# Showing papers in "Automatica in 2010"

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TL;DR: A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value.

Abstract: This paper studies some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. First, basic theoretical analysis is carried out for the case where for each agent the second-order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant. A necessary and sufficient condition is given to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is derived for the multi-agent system facing communication delays. A necessary and sufficient condition is provided, which shows that consensus can be achieved in a multi-agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.

1,284 citations

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TL;DR: An online algorithm based on policy iteration for learning the continuous-time optimal control solution with infinite horizon cost for nonlinear systems with known dynamics, which finds in real-time suitable approximations of both the optimal cost and the optimal control policy, while also guaranteeing closed-loop stability.

Abstract: In this paper we discuss an online algorithm based on policy iteration for learning the continuous-time (CT) optimal control solution with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real-time the solution to the optimal control design HJ equation. This method finds in real-time suitable approximations of both the optimal cost and the optimal control policy, while also guaranteeing closed-loop stability. We present an online adaptive algorithm implemented as an actor/critic structure which involves simultaneous continuous-time adaptation of both actor and critic neural networks. We call this 'synchronous' policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for both critic and actor networks, with extra nonstandard terms in the actor tuning law being required to guarantee closed-loop dynamical stability. The convergence to the optimal controller is proven, and the stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm.

1,012 citations

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TL;DR: An upper bound of the difference between both loops is derived, which shows that the approximation of the continuous state-feedback loop by the event-based control loop can be made arbitrarily tight by appropriately choosing the threshold parameter of the event generator.

Abstract: This paper proposes a new method for event-based state-feedback control in which a control input generator mimics a continuous feedback between two consecutive event times. The performance of the event-based control system is evaluated by comparing this loop with the continuous state-feedback loop. An upper bound of the difference between both loops is derived, which shows that the approximation of the continuous state-feedback loop by the event-based control loop can be made arbitrarily tight by appropriately choosing the threshold parameter of the event generator.

994 citations

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TL;DR: Novel time-dependent Lyapunov functionals in the framework of the input delay approach are introduced, which essentially improve the existing results and can guarantee the stability under the sampling which may be greater than the analytical upper bound on the constant delay that preserves the stability.

Abstract: This paper considers sampled-data control of linear systems under uncertain sampling with the known upper bound on the sampling intervals. Recently a discontinuous Lyapunov function method was introduced by using impulsive system representation of the sampled-data systems (Naghshtabrizi, Hespanha, & Teel, 2008). The latter method improved the existing results, based on the input delay approach via time-independent Lyapunov functionals. The present paper introduces novel time-dependent Lyapunov functionals in the framework of the input delay approach, which essentially improve the existing results. These Lyapunov functionals do not grow after the sampling times. For the first time, for systems with time-varying delays, the introduced Lyapunov functionals can guarantee the stability under the sampling which may be greater than the analytical upper bound on the constant delay that preserves the stability. We show also that the term of the Lyapunov function, which was introduced in the above mentioned reference for the analysis of systems with constant sampling, is applicable to systems with variable sampling.

982 citations

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TL;DR: A distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time.

Abstract: Distributed finite-time attitude containment control for multiple rigid bodies is addressed in this paper. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the attitudes of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors' information. We also discuss the special case of a single stationary leader and propose a control law using only the one-hop neighbors' information to guarantee cooperative attitude regulation in finite time. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time. We also explicitly show the finite settling time.

799 citations

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TL;DR: A unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named ''average impulsive interval'' which is theoretically and numerically proved to be less conservative than existing results.

Abstract: This paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks. Two types of impulses are considered: synchronizing impulses and desynchronizing impulses. In previous literature, all of the results are devoted to investigating these two kinds of impulses separately. Thus a natural question arises: Is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses? In this paper, a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named ''average impulsive interval''. The derived criterion is theoretically and numerically proved to be less conservative than existing results. Numerical examples including scale-free and small-world structures are given to show that our results are applicable to large-scale networks.

729 citations

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TL;DR: By allowing the Lyapunov-like function to increase during the running time of active subsystems, the extended stability results for switched systems with ADT in nonlinear setting are derived and the asynchronously switched stabilizing control problem for linear cases is solved.

Abstract: This paper concerns the asynchronously switched control problem for a class of switched linear systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. The so-called asynchronous switching means that the switchings between the candidate controllers and system modes are asynchronous. By further allowing the Lyapunov-like function to increase during the running time of active subsystems, the extended stability results for switched systems with ADT in nonlinear setting are first derived. Then, the asynchronously switched stabilizing control problem for linear cases is solved. Given the increase scale and the decrease scale of the Lyapunov-like function and the maximal delay of asynchronous switching, the minimal ADT for admissible switching signals and the corresponding controller gains are obtained. A numerical example is given to show the validity and potential of the developed results.

682 citations

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TL;DR: transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem and the LGL costate approximation is found to have an error that oscillates about the true solution.

Abstract: A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme.

648 citations

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TL;DR: An integral predictive and nonlinear robust control strategy to solve the path following problem for a quadrotor helicopter with parametric and structural uncertainties presented to corroborate the effectiveness and the robustness of the proposed strategy.

Abstract: This paper presents an integral predictive and nonlinear robust control strategy to solve the path following problem for a quadrotor helicopter The dynamic motion equations are obtained by the Lagrange-Euler formalism The proposed control structure is a hierarchical scheme consisting of a model predictive controller (mpc) to track the reference trajectory together with a nonlinear H"~ controller to stabilize the rotational movements In both controllers the integral of the position error is considered, allowing the achievement of a null steady-state error when sustained disturbances are acting on the system Simulation results in the presence of aerodynamic disturbances, parametric and structural uncertainties are presented to corroborate the effectiveness and the robustness of the proposed strategy

643 citations

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TL;DR: A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown.

Abstract: This paper is concerned with synchronization of distributed node dynamics to a prescribed target or control node dynamics. A design method is presented for adaptive synchronization controllers for distributed systems having non-identical unknown nonlinear dynamics, and for a target dynamics to be tracked that is also nonlinear and unknown. The development is for strongly connected digraph communication structures. A Lyapunov technique is presented for designing a robust adaptive synchronization control protocol. The proper selection of the Lyapunov function is the key to ensuring that the resulting control laws thus found are implementable in a distributed fashion. Lyapunov functions are defined in terms of a local neighborhood tracking synchronization error and the Frobenius norm. The resulting protocol consists of a linear protocol and a nonlinear control term with adaptive update law at each node. Singular value analysis is used. It is shown that the singular values of certain key matrices are intimately related to structural properties of the graph.

603 citations

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TL;DR: A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms and some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices.

Abstract: This paper is concerned with the stability analysis of linear systems with time-varying delays in a given range. A new type of augmented Lyapunov functional is proposed which contains some triple-integral terms. In the proposed Lyapunov functional, the information on the lower bound of the delay is fully exploited. Some new stability criteria are derived in terms of linear matrix inequalities without introducing any free-weighting matrices. Numerical examples are given to illustrate the effectiveness of the proposed method.

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TL;DR: A new controller design scheme based on a prescribed performance bound (PPB) which characterizes the convergence rate and maximum overshoot of the tracking error and can improve transient performance compared with the basic scheme is proposed.

Abstract: In order to accommodate actuator failures which are uncertain in time, pattern and value, we propose two adaptive backstepping control schemes for parametric strict feedback systems. Firstly a basic design scheme on the basis of existing approaches is considered. It is analyzed that, when actuator failures occur, transient performance of the adaptive system cannot be adjusted through changing controller design parameters. Then we propose a new controller design scheme based on a prescribed performance bound (PPB) which characterizes the convergence rate and maximum overshoot of the tracking error. It is shown that the tracking error satisfies the prescribed performance bound all the time. Simulation studies also verify the established theoretical results that the PPB based scheme can improve transient performance compared with the basic scheme, while both ensure stability and asymptotic tracking with zero steady state error in the presence of uncertain actuator failures.

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TL;DR: Two kinds of robust distributed H"~-consensus filters are designed for the system with norm-bounded uncertainties and polytopic uncertainties, and two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme.

Abstract: This paper is concerned with a new distributed H"~-consensus filtering problem over a finite-horizon for sensor networks with multiple missing measurements. The so-called H"~-consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. A set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors. A sufficient condition is first established in terms of a set of difference linear matrix inequalities (DLMIs) under which the expected H"~-consensus performance constraint is guaranteed. Given the measurements and estimates of the system state and its neighbors, the filter parameters are then explicitly parameterized by means of the solutions to a certain set of DLMIs that can be computed recursively. Subsequently, two kinds of robust distributed H"~-consensus filters are designed for the system with norm-bounded uncertainties and polytopic uncertainties. Finally, two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme.

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TL;DR: A new kernel-based approach for linear system identification of stable systems that model the impulse response as the realization of a Gaussian process whose statistics include information not only on smoothness but also on BIBO-stability.

Abstract: This paper describes a new kernel-based approach for linear system identification of stable systems. We model the impulse response as the realization of a Gaussian process whose statistics, differently from previously adopted priors, include information not only on smoothness but also on BIBO-stability. The associated autocovariance defines what we call a stable spline kernel. The corresponding minimum variance estimate belongs to a reproducing kernel Hilbert space which is spectrally characterized. Compared to parametric identification techniques, the impulse response of the system is searched for within an infinite-dimensional space, dense in the space of continuous functions. Overparametrization is avoided by tuning few hyperparameters via marginal likelihood maximization. The proposed approach may prove particularly useful in the context of robust identification in order to obtain reduced order models by exploiting a two-step procedure that projects the nonparametric estimate onto the space of nominal models. The continuous-time derivation immediately extends to the discrete-time case. On several continuous- and discrete-time benchmarks taken from the literature the proposed approach compares very favorably with the existing parametric and nonparametric techniques.

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TL;DR: It is shown that the closed loop tracking control system is stochastically stable in meansquare and the estimation errors converge to zero in mean square as well.

Abstract: In this paper, a distributed tracking control scheme with distributed estimators has been developed for a leader-follower multi-agent system with measurement noises and directed interconnection topology. It is supposed that each follower can only measure the relative positions of its neighbors in a noisy environment, including the relative position of the second-order active leader. A neighbor-based tracking protocol together with distributed estimators is designed based on a novel velocity decomposition technique. It is shown that the closed loop tracking control system is stochastically stable in mean square and the estimation errors converge to zero in mean square as well. A simulation example is finally given to illustrate the performance of the proposed control scheme.

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TL;DR: A class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs and require that the union of communication graphs over a bounded period of time be strongly connected.

Abstract: We propose a class of discrete-time dynamic average consensus algorithms that allow a group of agents to track the average of their reference inputs. The convergence results rely on the input-to-output stability properties of static average consensus algorithms and require that the union of communication graphs over a bounded period of time be strongly connected. The only requirement on the set of reference inputs is that the maximum relative deviation between the nth-order differences of any two reference inputs be bounded for some integer n>=1.

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TL;DR: This work presents a self-triggered implementation of linear controllers that reduces the amount of controller updates necessary to retain stability of the closed-loop system and exhibits an inherent trade-off between computation and potential savings on actuation.

Abstract: Nowadays control systems are mostly implemented on digital platforms and, increasingly, over shared communication networks. Reducing resources (processor utilization, network bandwidth, etc.) in such implementations increases the potential to run more applications on the same hardware. We present a self-triggered implementation of linear controllers that reduces the amount of controller updates necessary to retain stability of the closed-loop system. Furthermore, we show that the proposed self-triggered implementation is robust against additive disturbances and provide explicit guarantees of performance. The proposed technique exhibits an inherent trade-off between computation and potential savings on actuation.

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TL;DR: Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping to solve the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings.

Abstract: This paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings. Two classes of state feedback controllers and a common Lyapunov function (CLF) are simultaneously constructed by backstepping. The first class uses the common state feedback controller which is independent of switching signals; the other class utilizes individual state feedback controllers for the subsystems. As an extension of the designed method, the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied. An example is given to show the effectiveness of the proposed method.

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TL;DR: This paper describes a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph and proposes a decentralized gradient controller for eachAgent to maintain global connectivity during motion.

Abstract: The ability of a robot team to reconfigure itself is useful in many applications: for metamorphic robots to change shape, for swarm motion towards a goal, for biological systems to avoid predators, or for mobile buoys to clean up oil spills. In many situations, auxiliary constraints, such as connectivity between team members or limits on the maximum hop-count, must be satisfied during reconfiguration. In this paper, we show that both the estimation and control of the graph connectivity can be accomplished in a decentralized manner. We describe a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimator, we further propose a decentralized gradient controller for each agent to maintain global connectivity during motion.

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TL;DR: The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized, and to show that an optimal sensor- target configuration is not, in general, unique.

Abstract: The problem of target localization involves estimating the position of a target from multiple noisy sensor measurements. It is well known that the relative sensor-target geometry can significantly affect the performance of any particular localization algorithm. The localization performance can be explicitly characterized by certain measures, for example, by the Cramer-Rao lower bound (which is equal to the inverse Fisher information matrix) on the estimator variance. In addition, the Cramer-Rao lower bound is commonly used to generate a so-called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate, i.e. an estimate which achieves the lower bound. The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized. Deeming such sensor-target geometries to be optimal with respect to the chosen measure, the optimal sensor-target geometries for range-only, time-of-arrival-based and bearing-only localization are identified and studied in this work. The optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor-target configuration is not, in general, unique. The importance of understanding the influence of the sensor-target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples.

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TL;DR: Krasovskii's method to find Lyapunov functions, and recently obtained extensions of the LaSalle invariance principle for hybrid systems are used to obtain stability proofs of primal-dual laws in different scenarios, and applications to cross-layer network optimization are exhibited.

Abstract: This paper considers dynamic laws that seek a saddle point of a function of two vector variables, by moving each in the direction of the corresponding partial gradient. This method has old roots in the classical work of Arrow, Hurwicz and Uzawa on convex optimization, and has seen renewed interest with its recent application to resource allocation in communication networks. This paper brings other tools to bear on this problem, in particular Krasovskii's method to find Lyapunov functions, and recently obtained extensions of the LaSalle invariance principle for hybrid systems. These methods are used to obtain stability proofs of these primal-dual laws in different scenarios, and applications to cross-layer network optimization are exhibited.

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TL;DR: Not only is it proved that a consensus is reachable asymptotically but also an estimation of the convergence rate is given.

Abstract: In this paper, a leader-following consensus problem of second-order multi-agent systems with fixed and switching topologies as well as non-uniform time-varying delays is considered. For the case of fixed topology, a necessary and sufficient condition is obtained. For the case of switching topology, a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large. We not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate. An example with simulation is presented to illustrate the theoretical results.

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TL;DR: This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty that significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables.

Abstract: This paper presents a fault detection and isolation (FDI) scheme for a class of Lipschitz nonlinear systems with nonlinear and unstructured modeling uncertainty. This significantly extends previous results by considering a more general class of system nonlinearities which are modeled as functions of the system input and partially measurable state variables. A new FDI method is developed using adaptive estimation techniques. The FDI architecture consists of a fault detection estimator and a bank of fault isolation estimators. The fault detectability and isolability conditions, characterizing the class of faults that are detectable and isolable by the proposed scheme, are rigorously established. The fault isolability condition is derived via the so-called fault mismatch functions, which are defined to characterize the mutual difference between pairs of possible faults. A simulation example of a single-link flexible joint robot is used to illustrate the effectiveness of the proposed scheme.

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TL;DR: The effect of output Y on the X-space decomposition in PLS is analyzed and geometric properties of the PLS structure are revealed.

Abstract: Projection to latent structures or partial least squares (PLS) produces output-supervised decomposition on input X, while principal component analysis (PCA) produces unsupervised decomposition of input X. In this paper, the effect of output Y on the X-space decomposition in PLS is analyzed and geometric properties of the PLS structure are revealed. Several PLS algorithms are compared in a geometric way for the purpose of process monitoring. A numerical example and a case study are given to illustrate the analysis results.

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TL;DR: A discrete-time model for networked control systems (NCSs) that incorporates all network phenomena: time-varying sampling intervals, packet dropouts and time- varying delays that may be both smaller and larger than the sampling interval is presented.

Abstract: This paper presents a discrete-time model for networked control systems (NCSs) that incorporates all network phenomena: time-varying sampling intervals, packet dropouts and time-varying delays that may be both smaller and larger than the sampling interval. Based on this model, constructive LMI conditions for controller synthesis are derived, such that stabilizing state-feedback controllers can be designed. Besides the proposed controller synthesis conditions a comparison is made between the use of parameter-dependent Lyapunov functions and Lyapunov-Krasovskii functions for stability analysis. Several examples illustrate the effectiveness of the developed theory.

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TL;DR: By introducing some specified matrices, a new sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics.

Abstract: This paper is concerned with the sliding mode control (SMC) of nonlinear singular stochastic systems with Markovian switching. An integral sliding surface function is designed, and the resulting sliding mode dynamics is a full-order Markovian jump singular stochastic system. By introducing some specified matrices, a new sufficient condition is proposed in terms of strict linear matrix inequality (LMI), which guarantees the stochastic stability of the sliding mode dynamics. Then, a SMC law is synthesized for reaching motion. Moreover, when there exists an external disturbance, the @?"2 disturbance attenuation performance is analyzed for the sliding mode dynamics. Some related sufficient conditions are also established.

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TL;DR: A unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor's output, or affecting both the agent's own and its neighbors' output is developed.

Abstract: We investigate the robustness of consensus schemes for linear Multi-Agent Systems (MAS) to feedback delays. To achieve this, we develop a unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor's output, or affecting both the agent's own and its neighbors' output. This framework has the advantage of providing scalable, simple, and accurate set-valued conditions for consensus. Using these set-valued conditions, previous results on consensus in MAS with delays can be recovered and generalized. Moreover, we use them to derive conditions for the convergence rate of single integrator MAS with feedback delays. Finally, building on this framework, we propose a scalable delay-dependent design algorithm for consensus controllers for a large class of linear MAS.

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TL;DR: A method to model nonlinear systems using polynomial nonlinear state space equations by identifying first the best linear approximation of the system under test is proposed.

Abstract: In this paper, we propose a method to model nonlinear systems using polynomial nonlinear state space equations. Obtaining good initial estimates is a major problem in nonlinear modelling. It is solved here by identifying first the best linear approximation of the system under test. The proposed identification procedure is successfully applied to measurements of two physical systems.

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TL;DR: It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.

Abstract: The spectral properties of the incidence matrix of the communication graph are exploited to provide solutions to two multi-agent control problems. In particular, we consider the problem of state agreement with quantized communication and the problem of distance-based formation control. In both cases, stabilizing control laws are provided when the communication graph is a tree. It is shown how the relation between tree graphs and the null space of the corresponding incidence matrix encode fundamental properties for these two multi-agent control problems.

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TL;DR: In this paper, a set of algorithms based on pairwise ''gossip'' communications and updates is proposed to solve the average consensus problem on a network of digital links, and the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature.

Abstract: This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise ''gossip'' communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.