sufficiently large gains an additional advantage of networking is that the asymptotic stabilization objective can be achieved by using lower gains into the loop some experimental results using two nonlinear manipulators given support to the main results of the paper c 2013 elsevier ltd all rights reserved

edge agreement graph theoretic performance bounds and passivity analysis this work explores the properties of the edge variant of the graph laplacian in the context of the edge agreement problem we show that the edge laplacian and its corresponding agreement protocol provides a useful perspective on the well known node agreement or the consensus algorithm specifically the dynamics induced by the edge laplacian facilitates a better understanding of the role of certain subgraphs e g cycles and spanning trees in the original agreement problem using the edge laplacian we proceed to examine graph theoretic characterizations of the h2 and h performance for the agreement protocol these results are subsequently applied in the contexts of optimal sensor placement for consensus based applications finally the edge laplacian is employed to provide new insights into the nonlinear extension of linear agreement to agents with passive dynamics