control of a three coleader formation in the plane this paper considers a formation of three point agents moving in the plane where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbour further each agent is allowed to determine its movement strategy using local knowledge only of the direction of its neighbour and the current and desired distance from its neighbour the motion of the formation is studied when distances are initially incorrect a convergence result is established to the effect that provided agents never become collinear the correct distances will be approached exponentially fast and the formation as a whole will rotate by a finite angle and translate by a finite distance

subspace identification a markov parameter approach estimating observability matrices or state sequences is the central component of existing subspace identification methods in this paper a different approach in which markov parameters are first estimated under general input excitation is proposed the prominent difference of this approach is that a three block arrangement of data matrices is used it is shown that one advantage of this approach over other subspace algorithms is that several unbiased estimating procedures can be carried out one immediate application is to obtain balanced or nearly balanced models directly from the estimated markov parameters another application is that with the estimated markov parameters consistently initialized kalman filter state sequences can be obtained from which the system matrices can be easily determined without bias performance of the proposed algorithms is investigated in two case studies which are based on real data taken from two industrial systems the algorithms developed in this paper have been impl

formation control of mobile agents based on inter agent distance dynamics we propose a novel formation control strategy based on inter agent distances for single integrator modeled agents in the plane attempting to directly control the inter agent distances we derive a control law from the distance dynamics the proposed control law achieves the local asymptotic stability of infinitesimally rigid formations triangular infinitesimally rigid formations are globally asymptotically stable under the proposed control law with all squared distance errors exponentially and monotonically converging to zero as an extension of existing results the stability analysis in this paper reveals that any control laws related with the gradient law by multiplication of a positive matrix ensure the local asymptotic stability of infinitesimally rigid formations

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

brief paper estimation of the disturbance structure from data using semidefinite programming and optimal weighting designing a state estimator for a linear state space model requires knowledge of the characteristics of the disturbances entering the states and the measurements in odelson b j rajamani m r rawlings j b 2006 a new autocovariance least squares method for estimating noise covariances automatica 42 2 303 308 the correlations between the innovations data were used to form a least squares problem to determine the covariances for the disturbances in this paper we present new and simpler necessary and sufficient conditions for the uniqueness of the covariance estimates we also formulate the optimal weighting to be used in the least squares objective in the covariance estimation problem to ensure minimum variance in the estimates a modification to the above technique is then presented to estimate the number of independent stochastic disturbances affecting the states this minimum number of disturbances is usually unknown and must be determined from data a semidefinite optimization problem is solved to estimate the number of independent disturbances entering the system and their covariances

distributed formation control of multi agent systems using complex laplacian the paper concentrates on the fundamental coordination problem that requires a network of agents to achieve a specific but arbitrary formation shape a new technique based on complex laplacian is introduced to address the problems of which formation shapes specified by inter agent relative positions can be formed and how they can be achieved with distributed control ensuring global stability concerning the first question we show that all similar formations subject to only shape constraints are those that lie in the null space of a complex laplacian satisfying certain rank condition and that a formation shape can be realized almost surely if and only if the graph modeling the inter agent specification of the formation shape is 2 rooted concerning the second question a distributed and linear control law is developed based on the complex laplacian specifying the target formation shape and provable existence conditions of stabilizing gains to assign the eigenvalues of the closed loop system at desired locations are given moreover we show how the formation shape control law is extended to achieve a rigid formation if a subset of knowledgable agents knowing the desired formation size scales the formation while the rest agents do not need to re design and change their control laws

three and higher dimensional autonomous formations rigidity persistence and structural persistence in this paper we generalize the notion of persistence which has been originally introduced for two dimensional formations to r d for d 3 seeking to provide a theoretical framework for real world applications which often are in three dimensional space as opposed to the plane persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents we verify that many of the properties of rigid and or persistent formations established in r 2 are also valid for higher dimensions analysing the closed subgraphs and directed paths in persistent graphs we derive some further properties of persistent formations we also provide an easily checkable necessary condition for persistence we then turn our attention to consider some practical issues raised in multi agent formation control in three dimensional space we display a new phenomenon not present in r 2 whereby subsets of agents can behave in a problematic way when this behaviour is precluded we say that the graph depicting the multi agent formation has structural persistence in real deployment of controlled multi agent systems formations with underlying structurally persistent graphs are of interest we analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence we study the connections between the allocation of degrees of freedom dofs across agents and the characteristics of persistence and or structural persistence of a directed graph we also show how to transfer dofs among agents when the formation changes with new agent s added to preserve persistence and or structural persistence

brief paper stochastic system transformation using generalized orthonormal basis functions with applications to continuous time system identification this paper studies the system transformation using generalized orthonormal basis functions that include the laguerre basis as a special case the transformation of the deterministic systems is studied in the literature which is called the hambo transform the aim of the paper is to develop a transformation theory for stochastic systems the paper establishes the equivalence of continuous and transformed discrete time stochastic systems in terms of solutions the method is applied to the continuous time system identification problem it is shown that using the transformed signals the po moesp subspace identification algorithm yields consistent estimates for system matrices an example is included to illustrate the efficacy of the proposed identification method and to make a comparison with the method using the laguerre filter

matchable observable linear models and direct filter tuning an approach to multivariable identification identification of linear time invariant multivariable systems can best be understood as comprising three separate problems selection of system model structure filter design and parameter estimation itself approaching the first using matchable observable models originally developed in the adaptive control literature and the second via direct or derivative free optimization effective least squares algorithms can be used for parameter estimation the accuracy robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data the results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature

subspace identification methods for hammerstein systems rank constraint and dimension problem this article studies the subspace identification methods sims for hammerstein systems with major focus on a rank constraint and the related dimension problem we analyse the effects of the rank constraint on the three steps of a unifying framework for sims the rank constraint has no effect on the first two steps but does so on the third step if the rank constraint is ignored as in the existing over parametrised method opm for hammerstein system identification the optimality of the resulting estimate can still be established even so the opm may suffer from the dimension problem resulting in a low numerical efficiency to resolve the dimension problem we propose a new subspace based method named as the least parametrised method lpm for identification of hammerstein systems with non coupling input nonlinearities simulation results are provided to demonstrate the effectiveness of the lpm and show the necessity of considering the rank constraint to improve the numerical efficiency

distributed formation control via global orientation estimation in this paper we propose a novel distributed formation control strategy which is based on the measurements of relative position of neighbors with global orientation estimation since agents do not share a common reference frame orientations of the local reference frames are not aligned with each other the proposed strategy includes a combination of global orientation estimation and formation control law under the proposed strategy the orientation of each agent is estimated in the global sense if interaction graph has a spanning tree with the estimated orientations of local frames formation control strategy ensures that the formation globally exponentially converges to the desired formation

frequency weighted model reduction via quasi kalman decomposition a frequency weighted model reduction method based on quasi kalman decomposition is proposed for discrete systems the method is essentially an extension of the technique presented by lu and lee 1985 to the frequency weighted case and can handle both single sided as well as double sided weights two illustrative examples show the effectiveness of the method and results are compared with the method developed by enns 1984

a common framework for complete and incomplete attitude synchronization in networks with switching topology in this paper we study attitude synchronization for elements in the unit sphere in mathbb r scriptscriptstyle scriptscriptstyle 3 and for elements in the three dimensional 3 d rotation group for a network with switching topology the agents angular velocities are assumed to be the control inputs and a switching control law for each agent is devised that guarantees synchronization provided that all elements are initially contained in a region which we identify later in the paper the control law is decentralized and it does not require a common orientation frame among all agents we refer to synchronization of unit vectors in mathbb r scriptscriptstyle 3 as incomplete synchronization and of 3 d rotation matrices as complete synchronization our main contribution lies in showing that these two problems can be analyzed under a common framework where all agents dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension

bearing rigidity and almost global bearing only formation stabilization a fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter neighbor bearings while many previous works focused on the bearing rigidity of two dimensional frameworks a first contribution of this paper is to extend these results to arbitrary dimensions it is shown that a framework in an arbitrary dimension can be uniquely determined up to a translation and a scaling factor by the bearings if and only if the framework is infinitesimally bearing rigid in this paper the proposed bearing rigidity theory is further applied to the bearing only formation stabilization problem where the target formation is defined by inter neighbor bearings and the feedback control uses only bearing measurements nonlinear distributed bearing only formation control laws are proposed for the cases with and without a global orientation it is proved that the control laws can almost globally stabilize infinitesimally bearing rigid formations numerical simulations are provided to support the analysis

distributed self localization for relative position sensing networks in 2d space this paper studies the 2d localization problem of a sensor network given anchor node positions in a common global coordinate frame and relative position measurements in local coordinate frames between node pairs it is assumed that the local coordinate frames of different sensors have different orientations and the orientation difference with respect to the global coordinate frame are not known in terms of graph connectivity a necessary and sufficient condition is obtained for self localizability that leads to a fully distributed localization algorithm moreover a distributed verification algorithm is developed to check the graph connectivity condition which can terminate successfully when the sensor network is self localizable finally a fully distributed linear and iterative algorithm based on the complex valued laplacian associated with the sensor network is proposed which converges globally and gives the correct localization result

lower bounds on the proportion of leaders needed for expected consensus of 3 d flocks this paper considers the consensus behavior of a spatially distributed 3 d dynamical network composed of heterogeneous agents leaders and followers in which the leaders have the preferred information about the destination while the followers do not have all followers move in a 3 d euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors compared with the 2 d model a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents using the network structure and the estimation of some characteristics for the initial states we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases 1 fixed speed and neighborhood radius and 2 variable speed and neighborhood radius with respect to the population size some simulation examples are given to justify the theoretical results

embedded trees estimation of gaussian processes on graphs with cycles graphical models provide a powerful general framework for encoding the structure of large scale estimation problems however the graphs describing typical real world phenomena contain many cycles making direct estimation procedures prohibitively costly in this paper we develop an iterative inference algorithm for general gaussian graphical models it operates by exactly solving a series of modified estimation problems on spanning trees embedded within the original cyclic graph when these subproblems are suitably chosen the algorithm converges to the correct conditional means moreover and in contrast to many other iterative methods the tree based procedures we propose can also be used to calculate exact error variances although the conditional mean iteration is effective for quite densely connected graphical models the error variance computation is most efficient for sparser graphs in this context we present a modeling example suggesting that very sparsely connected graphs with cycles may provide significant advantages relative to their tree structured counterparts thanks both to the expressive power of these models and to the efficient inference algorithms developed herein the convergence properties of the proposed tree based iterations are characterized both analytically and experimentally in addition by using the basic tree based iteration to precondition the conjugate gradient method we develop an alternative accelerated iteration that is finitely convergent simulation results are presented that demonstrate this algorithm s effectiveness on several inference problems including a prototype distributed sensing application

subspace identification for non linear systems with measured input non linearities this paper uses subspace methods to identify a class of multi input multi output discrete time non linear time varying systems specifically we identify systems that are non linear in measured data and linear in unmeasured states numerical examples are presented to demonstrate the efficacy of the method

comments on global stabilization of rigid formations in the plane automatica 49 2013 14361441 this paper shows that the modified gradient control law proposed in tian and wang 2013 does not globally stabilize rigid formation shapes also further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided

subspace based prediction of linear time varying stochastic systems in this paper a new subspace method for predicting time varying stochastic systems is proposed using the concept of angle between past and present subspaces spanned by the extended observability matrices the future signal subspace is predicted by rotating the present subspace in the geometrical sense and time varying system matrices are derived from the resultant signal subspace proposed algorithm is improved for fast varying systems furthermore recursive implementation of both algorithms is developed

a graph laplacian approach to coordinate free formation stabilization for directed networks this paper concentrates on coordinate free formation control for directed networks for which the dynamic motion of each agent is assumed to be governed only by a local control we develop a graph laplacian approach to solve the global and exponential formation stablization problem using merely relative position measurements between neighbors first to capture the sensing and control architectures that are needed to maintain the shape of a formation a necessary and sufficient topological condition is proposed second a laplacian based control law is developed for the stablization problem of a group of mobile agents to a desired formation shape under both fixed and switching topologies due to temporal node failures simulation results are provided to demonstrate that our laplacian based formation control strategy is inherently fault tolerant and robust to node failures

formation tracking of the second order multi agent systems using position only information via impulsive control with input delays in this paper the formation tracking problem for the second order multi agent system with and without input delay are investigated respectively the objective is to design the formation tracking algorithm such that a certain follower follows the trajectory of the leader while also maintains a certain desired geometric formation with other agents simultaneously the impulsive algorithms are designed by using only the relative position information of the neighbors for both the cases with and without the input delay by using properties of the laplacian matrix and combining the stability theory of impulsive systems necessary and sufficient conditions are derived to achieve the formation tracking of the second order multi agent system with and without the input delay respectively the numerical examples are given to illustrate the effectiveness of our theoretical results

time varying formation control for general linear multi agent systems with switching directed topologies time varying formation analysis and design problems for multi agent systems with general linear dynamics and switching directed interaction topologies are investigated different from the previous results the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed firstly necessary and sufficient conditions for general linear multi agent systems with switching directed topologies to achieve time varying formations are proposed where a description of the feasible time varying formation set and approaches to expand the feasible formation set are given then an explicit expression of the time varying formation reference function is derived to describe the macroscopic movement of the whole formation an approach to assign the motion modes of the formation reference is provided moreover an algorithm consisting of four steps to design the formation protocol is presented in the case where the given time varying formation belongs to the feasible formation set it is proven that by designing the formation protocol using the proposed algorithm time varying formation can be achieved by multi agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold finally numerical simulations are presented to demonstrate the effectiveness of the theoretical results

a unifying theorem for three subspace system identification algorithms the aim of this paper is to indicate and explore the similarities between three different subspace algorithms for the identification of combined deterministic stochastic systems the similarities between these algorithms have been obscured due to different notations and backgrounds it is shown that all three algorithms are special cases of one unifying theorem the comparison also reveals that the three algorithms use exactly the same subspace to determine the order and the extended observability matrix but that the weighting matrix used to calculate a basis for the column space of the observability matrix is different in the three cases

target point formation control in this paper a new distributed feedback strategy is proposed for controlling a rigid acyclic formation of kinematic point modeled mobile autonomous agents in the plane the strategy makes use of a new concept called a target point and is applicable to any two dimensional acyclic formation whose underlying directed graph can be generated by a sequence of henneberg vertex additions it is shown that the method can cause a group of agents starting in any given initial positions in the plane to move into a prescribed formation exponentially fast provided the formation s designated leader and first follower start in different positions

on the relation between cca and predictor based subspace identification in this paper we investigate the relation between a recently proposed subspace method based on predictor identification pbsid known also as ldquowhitening filter algorithm rdquo and the classical cca algorithm the comparison is motivated by i the fact that cca is known to be asymptotically efficient for time series identification and optimal for white measured inputs and ii some recent results showing that a number of recently developed algorithms are very closely related to pbsid we show that pbsid is asymptotically equivalent to cca precisely in the situations in which cca is optimal while an ldquooptimizedrdquo version of pbsid behaves no worse than cca also for nonwhite inputs even though pbsid and its optimized version are consistent regardless of the presence of feedback in this paper we work under the assumption that there is no feedback to make the comparison with cca meaningful the results of this paper imply that the ldquooptimizedrdquo pbsid besides being able to handle feedback is to be preferred to cca also when there is no feedback only in very specific cases white or no inputs are the two algorithms asymptotically equivalent

formation control and network localization via orientation alignment we propose a formation control strategy based on inter agent displacements for single integrator modeled agents in the plane since the orientations of the local reference frames of the agents are not aligned with each other due to the absence of a common sense of orientation the proposed strategy consists of an orientation alignment law and a formation control law under the proposed strategy if the interaction graph is uniformly connected and all the initial orientation angles belong to an interval with length less than the orientations are exponentially aligned and the formation exponentially converges to the desired formation we also show that the proposed strategy can be utilized for network localization as a dual problem

subspace identification for continuous time stochastic systems via distribution based approach this paper presents a novel approach for system identification of continuous time stochastic state space models from random input output continuous data the approach is based on the introduction of random distribution theory in describing higher time derivatives of stochastic processes and the input output algebraic relationship is derived which is treated in the time domain the efficacy of the approach is examined by comparing with other approaches employing the filters

criteria for informative experiments with subspace identification informative experiments are identification experiments which contain sufficient information for an identification algorithm to discriminate between different models in an intended model set in this paper a particular set of identification algorithms namely subspace based identification is considered criteria for experiments to be informative with these methods in the deterministic setup and the combined deterministic stochastic setup are presented it is pointed out that if these criteria are not satisfied interesting phenomena in which perfect cancellations of the deterministic components and the stochastic components occur in a subspace projection may occur it is further shown that such cancellations can indeed be avoided under mild conditions

finite time stabilisation of cyclic formations using bearing only measurements this paper studies decentralised formation control of multiple vehicles in the plane when each vehicle can only measure the local bearings of their neighbours by using bearing only sensors since the inter vehicle distance cannot be measured the target formation involves no distance constraints more specifically the target formation considered in this paper is an angle constrained cyclic formation where each vehicle has exactly two neighbours and the angle at each vehicle subtended by its two neighbours is pre specified to stabilise the target formation we propose a discontinuous control law that only requires the sign information of the angle errors due to the discontinuity of the proposed control law the stability of the closed loop system is analysed by employing a locally lipschitz lyapunov function and nonsmooth analysis tools we prove that the target formation is locally finite time stable with collision avoidance guaranteed

on consistency of subspace methods for system identification subspace methods for identification of linear time invariant dynamical systems typically consist of two main steps first a so called subspace estimate is constructed this first step usually consists of estimating the range space of the extended observability matrix secondly an estimate of system parametersis obtained based on the subspace estimate in this paper the consistency of a large class of methods for estimating the extended observability matrix is analyzed persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise for systems with process noise it is shown that a persistence of excitation condition on the input is not sufficient more precisely an example for which the subspace methods fail to give a consistent estimate of the transfer function is given this failure occurs even if the input is persistently exciting of any order it is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

multi consensus of multi agent networks via a rectangular impulsive approach abstract a multi consensus problem is studied in multi agent networks the interaction mechanism of competition abstention cooperation among agents is introduced three rectangular impulsive protocols are proposed to solve multi consensus of second order multi agent networks with a directed topology these algorithms have the performance of dirac impulsive control and discrete time control necessary and sufficient conditions are obtained for the stationary multi consensus and the dynamic multi consensus numerical examples are provided to illustrate the effectiveness of the obtained criteria

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

optimal role and position assignment in multi robot freely reachable formations abstract many multi robot problems require the achievement of formations as part of the overall mission this work considers a scenario in which unlabeled homogeneous robots must adopt a given formation pattern buildable anywhere in the environment this involves finding the relative pose of the formation in regard to the initial robot positions understood as a translation and a rotation and the optimal assignment of the role of each robot within the formation this paper provides an optimal solution for the combined parameters of translation rotation and assignment that minimizes total displacement to achieve this objective we first formally prove that the three decision variables are separable since computing the optimal assignment without accounting for the rotation is a computationally expensive problem we propose an algorithm that efficiently computes the optimal roles together with the rotation the algorithm is provably correct and finds the optimal solution in finite time a distributed implementation is also discussed simulation results characterize the complexity of our solution and demonstrate its effectiveness

analysis of state space system identification methods based on instrumental variables and subspace fitting subspace based state space system identification 4sid methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification the advantages are that the user has simple and few design variables and that the methods have robust numerical properties and relatively low computational complexities though subspace techniques have been demonstrated to perform well in a number of cases the performance of these methods is neither fully understood nor analyzed our principal objective is to undertake a statistical investigation of subspace based system identification techniques the studied methods consist of two steps the subspace spanned by the extended observability matrix is first estimated the asymptotic properties of this subspace estimate are derived herein in the second step the structure of the extended observability matrix is used to find a system model estimate two possible methods are considered the simplest one only uses a certain shift invariance property while in the other method a parametric representation of the null space of the observability matrix is exploited explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given

subspace identification with guaranteed stability using constrained optimization in system identification the true system is often known to be stable however due to finite sample constraints modeling errors plant disturbances and measurement noise the identified model may be unstable we present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods in subspace identification we first obtain an estimate of the state sequence or extended observability matrix and then solve a least squares optimization problem to estimate the system parameters to ensure asymptotic stability of the identified model we write the least squares optimization problem as a convex linear programming problem with mixed equality quadratic and positive semidefinite constraints suitable for existing convex optimization codes such as sedumi we present examples to illustrate the method and compare to existing approaches

on the stable equilibrium points of gradient systems this paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f in particular it is shown that under the assumption that f is real analytic local minimality is necessary and sufficient for stability under the weaker assumption that f is indefinitely continuously differentiable local minimality is neither necessary nor sufficient for stability

subspace algorithms for the stochastic identification problem abstract in this paper we derive a new subspace algorithm to consistently identify stochastic state space models from given output data without forming the covariance matrix and using only semi infinite block hankel matrices the algorithm is based on the concept of principal angles and directions we describe how they can be calculated with qr and quotient singular value decomposition we also provide an interpretation of the principal directions as states of a non steady state kalman filter bank

a bernstein type theorem for minimal hypersurfaces via gauss maps abstract let m be an n dimensional smooth oriented complete embedded minimal hypersurface in r n 1 with euclidean volume growth we show that if the image under the gauss map of m avoids some neighborhood of a half equator then m must be an affine hyperplane

brief paper sufficient conditions for connectivity maintenance and rendezvous in leader follower networks in this paper we derive a set of constraints that are sufficient to guarantee maintained connectivity in a leader follower multi agent network with a proximity based communication topology in the scenario we consider only the leaders are aware of the global mission which is to converge at a known destination point thus the followers need to stay in contact with the group of leaders in order to reach the goal in the paper we show that we can maintain the initial network structure and thereby connectivity by setting up bounds on the ratio of leaders to followers and on the magnitude of the goal attraction force experienced by the leaders the results are first established for an initially complete communication graph and then extended to an incomplete graph the results are illustrated by computer simulations

exponential stability for formation control systems with generalized controllers a unified approach this paper discusses generalized controllers for distance based rigid formation shape stabilization and aims to provide a unified approach for the convergence analysis we consider two types of formation control systems according to different characterizations of target formations minimally rigid target formation and non minimally rigid target formation for the former case we firstly prove the local exponential stability for rigid formation systems when using a general form of shape controllers with certain properties from this viewpoint different formation controllers proposed in previous literature can be included in a unified framework we then extend the result to the case that the target formation is non minimally rigid and show that exponential stability of the formation system is still guaranteed with generalized controllers

global and robust formation shape stabilization of relative sensing networks this paper proposes a simple distributed algorithm that achieves global stabilization of formations for relative sensing networks in arbitrary dimensions with fixed topology assuming the network runs an initialization procedure to equally orient all agent reference frames convergence to the desired formation shape is guaranteed even in partially asynchronous settings we characterize the algorithm robustness against several sources of errors link failures measurement errors and frame initialization errors the technical approach combines algebraic graph theory multidimensional scaling and distributed linear iterations

brief paper convergence analysis of instrumental variable recursive subspace identification algorithms the convergence properties of recently developed recursive subspace identification methods are investigated in this paper the algorithms operate on the basis of instrumental variable iv versions of the propagator method for signal subspace estimation it is proved that under suitable conditions on the input signal and the system the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and by extension to the state space system matrices

subspace identification of hammerstein systems using least squares support vector machines this paper presents a method for the identification of multiple input multiple output mimo hammerstein systems for the goal of prediction the method extends the numerical algorithms for subspace state space system identification n4sid mainly by rewriting the oblique projection in the n4sid algorithm as a set of componentwise least squares support vector machines ls svms regression problems the linear model and static nonlinearities follow from a low rank approximation of a matrix obtained from this regression problem

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

distributed event triggered cooperative attitude control of multiple groups of rigid bodies on manifold so 3 in this note the distributed event triggered cooperative attitude control of multiple groups of rigid bodies evolved on nonlinear manifold so 3 is investigated the distributed event triggered mechanism is introduced into the controller design to reduce the communication pressure it is verified that the orientations of rigid bodies in each group converge to a common value with zero angular velocities and these common values in all groups achieve an anti consensus configuration under the proposed intra and inter group cooperative control law simulation results show the effectiveness of the proposed method

rigid formation control of double integrator systems in this chapter we move our focus from formation control systems modelled by single integrators e g those considered in previous chapters to formation systems modelled by double integrators two kinds of double integrator formation systems are considered namely formation stabilization systems and flocking control systems novel observations on the measurement requirement the null space and eigenvalues of the system jacobian matrix will be provided which reveal important properties of system dynamics and the associated convergence results we also establish some new links between single integrator formation systems and double integrator formation systems via a parameterized hamiltonian system which in addition provide novel stability criteria for different equilibria in double integrator formation systems by using available results from single integrator formation systems

choice of state space basis in combined deterministic stochastic subspace identification this paper describes how the state space basis of models identified with subspace identification algorithms can be determined it is shown that this basis is determined by the input spectrum and by user defined input and output weightings through the connections between subspace identification and frequency weighted balancing the state space basis of the subspace identified models is shown to coincide with a frequency weighted balanced basis

geometric analysis of the formation problem for autonomous robots in the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation a local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a lyapunov based approach besides the target formation the closed loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations this note addresses a global stability analysis of the closed loop formation control dynamics we pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds these theoretical results are then applied to the well known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation

global stabilization of rigid formations in the plane this paper considers the problem of distributed control of rigid formation shapes in the plane for multi agent systems a constructive perturbation method is proposed and combined with the conventional gradient control law the proposed control law stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location it also avoids collisions between any two communicating agents during the motion simulation results are provided to illustrate the effectiveness of the control algorithm

parameterization and identification of multivariable state space systems a canonical approach in this paper the problem of determining a canonical state space representation for multivariable systems is revisited a method is derived to build a canonical state space representation directly from data generated by a linear time invariant system contrary to the classic construction methods of canonical parameterizations the technique developed in this paper does not assume the availability of any observability or controllability indices however it requires the a matrix of any minimal realization of the system to be non derogatory a subspace based identification algorithm is also introduced to estimate such a canonical state space parameterization directly from input output data

distributed sensor localization in random environments using minimal number of anchor nodes the paper introduces diloc a distributed iterative algorithm to locate m sensors with unknown locations in rm m ges 1 with respect to a minimal number of m 1 anchors with known locations the sensors and anchors nodes in the network exchange data with their neighbors only no centralized data processing or communication occurs nor is there a centralized fusion center to compute the sensors locations diloc uses the barycentric coordinates of a node with respect to its neighbors these coordinates are computed using the cayley menger determinants i e the determinants of matrices of internode distances we show convergence of diloc by associating with it an absorbing markov chain whose absorbing states are the states of the anchors we introduce a stochastic approximation version extending diloc to random environments i e when the communications among nodes is noisy the communication links among neighbors may fail at random times and the internodes distances are subject to errors we show a s convergence of the modified diloc and characterize the error between the true values of the sensors locations and their final estimates given by diloc numerical studies illustrate diloc under a variety of deterministic and random operating conditions

time varying formation control for second order swarm systems with switching directed topologies abstract formation control problems for second order swarm systems with general directed topologies are addressed in this paper where the desired formation can be time varying and the directed topology can be switching firstly a distributed time varying formation control policy using local neighboring state information is proposed then an algorithm to design the policy with switching directed topologies is presented sufficient conditions for second order swarm systems to achieve the predefined time varying formation under the designed policy are derived based on the piecewise lyapunov function theory where the formation feasibility constraint and the threshold for the dwell time are proposed respectively moreover an explicit expression of the formation reference function is obtained to describe the macroscopic trajectory of the whole time varying formation under the influence of the switching directed topologies finally a numerical simulation is provided to demonstrate the effectiveness of the obtained results

simultaneous velocity consensus and shape control for a finite number of point agents on the unit circle in this paper we study a second order distributed control system for a finite number of point agents on the unit circle that achieves simultaneously velocity consensus and distance based formation shape control based on tools from riemannian geometry we propose a system of second order differential equations on the n dimensional torus that achieves these two goals we prove convergence of the trajectories to single closed geodesics on a torus and investigate the stability properties of the distributed algorithm

riemannian optimal identification method for linear systems with symmetric positive definite matrix this article develops identification methods for linear continuous time symmetric systems such as electrical network systems multiagent network systems and temperature dynamics in buildings to this end we formulate three system identification problems for the corresponding discrete time systems the first is a least squares problem in which we wish to minimize the sum of squared errors between the true and model outputs on the product manifold of the manifold of symmetric positive definite matrices and two euclidean spaces in the second problem to reduce the search dimensions the product manifold is replaced with the quotient set under a specified group action by the orthogonal group in the third problem the manifold of symmetric positive definite matrices in the first problem is replaced by the manifold of matrices with only positive diagonal elements in particular we examine the quotient geometry in the second problem we propose riemannian conjugate gradient methods for the three problems and select initial points using a popular subspace method the effectiveness of our proposed methods is demonstrated through numerical simulations and comparisons with the gauss newton method which is one of the most popular approach for solving least squares problems

brief paper a connection between formation infeasibility and velocity alignment in kinematic multi agent systems in this paper a feedback control strategy that achieves convergence of a multi agent system to a desired formation configuration is proposed for both the cases of agents with single integrator and nonholonomic unicycle type kinematics when inter agent objectives that specify the desired formation cannot occur simultaneously in the state space the desired formation is infeasible it is shown that under certain assumptions formation infeasibility forces the agents velocity vectors to a common value at steady state this provides a connection between formation infeasibility and flocking behavior for the multi agent system we finally also obtain an analytic expression of the common velocity vector in the case of formation infeasibility

distributed formation stabilization using relative position measurements in local coordinates in this paper we present a novel distributed method to stabilize a set of agents moving in a two dimensional environment to a desired rigid formation in our approach each agent computes its control input using the relative positions of a set of formation neighbors but contrary to most existing works this information is expressed in the agent s own independent local coordinate frame without requiring any common reference the controller is based on the minimization of a lyapunov function that includes locally computed rotation matrices which are required due to the absence of a common orientation our contribution is that the proposed distributed coordinate free method achieves global stabilization to a rigid formation with the agents using only partial information of the team does not require any leader units and is applicable to both single integrator or unicycle agents to guarantee global stability we require that the network induced by the agent interactions belongs to a certain class of undirected rigid graphs in two dimensions which we explicitly characterize the performance of the proposed method is illustrated with numerical simulations

brief backstepping for nonsmooth systems the paper presents a constructive control design for integrator backstepping in nonsmooth systems the approach is based on non smooth analysis and lyapunov stability for nonsmooth systems and is similar in spirit with the robust control designs that have appeared in literature but is applicable to a larger class of systems the backstepping controller is first applied to the case of a unicycle driven by a new discontinuous kinematic controller yielding global asymptotic convergence with bounded inputs then it is used to implement a sliding mode controller in a hybrid system simulations results not only verify the convergence properties but also reveal the ability of the new backstepping controller to suppress chattering

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

subspace based identification of linear time varying system a physical parameter identification method for the linear time varying system is presented in this paper for an arbitrarily time varying system a series of hankel matrices are established directly from the combined measurements of displacement velocity and acceleration together with the input excitations from a single experiment with the system the time varying equivalent state space system matrices of the structure at each time instance are then identified by singular value decomposition using the free or random responses a time varying transformation matrix for transforming the identified equivalent system matrices into the physical system matrices is developed to determine the mass stiffness and damping matrices details of the proposed approach are investigated with a two degrees of freedom spring mass damper system with three kinds of time varying parameters numerical results show that the proposed method is accurate and effective in identifying time varying physical parameters

a novel subspace identification approach with enforced causal models subspace identification methods sims for estimating state space models have been proven to be very useful and numerically efficient they exist in several variants but all have one feature in common as a first step a collection of high order arx models are estimated from vectorized input output data in order not to obtain biased estimates this step must include future outputs however all but one of the submodels include non causal input terms the coefficients of them will be correctly estimated to zero as more data become available they still include extra model parameters which give unnecessarily high variance and also cause bias for closed loop data in this paper a new model formulation is suggested that circumvents the problem within the framework the system matrices a b c d and markov parameters can be estimated separately it is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles

formation control of mobile agents based on distributed position estimation we propose a formation control strategy based on distributed position estimation for single integrator modeled agents by using relative position measurements under the proposed strategy the estimated and the actual formations globally exponentially converge to the actual and the desired formations respectively up to translation if and only if the interaction graph for the agents has a spanning tree a sufficient condition is provided for the case that the edge weights of the interaction graph are time varying further the proposed strategy is applied to formation control of unicycle like agents

sequential localization of sensor networks the sensor network localization problem with distance information is to determine the positions of all sensors in a network given the positions of some of the sensors and the distances between some pairs of sensors a definition is given for a sensor network in the plane to be sequentially localizable it is shown that the graph of a sequentially localizable network must have a bilateration ordering and a polynomial time algorithm is given for deciding whether or not a network s graph has such an ordering a provably correct algorithm is given which consists of solving a sequence of quadratic equations and it is shown that the algorithm can localize any localizable network in the plane whose graph has a bilateration ordering

stabilisation of infinitesimally rigid formations of multi robot networks this article considers the design of a formation control for multivehicle systems that uses only local information the control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation a potential function is obtained from the graph from which a gradient control is derived under this controller the target formation becomes a manifold of equilibria for the multivehicle system it is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold a complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well finally the controller is validated experimentally

the regularity of harmonic maps into spheres and applications to bernstein problems we show the regularity of and derive a priori estimates for weakly harmonic maps from a riemannian manifold into a euclidean sphere under the assumption that the image avoids some neighborhood of a half equator the proofs combine constructions of strictly convex functions and the regularity theory of quasilinear elliptic systems we apply these results to the spherical and euclidean bernstein problems for minimal hypersurfaces obtaining new conditions under which compact minimal hypersurfaces in spheres or complete minimal hypersurfaces in euclidean spaces are trivial

consensus optimization on manifolds the present paper considers distributed consensus algorithms that involve n agents evolving on a connected compact homogeneous manifold the agents track no external reference and communicate their relative state according to a communication graph the consensus problem is formulated in terms of the extrema of a cost function this leads to efficient gradient algorithms to synchronize i e maximizing the consensus or balance i e minimizing the consensus the agents a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time varying the cost function is linked to a specific centroid definition on manifolds introduced here as the induced arithmetic mean that is easily computable in closed form and may be of independent interest for a number of manifolds the special orthogonal group so n and the grassmann manifold text it grass p n are treated as original examples a link is also drawn with the many existing results on the circle

minimal and redundant bearing rigidity conditions and applications this article studies the notions of minimal and 1 redundant bearing rigidity a necessary and sufficient condition for the numbers of edges in a graph of n n geq 3 vertices to be minimally bearing rigid mbr in mathbb r d d geq 2 is proposed if 3 leq n leq d 1 a graph is mbr if and only if it is the cycle graph in case n d 1 a generically bearing rigid graph is minimal if it has precisely 1 lfloor frac n 2 d 1 rfloor times d text mod n 2 d 1 text sgn text mod n 2 d 1 edges then several conditions for 1 redundant bearing rigidity are derived based on the mathematical conditions some algorithms for generating generically minimally and 1 redundantly bearing rigid graphs are given furthermore two applications of the new notions to optimal network design and formation merging are also reported

ratio of distance rigidity theory with application to similar formation control this paper develops a ratio of distance rod rigidity theory to study when a framework can be uniquely determined by a set of rod constraints up to similar transformations translation rotation scaling and reflection in particular a framework is specified by a set of rod constraints the rod of a pair of edges joining a common vertex instead of distance bearing and angle constraints assumed in existing literature its relations to three existing rigidity theories distance bearing and angle rigidity theories are established the proposed rod rigidity theory is further applied to the rod based similar formation stabilization problem where the desired formation shape is expressed as a set of rod constraints finally numerical simulations are presented to illustrate the effectiveness of the theoretical results

lyapunov stability theory of nonsmooth systems this paper develops nonsmooth lyapunov stability theory and lasalle s invariance principle for a class of nonsmooth lipschitz continuous lyapunov functions and absolutely continuous state trajectories computable tests based on filipov s differential inclusion and clarke s generalized gradient are derived the primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right hand side such as in nonsmooth dynamic systems or variable structure control

connectivity graphs as models of local interactions in this paper we study graphs that arise from certain sensory and communication limitations on the local interactions in multi agent systems in particular we show that the set of graphs that can represent formations corresponds to a proper subset of all graphs and we denote such graphs as connectivity graphs these graphs have a special structure that allows them to be composed from a small number of atomic generators using a certain kind of graph amalgamation this structure moreover allows us to give connectivity graphs a topological characterization in terms of their simplicial complexes finally we outline some applications of this topological characterization to the construction of decentralized algorithms