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

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

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

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

generating directional residuals with dynamic parity relations abstract it is shown how diagnostic residuals which exhibit directional properties at all times in response to an arbitrary mix of input and output faults can be generated using dynamic parity relations the parity relations are applied directly to the observables of the monitored plant the design relies on the plant s dynamic input output model this residual generator can be made computationally polynomial moving average by including the invariant zero polynomial of the fault system in the specified fault responses the polynomial design yields moving average noise transfers as well white noise transfer and disturbance decoupling are achieved by extending the response specification the parity relation approach is compared with the traditional detection filter design and is shown to be more straightforward and have milder existence conditions if subjected to the same specification the two approaches yield identical residual generators

parity equations based unknown input reconstruction for mimo stochastic systems with an application in this paper an approach for reconstructing an unknown input for multiple input multiple output systems is presented it is assumed that the system is affected by process noise whereas the available system inputs are contaminated by measurement noise the novel approach is based on a parity equations concept and forms an extension of the idea developed previously by the authors a modification of the algorithm is also provided which allows the approach to deal with systems whose zero is close to unity the order of the parity space can be treated as a tuning parameter allowing for a trade off between the smoothness of the reconstructed unknown input and a phase lag an analytical solution of the overall problem is obtained by making use of a lagrange multiplier method the utility of the scheme is demonstrated when applied to a practical hydrological system

a new interpretation of the fault detection filter part 1 closed form algorithm a novel interpretation is presented of the detection filter in the context of an eigenstructure assignment problem the detection filter is shown to be equivalent to the combination of two decoupled observers with the advantage that theories already developed for conventional observers can be utilized as design aids detection space and detection order are re defined accordingly and it is shown that of the two observers that constitute a detection filter the one associated with the detection space is a single output system this fact is important since it explains important properties of the fault detection filter in a very uncomplicated fashion leading to a clear interpretation of the freedom available in designing the filter in particular it is proven that the detection filter gains are unique given the eigenvalues of the detection space further the formulation leads to a closed form expression for the detection filter and is therefore well suited to the development of simple design algorithms

invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

distributed control for identical dynamically coupled systems a decomposition approach we consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems if the state space matrices of these systems satisfy a certain structural property then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant this procedure is basically a multiobjective optimization under linear matrix inequality constraints with system norms as performance indices the explicit expressions for computing these controllers are given for both h infin or h 2 performance and both for static state feedback and dynamic output feedback in discrete time at the end of the paper two application examples illustrate the effectiveness of the approach

parity space based fault detection for linear discrete time varying systems with unknown input in this paper a new approach to parity space based fault detection fd is put forward for linear discrete time varying ldtv systems the focus of our study is on solving the problem with heavy online computational burden the main contributions are two folds firstly the problem of parity space based fd is formulated as finding a minimum of quadratic form of unknown input secondly by applying projection in krein space a solution of optimal parity space based fd is obtained via recursively computing innovations it is shown that the reduction of computation cost is achievable especially with the increase of parity space order finally a numerical example is given to demonstrate the application of the proposed method

2d residual generation and dead beat observers abstract in this paper we consider the 2d residual generation problem in an algebraic context an algorithmic method that provides a complete family of residual generators is presented and some connections between 2d residual generation and 2d dead beat observer synthesis are investigated

on residual generation by observer and parity space approaches a unifying framework for observer design by eigenstructure assignment is described a new technique for structured residual generation based on this framework is proposed one of the main features of this technique is that the equivalence between residual generation by means of observers or parity space devices are made conspicuous more precisely from a computational point of view the equations to solve in both cases are shown to be similar and for implementation both devices are shown to be identical a necessary and sufficient condition for the existence of structured residuals is given finally the sensitivity of structured residuals to nondecoupled failures is studied and a procedure for maximizing this sensitivity is described

strong and weak constraint variational assimilations for reduced order fluid flow modeling in this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a galerkin projection of the navier stokes equation the techniques proposed differ in the control variables they involve the first one introduces a weak dynamical model defined only up to an additional uncertainty time dependent function whereas the second one handles a strong dynamical constraint in which the dynamical system s coefficients constitute the control variables both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction the techniques have been assessed on numerical data and for real experimental conditions with noisy particle image velocimetry data

new nonlinear residual feedback observer for fault diagnosis in nonlinear systems the increased complexity of plants and the development of sophisticated control systems have necessitated the parallel development of efficient fault detection and isolation fdi systems this paper discusses a model based technique viz observers for detecting and isolating parametric and sensor faults in this paper a novel diagonal nonlinear residual feedback observer is proposed which is valid for a certain class of nonlinear systems where subject to other conditions the state depends nonlinearly on the fault a number of typical chemical engineering systems can be represented by models of this form the structure of the observer ensures that the residuals are diagonally affected by the faults conditions for exact decoupling of residuals are presented and convergence of the observer in the presence of step faults is proved using lyapunov like analysis multiple observers and a decision logic module are used for fdi when there are un monitored faults results are presented from numerical simulations of an illustrative example and a typical chemical engineering system a counter current heat exchanger

technical communique average consensus in networks with nonlinearly delayed couplings and switching topology the paper addresses consensus under nonlinear couplings and bounded delays for multi agent systems where the agents have the single integrator dynamics the network topology is undirected and may alter as time progresses the couplings are uncertain and satisfy a conventional sector condition with known sector slopes the delays are uncertain time varying and obey known upper bounds the network satisfies a symmetry condition that resembles the newton s third law explicit analytical conditions for the robust consensus are offered that employ only the known upper bounds for the delays and the sector slopes

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature

discrete adjoint of fractional step incompressible navier stokes solver in curvilinear coordinates and application to data assimilation abstract the discrete adjoint of an incompressible navier stokes algorithm in generalized coordinates is derived and applied to estimate the states of saturated and turbulent circular couette flows the forward navier stokes model is based on the fractional step algorithm in curvilinear coordinates on a structured grid 1 which has been widely adopted in direct numerical simulations of transitional and turbulent flows the discrete adjoint equations adopt the same stencil and temporal scheme as the forward discretization and expressions are derived that relate the discrete adjoint variables to their continuous counterpart the key ingredients of the forward algorithm can be retained in the adjoint including the computation of the cell geometry the approximate factorization method and the parallelization strategy the accuracy efficiency and stability of the adjoint solver are also commensurate with the forward model in addition a novel symmetric projector is proposed to guarantee that the the outcome of the adjoint algorithm is divergence free the implementation of the algorithm in double precision satisfies the forward adjoint relation up to eight significant figures and further validation is performed using circular couette flow the forward and adjoint growth rates of instability modes from linear theory are accurately reproduced in addition an adjoint variational data assimilation algorithm 4dvar is adopted to reconstruct the initial condition of circular couette flows from limited measurements obtained from an independent simulation when the flow is comprised of saturated wavy vortices wall measurements are sufficient to reconstruct an initial condition that latches onto the target state after a short time for the more challenging turbulent case coarse grained velocity data are used to estimate the initial condition

infinitesimals and infinites in the history of mathematics a brief survey abstract we will review the main episodes of the history of the infinite in mathematics stressing the asymmetry between infinitesimals and infinites while the actual infinite after being avoided for so long when it became a mathematical object it entered mathematics to stay infinitesimals have had a troubled history of condemnations and resurrections this has probably to do with the ambiguous basic act of mathematization as revealed by the passage from the egyptians ropes to the length without largeness of euclid s definition of the line the main characters of the narration are aristotle archimedes cavalieri euler cantor in the end we will give some information on the last re emergence of infinitesimals in nonstandard analysis and on some quite recent and intriguing new ideas

consensus reaching in multi agent packet switched networks with non linear coupling an important task for multi agent systems mas is to reach a consensus e g to align their velocity vectors recent results propose appropriate consensus protocols to achieve such tasks but most of them do not consider the effect of communication constraints such as the presence of time delays in the exchange of information between the agents in this article we provide conditions for a non linear locally passive mas of arbitrary size to reach a consensus when the agents communicate over a packet switched network that is characterised by a given topology both the cases of constant and switching topologies are considered the nature of the communication channel imposes constraints that are modelled using stochastic delays of arbitrary distribution we first embed this model in another distributed but deterministic delay model and provide conditions for the error introduced by this simplification in our main result we provide conditions for the locally passive mas with distributed delays to reach

robust detection filter design in the presence of time varying system perturbations this paper discusses the problem of designing detection filters for a class of linear time varying systems the basic contribution of the paper is that by applying a time invariant equivalent representation of the original time varying system it is possible to construct a detection filter such that the solution of the design problem can be solved using algebraic methods and geometric concepts similar to the case of time invariant situations

fault detection and isolation of linear discrete time periodic systems using the geometric approach this technical note solves the problem to detect and isolate faults in linear periodic discrete time systems a residual generator is designed through a suitable unknown input observer with the requirement that each residual should be sensitive only to one fault and simultaneously insensitive to the other faults that can affect the system and with the additional requirement of detectability that is the transition matrix of its relative error system has all eigenvalues smaller than in modulus for a given positive p 1 the solution is based on geometric tools and it makes use of the outer observable subspace notion

unknown input observer for state affine systems a necessary and sufficient condition the problem of designing an unknown input observer for linear systems and its application to fault detection is widely studied in the literature for nonlinear systems only subclasses of nonlinear systems and sufficient conditions have been stated in this paper an unknown input observer design for state affine systems is considered based on the geometric approach a necessary and sufficient condition is given for the existence of an unknown input observer

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

technical communique sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms this paper is concerned with the convergence of a class of continuous time nonlinear consensus algorithms for single integrator agents in the consensus algorithms studied here the control input of each agent is assumed to be a state dependent combination of the relative positions of its neighbors in the information flow graph using a novel approach based on the smallest order of the nonzero derivative it is shown that under some mild conditions the convex hull of the agents has a contracting property a set valued lasalle like approach is subsequently employed to show the convergence of the agents to a common point the results are shown to be more general than the ones reported in the literature in some cases an illustrative example demonstrates how the proposed convergence conditions can be verified

a bayesian tutorial for data assimilation data assimilation is the process by which observational data are fused with scientific information the bayesian paradigm provides a coherent probabilistic approach for combining information and thus is an appropriate framework for data assimilation viewing data assimilation as a problem in bayesian statistics is not new however the field of bayesian statistics is rapidly evolving and new approaches for model construction and sampling have been utilized recently in a wide variety of disciplines to combine information this article includes a brief introduction to bayesian methods paying particular attention to data assimilation we review linkages to optimal interpolation kriging kalman filtering smoothing and variational analysis discussion is provided concerning monte carlo methods for implementing bayesian analysis including importance sampling particle filtering ensemble kalman filtering and markov chain monte carlo sampling finally hierarchical bayesian modeling is reviewed we indicate how this approach can be used to incorporate significant physically based prior information into statistical models thereby accounting for uncertainty the approach is illustrated in a simplified advection diffusion model

solution of the static state feedback decoupling problem for linear systems with two outputs we give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem rdp in terms of some structural invariants a geometric characterization is also given which provides the least dynamical extension needed when rdp is not solvable

fault detection for linear periodic systems using a geometric approach using the geometric approach a solution is given to the problem of detecting faults in linear periodic discrete time systems the solution consists on developing an unknown input observer the existing conditions are provided in terms of new geometric notion of outer observable subspace that is the dual notion of inner reachable subspace making use of the new notion a residual generator is developed such that the residual is made independent of unknown input disturbance and its output free response goes asymptotically to zero

on the observability codistributions of a nonlinear system abstract the purpose of this is to introduce the notion of observability codistribution for a nonlinear system which extends the dual of the notion of unobservability subspace then we study its properties which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems

reconstruction of unsteady viscous flows using data assimilation schemes this paper investigates the use of various data assimilation da approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts variational ensemble kalman filter based and ensemble based variational da techniques are deployed along with a 2d compressible navier stokes flow solver which is also used to generate synthetic observations of a reference flow the performance of these da schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2d flow field moreover different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale da problems with up to 105 control variables in particular we show how an iterative procedure can be used within the framework of ensemble based methods to deal with both non uniform unsteady boundary conditions and initial field reconstruction the different methodologies developed and assessed in this work give a review of what can be done with da schemes in computational fluid dynamics cfd paradigm in the same time this work also provides useful information which can also turn out to be rational arguments in the da scheme choice dedicated to a specific cfd application

a new scheme of fault detection for linear discrete time varying systems in this note a new scheme of fault detection fd is proposed for linear discrete time varying ldtv systems subject to l 2 norm bounded unknown inputs the basic idea is to find an optimal estimation of the l 2 norm of the unknown inputs including the unknown initial state variables this leads to a natural design of the fd system with the l 2 norm boundedness of the unknown inputs as a threshold and the l 2 norm of the unknown input estimate as the evaluation function to avoid heavy computational burden projection technique in krein space is applied which allows a recursive computation of the evaluation function it is shown that the achieved fd system satisfies both the worst case and best case sensitivity robustness ratio criteria and further applications to observer based fd lead to an alternative design of h infty h infty and or h h infty fault detection filter

detection filter design for lpv systems a geometric approach this paper investigates fault detection and isolation of linear parameter varying lpv systems by using parameter varying c a invariant subspace and parameter varying unobservability subspaces the so called detection filter approach formulated as the fundamental problem of residual generation fprg for linear time invariant lti systems is extended for a class of lpv systems the question of stability is addressed in the terms of lyapunov quadratic stability by using linear matrix inequalities the results are applied to the model of a generic small commercial aircraft

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

network flows that solve linear equations we study distributed network flows as solvers in continuous time for the linear algebraic equation mathbf z mathbf h mathbf y each node i has access to a row mathbf h i mathrm t of the matrix mathbf h and the corresponding entry z i in the vector mathbf z the first consensus projection flow under investigation consists of two terms one from standard consensus dynamics and the other contributing to projection onto each affine subspace specified by the mathbf h i and z i the second projection consensus flow on the other hand simply replaces the relative state feedback in consensus dynamics with projected relative state feedback without dwell time assumption on switching graphs we prove that all node states converge to a common solution of the linear algebraic equation if there is any the convergence is global for the consensus projection flow while local for the projection consensus flow in the sense that the initial values must lie on the affine subspaces if the linear equation has no exact solutions we show that the node states can converge to a ball around the least squares solution whose radius can be made arbitrarily small through selecting a sufficiently large gain for the consensus projection flow for a fixed bidirectional graph semi global convergence to approximate least squares solutions is also demonstrated for switching balanced directed graphs under suitable conditions it is also shown that the projection consensus flow drives the average of the node states to the least squares solution with a complete graph numerical examples are provided as illustrations of the established results

infinigons of the hyperbolic plane and grossone in this paper we study the contribution of the theory of grossone to the study of infinigons in the hyperbolic plane we can see that the theory of grossone can help us to obtain a much more precise classification for these objects than in the traditional setting

iterative residual generator for fault detection with linear time invariant state space models in this paper an iterative residual generator irg is proposed for discrete time invariant state space model with the aim of detecting faulty signals by minimizing the mean square errors subject to unbiasedness constraint a new filter with finite impulse response structure is derived the resulting irg is then obtained by extracting residual signal from the batch filter through several predictor corrector iterations it shows that irg can provide a zero mean gaussian process regardless of previous estimation errors more importantly it includes the residual generation process in the kalman filter as its special case with the chi square test a numerical example is simulated to demonstrate that irg can reduce the false alarm significantly compared with the traditional recursive strategy in the presence of actuator or sensor faults and the estimation horizon length in irg serves as a tuning parameter providing a tradeoff between the missed alarm and false alarm

connectivity and set tracking of multi agent systems guided by multiple moving leaders in this paper we investigate distributed multi agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking based on the connectivity of the time varying multi agent system necessary and sufficient conditions are obtained for set input to state stability and set integral input to state stability for a nonlinear neighbor based coordination rule with switching directed topologies conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders

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

robust fault estimation using relative information in linear multi agent networks in this technical note a robust fault estimation method based on sliding mode observers is proposed for a collection of agents undertaking a shared task and exchanging only relative information over a communication network since the system of systems formed by the agents is not observable with respect to relative sensing information by appropriate transformations and scalings of the inputs and outputs of the actual system a meaningful observable subsystem is created for this new subsystem after modal decomposition based on the associated laplacian decoupled sliding mode observers depending only on the individual node level dynamics of the network can be created exploiting an existing design philosophy these collectively form a centralized fault estimation scheme for the original system

brief paper robust fault detection based on observers for bilinear systems the design of a residual generator for robust fault detection in bilinear systems is considered two methods are presented the first one is based on a linear time invariant observer up to output injection while the second one relies on a so called kalman like observer it is shown via examples that the approach based on a kalman like observer allows one to handle a larger class of bilinear systems than the other observer based methods presented in the literature

decoupling by restricted static state feedback the general case in this paper we tackle the general block decoupling problem for linear constant dynamical systems c a b with m inputs and p outputs with restricted static state feedback in other words with control laws of type u gfx gv we give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in 2 for the simple case k p leq m where k denotes the number of blocks to be decoupled

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

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

a general approach to the eigenstructure assignment for reachability and stabilizability subspaces abstract this paper is concerned with the problem of determining basis matrices for the supremal output nulling reachability and stabilizability subspaces and the simultaneous computation of the associated friends that place the assignable closed loop eigenvalues at desired locations our aim is to show that the moore laub algorithm in moore and laub 1978 for the computation of these subspaces was stated under unnecessary restrictive assumptions we prove the same result under virtually no system theoretic hypotheses this provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust and as general as the standard ones based on the computation of sequences of subspaces

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

a reduced order model based on kalman filtering for sequential data assimilation of turbulent flows abstract a kalman filter based sequential estimator is presented in this work the estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows this technique provides an augmented flow state integrating available observation in the cfd model naturally preserving a zero divergence condition for the velocity field because of the prohibitive costs associated with a complete kalman filter application two model reduction strategies have been proposed and assessed these strategies dramatically reduce the increase in computational costs of the model which can be quantified in an augmentation of 10 15 with respect to the classical numerical simulation in addition an extended analysis of the behavior of the numerical model covariance q has been performed optimized values are strongly linked to the truncation error of the discretization procedure the estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity including turbulent flow configurations the results show that the augmented flow successfully improves the prediction of the physical quantities investigated even when the observation is provided in a limited region of the physical domain in addition the present work suggests that these data assimilation techniques which are at an embryonic stage of development in cfd may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

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

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

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

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

fault detection in a mixed h sub 2 h sub spl infin setting in this note we study the problem of fault detection in linear time invariant lti systems which are simultaneously effected by two classes of unknown inputs noises having fixed spectral densities and unknown finite energy disturbances this problem is formulated as a mixed h sub 2 h sub spl infin filtering problem necessary and sufficient conditions for local optimality are presented moreover it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality lmi constrains a numerical example is given to illustrate the advantage of the mixed h sub 2 h sub spl infin approach as compared to existing techniques which are based on optimization of h sub 2 and h sub spl infin criteria

a game theoretic fault detection filter the fault detection process is approximated with a disturbance attenuation problem the solution to this problem for both linear time varying and time invariant systems leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected in the limit when the disturbance attenuation bound is brought to zero a complete transmission block is achieved by embedding the nuisance inputs into an unobservable invariant subspace since this is the same invariant subspace structure seen in some types of detection filters we can claim that the asymptotic game filter is itself a detection filter one can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space the resulting lower dimensional filter will then be sensitive only to the failure to be detected a pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time invariant and time varying problems in both full order and reduced order forms

optimal stochastic fault detection filter a fault detection and identification algorithm called optimal stochastic fault detection filter is determined the objective of the filter is to detect a single fault called the target fault and block other faults called the nuisance faults in the presence of the process and sensor noises the filter is derived by maximizing the transmission from the target fault to the projected output error while minimizing the transmission from the nuisance faults therefore the residual is affected primarily by the target fault and minimally by the nuisance faults the transmission from the process and sensor noises is also minimized so that the filter is robust with respect to these disturbances it is shown that the filter recovers the geometric structure of the unknown input observer in the limit where the weighting on the nuisance fault transmission goes to infinity further the asymptotic behavior of the filter near the limit is determined by using a perturbation method filter designs can be obtained for both time invariant and time varying systems

distributed circular formation stabilization for dynamic unicycles this paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius whose center is stationary but dependent on the initial conditions and travel around the circle in a desired direction the vehicles are required to converge to a formation on the circle expressed by desired separations and ordering of the unicycles the information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree a hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation

solving ordinary differential equations on the infinity computer by working with infinitesimals numerically there exists a huge number of numerical methods that iteratively construct approximations to the solution y x of an ordinary differential equation ode y x f x y starting from an initial value y 0 y x 0 and using a finite approximation step h that influences the accuracy of the obtained approximation in this paper a new framework for solving odes is presented for a new kind of a computer the infinity computer it has been patented and its working prototype exists the new computer is able to work numerically with finite infinite and infinitesimal numbers giving so the possibility to use different infinitesimals numerically and in particular to take advantage of infinitesimal values of h to show the potential of the new framework a number of results is established it is proved that the infinity computer is able to calculate derivatives of the solution y x and to reconstruct its taylor expansion of a desired order numerically without finding the respective derivatives analytically or symbolically by the successive derivation of the ode as it is usually done when the taylor method is applied methods using approximations of derivatives obtained thanks to infinitesimals are discussed and a technique for an automatic control of rounding errors is introduced numerical examples are given

inflow and initial conditions for direct numerical simulation based on adjoint data assimilation a method for generating inflow conditions for direct numerical simulations dns of spatially developing flows is presented the proposed method is based on variational data assimilation and adjoint based optimization the estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system the approach s robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder the performance of the technique is also illustrated in a real world application by using noisy large scale piv measurements this method denoises experimental velocity fields and reconstructs a continuous trajectory of motion fields from discrete and unstable measurements

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

on the approximation of fault directions for mutual detectability an invariant zero approach this note is concerned with the approximation of fault directions in relation to mutual detectability in detection filter problems as an efficient system representation for analysis of detection order we utilize the observer canonical form by which we show that the invariant zero and the detection order can be analytically calculated by a set of polynomials associated with fault directions noting that this approach clearly shows the condition for the detection order to be plural we propose a fault direction approximation method which increases its detection order for obtaining a mutually detectable system regarding the resulting degradation of fault isolation performance as a disturbance we present its quantitative analysis and propose a method of selecting a threshold in order to guarantee proper fault isolation

on discrete time convergence for general linear multi agent systems under dynamic topology this note aims to develop the nonnegative matrix theory in particular the product properties of infinite row stochastic matrices which is widely used for multiple integrator agents to deal with the convergence analysis of general discrete time linear multi agent systems mass with the proposed approach it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions i e the individual uncoupled system is allowed to be strictly unstable in the discrete time sense and it is only required that the joint of the communication topologies has a spanning tree frequently enough moreover a least convergence rate as well as an upper bound for the strictly unstable mode which are independent of the switching mode of the system are specified as well

stochastic and deterministic fault detection for randomized gossip algorithms this paper addresses the problem of detecting faults in linear randomized gossip algorithms where the selection of the dynamics matrix is stochastic a fault is a disturbance signal injected by an attacker to corrupt the states of the nodes we propose the use of set valued observers svos to detect if the state observations are compatible with the system dynamics for the worst case in a deterministic setting the concept of stochastic set valued observers ssvos is also introduced to construct a set that is guaranteed to contain all possible states with at least a pre specified desired probability the proposed algorithm is stable in the sense that it requires a finite number of vertices to represent polytopic sets and it allows for the computation of the largest magnitude of the disturbance that an attacker can inject in the network without being detected results are presented to reduce the computational cost of this approach and in particular by considering only local information and representing the remainder of the network as a disturbance the case of a consensus algorithm is discussed leading to the conclusion that by using the proposed svos finite time consensus is achieved in non faulty environments a novel algorithm is proposed that produces less conservative set valued state estimates by having nodes exchanging local estimates the algorithm inherits all the previous properties and also enables finite time consensus computation regardless of the value of the horizon

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

fault detection and isolation of two dimensional 2d systems abstract in this work we develop a novel fault detection and isolation fdi scheme for discrete time two dimensional 2d systems that are represented by the fornasini marchesini model ii fmii this is accomplished by generalizing the basic invariant subspaces including unobservable conditioned invariant and unobservability subspaces of 1d systems to 2d models these extensions have been achieved and facilitated by representing a 2d model as an infinite dimensional inf d system on a banach vector space and by particularly constructing algorithms that compute these subspaces in a finite and known number of steps by utilizing the introduced subspaces the fdi problem is formulated and necessary and sufficient conditions for its solvability are provided sufficient conditions for solvability of the fdi problem for 2d systems using both deadbeat and lmi based filters have also been developed moreover the capabilities and advantages of our proposed approach are demonstrated by performing an analytical comparison with the currently available 2d geometric methods in the literature

an eigenstructure assignment algorithm for the design of fault detection filters in this paper we present an algorithm for the construction of detection spaces in a fault detection filter by direct eigenstructure assignment the algorithm permits great flexibility and simplifies the process of designing fault detection filters

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

fault detection via factorization approach abstract problems of designing fault detection and identification filters in the frequency domain are formulated and solved using the factorization approach a characterization of all fault detection filters is derived this enables the derivation of necessary and sufficient conditions for the existence of fault identification as well as detection and isolation filters it is shown that these conditions are a generalization of existing results the formulas of constructing the filters are also derived in comparison with the algorithms given in previous work they are computationally straightforward and simple finally the proposed method for designing fault identification filters is extended so that more practical cases can be handled

a correspondence about fdi observers an explicit existence condition for linear fdi observers is provided this amends an earlier result of the authors and clarifies some surrounding points

fault detection and isolation observers a design of reduced order observers is proposed for linear time invariant systems with unknown inputs including unknown measurement disturbances based on the unknown input observer design a systematic treatment of designing fault detection and isolation fdi observers is provided the core of the fdi observer design is to find an observable subsystem where the faults of interest show up and the rest of the faults disappear the fdi observer design procedure has a clear physical meaning robust fdi observers for uncertain systems can also be obtained using the fdi observer design provided the uncertainties of the system can be formulated as unknown inputs it is shown that the parity equations of another important fdi method can be generated in an elegant way using a dead beat fdi observer scheme directly in the time domain examples are included to show some concepts and to illustrate the fdi observer design method

counting systems and the first hilbert problem the first hilbert problem is studied in this paper by applying two instruments a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets several counting systems are taken into consideration it is emphasized in the paper that different mathematical languages can describe mathematical objects in particular sets and the number of their elements with different accuracies the traditional and the new approaches are compared and discussed

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

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

brief generic solvability of the failure detection and identification problem necessary and sufficient conditions for the generic solvability of the extended fundamental problem in residual generation efprg massoumnia et al 1989 ieee trans automat control 34 316 321 in the case of simultaneous actuator and sensor failures are presented in the process of deriving these conditions the generic forms of supremal controllability and infimal unobservability subspaces of lti systems having diagonal state space matrices are obtained

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

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

optimal residual decoupling for robust fault diagnosis his paper deals with residual generation for the diagnosis of faults in the presence of disturbances the emphasis is on modelling errors represented as multiplicative disturbances and on parametric faults these are both characterized as discrepancies in a set of underlying parameters the residuals are obtained using parity equations to address the situation when the number of uncertain parameters is too high to allow perfect decoupling two approximate decoupling methods are introduced one utilizes rank reduction of the model error fault entry matrix via singular value decomposition the other minimizes a least squares performance index formulated on the residuals under a set of equality constraints it is shown that by the appropriate construction of the entry matrix or of the performance index and the constraints a broad variety of structured and directional residual strategies can be implemented