Dynamic Average Consensus Problem Research Articles

Adaptive distributed dynamic average consensus with prescribed performance

AbstractA novel adaptive distributed estimation algorithm is developed for dynamic average consensus problem. The algorithm enables a group of agents to accurately track the average value of signals that are available locally to each agent. Unlike most of existing approaches that rely on error transformation techniques, our algorithm employs an adaptive‐gain based barrier function to simultaneously meet prescribed performance specifications of transient and steady state. It is both simple and easy to implement and is not dependent on bounded reference signals and their derivatives. Additionally, it can operate under less strict assumptions than those that assume absolute bounds on the signals. Simulation results are presented to demonstrate the effectiveness of the developed algorithm.

A novel dynamic event-triggered mechanism for dynamic average consensus

This paper studies a challenging issue introduced in a recent survey, namely designing a distributed event-based scheme to solve the dynamic average consensus (DAC) problem. First, a robust adaptive distributed event-based DAC algorithm is designed without imposing specific initialization criteria to perform estimation task under intermittent communication. Second, a novel adaptive distributed dynamic event-triggered mechanism is proposed to determine the triggering time when neighboring agents broadcast information to each other. Compared to the existing event-triggered mechanisms, the novelty of the proposed dynamic event-triggered mechanism lies in that it guarantees the existence of a positive and uniform minimum inter-event interval without sacrificing any accuracy of the estimation, which is much more practical than only ensuring the exclusion of the Zeno behavior or the boundedness of the estimation error. Third, a composite adaptive law is developed to update the adaptive gain employed in the distributed event-based DAC algorithm and dynamic event-triggered mechanism. Using the composite adaptive update law, the distributed event-based solution proposed in our work is implemented without requiring any global information. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Appointed-Time Dynamic Average Consensus: A Holistic Planning and Multi-Step Control Framework

Most existing solutions to the dynamic average consensus (DAC) problem assume access to the full dynamic of reference signals or their derivatives. Such constraints are more stringent and impose restrictions on use. Hence, we revisit the DAC problem in this paper and present its solution by developing a holistic planning and multi-step control (HPMSC) framework. Here, the HPMSC allows the agents to achieve DAC in an appointed settling time without involving any other parameters, which is called appointed-time dynamic average consensus (AT-DAC). Under the HPMSC framework, a sampling-data-based AT-DAC controller is designed, which guarantees that agents can track the average value of dynamic reference signals at a pre-appointed time. Compared with the existing results on DAC, a nice highlight of this paper is the implementation of zero-error DAC with weaker conditions imposed on the reference signals, without the need to know the upper bounds on their derivatives and without additional common function conditions. Finally, the performance validation of theoretical results is demonstrated by a numerical simulation.

An Operator-Theoretic Approach to Robust Event-Triggered Control of Network Systems With Frequency-Domain Uncertainties

In this paper, we study the robustness of the event-triggered consensus algorithms against frequency- domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain L2-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicative uncertainties are considered, respectively. In both cases, quantitative relationships among the parameters of the controllers, the Laplacian matrix of the network topology, and the robustness against aperiodic event triggering and frequency-domain uncertainties are unveiled. Furthermore, the event-triggered dynamic average consensus (DAC) problem is also investigated, wherein the sampling errors are shown to be images of nonlinear finite-gain operators. The robust performance of the proposed DAC algorithm is analyzed, which indicates that the robustness and the performance are negative

Robust dynamic average consensus with prescribed transient and steady state performance

In this paper, we consider the dynamic average consensus problem for a group of multiple agents that cooperate to estimate the average of locally available time-varying reference signals, under an undirected communication topology. More specifically, we develop a novel robust distributed estimation algorithm, capable of achieving practically zero average tracking error even for fast time-varying reference signals. The proposed scheme is purely distributed, since the estimation algorithm is based solely on local computations and local communication among neighboring agents, and guarantees prescribed performance in the sense that any convergence rate and steady state deviation among the agents’ estimates may be achieved via the appropriate selection of certain design parameters. Moreover, the consensus and average tracking performance are fully decoupled, thus allowing easy tuning of the gains. Additionally, intermittent implementation is proposed via appropriately selected event- and self-triggering mechanisms. Finally, the approach is clarified and verified through various simulation paradigms.

DACFL: Dynamic Average Consensus-Based Federated Learning in Decentralized Sensors Network.

Federated Learning (FL) is a privacy-preserving way to utilize the sensitive data generated by smart sensors of user devices, where a central parameter server (PS) coordinates multiple user devices to train a global model. However, relying on centralized topology poses challenges when applying FL in a sensors network, including imbalanced communication congestion and possible single point of failure, especially on the PS. To alleviate these problems, we devise a Dynamic Average Consensus-based Federated Learning (DACFL) for implementing FL in a decentralized sensors network. Different from existing studies that replace the model aggregation roughly with neighbors’ average, we first transform the FL model aggregation, which is the most intractable in a decentralized topology, into the dynamic average consensus problem by treating a local training procedure as a discrete-time series.We then employ the first-order dynamic average consensus (FODAC) to estimate the average model, which not only solves the model aggregation for DACFL but also ensures model consistency as much as possible. To improve the performance with non-i.i.d data, each user also takes the neighbors’ average model as its next-round initialization, which prevents the possible local over-fitting. Besides, we also provide a basic theoretical analysis of DACFL on the premise of i.i.d data. The result validates the feasibility of DACFL in both time-invariant and time-varying topologies and declares that DACFL outperforms existing studies, including CDSGD and D-PSGD, in most cases. Take the result on Fashion-MNIST as a numerical example, with i.i.d data, our DACFL achieves 19∼34% and 3∼10% increases in average accuracy; with non-i.i.d data, our DACFL achieves 30∼50% and 0∼10% increases in average accuracy, compared to CDSGD and D-PSGD.

Deterministic Privacy Preservation in Static Average Consensus Problem

In this letter, we consider the problem of privacy preservation in the static average consensus problem. This problem normally is solved by proposing privacy preservation augmentations for the popular first order Laplacian-based algorithm. These mechanisms however come with computational overhead, may need coordination among the agents to choose their parameters and also alter the transient response of the algorithm. In this letter, we show that an alternative iterative algorithm that is proposed in the literature in the context of dynamic average consensus problem has intrinsic privacy preservation and can be used as a privacy preserving algorithm that yields the same performance behavior as the well-known Laplacian consensus algorithm but without the overheads that come with the existing privacy preservation methods.

Robust Dynamic Average Consensus Algorithms

This technical note considers the dynamic average consensus problem, where a group of networked agents are required to estimate the average of their time-varying reference signals. Almost all existing solutions to this problem require a specific initialization of the estimator states, and such constraints render the algorithms vulnerable to network disruptions. Here, we present three robust algorithms that do not entail any initialization criteria. Furthermore, the proposed algorithms do not rely on the full knowledge of the dynamics generating the reference signals nor assume access to its time derivatives. Two of the proposed algorithms focus on undirected networks and make use of an adaptive scheme that removes the explicit dependence of the algorithm on any upper bounds on the reference signals or its time derivatives. The third algorithm presented here provides a robust solution to the dynamic average consensus problem on directed networks. Compared to the existing algorithms for directed networks, the proposed algorithm guarantees an arbitrarily small steady-state error bound that is independent of any bounds on the reference signals or its time derivatives. The current formulation allows each agent to select its own performance criteria, and the algorithm parameters are distributedly selected such that the most stringent requirement among them is satisfied. A performance comparison of the proposed approach to existing algorithms is presented.

Distributed dynamic average consensus for nonlinear multi-agent systems in the presence of external disturbances over a directed graph

This paper investigates distributed dynamic average consensus problems for a class of nonlinear multi-agent systems in the presence of local disturbances over a directed graph, where local disturbances are generated by an external system. In order to solve such problems, we establish a distributed consensus protocol based on the internal model (IM) principle such that states of the first-order nonlinear system converge to the average of multiple time-varying inputs and local disturbances are rejected. By means of Lyapunov stability theory and graph theory, a two-step mechanism is established to certify that the proposed algorithm is exponentially convergent. Furthermore, a neoteric distributed consensus algorithm is proposed to solve a dynamic average consensus problem of the second-order nonlinear multi-agent system. The proposed algorithm can guarantee that positions and velocities of the second-order nonlinear multi-agent system converge exponentially to the average of multiple time-varying inputs and their derivative and local disturbances are rejected, respectively. Finally, three numerical examples are provided to demonstrate the effectiveness of the obtained results.

Multi-stage discrete time and randomized dynamic average consensus

In this paper we propose a novel local interaction protocol which solves the discrete time dynamic average consensus problem, i.e., the consensus problem on the average value of a set of time-varying input signals in an undirected graph. The proposed interaction protocol is based on a multi-stage cascade of dynamic consensus filters which tracks the average value of the inputs with small and bounded error. We characterize its convergence properties for time-varying discrete-time inputs with bounded variations. The main novelty of the proposed algorithm is that, with respect to other dynamic average consensus protocols, we obtain the next unique set of advantages: i) The protocol, inspired by proportional dynamic consensus, does not exploit integral control actions or input derivatives, thus exhibits robustness to re-initialization errors, changes in the network size and noise in the input signals; ii) The proposed design allows to trade-off the quantity of information locally exchanged by the agents, i.e., the number of stages, with steady-state error, tracking error and convergence time; iii) The protocol can be implemented with randomized and asynchronous local state updates and keep in expectation the performance of the discrete-time version. Numerical examples are given to corroborate the theoretical findings, including the case where a new agent joins and leaves the network during the algorithm execution to show robustness to re-initialization errors during runtime.

New Internal Model Average Consensus Estimators with Light Communication Load

The dynamic average consensus problem for a group of agents is considered. Each agent in the group is supposed to estimate the average of inputs applied to all agents and the estimation should be done in a distributed way. By reinterpreting the proportional integral type estimator, a new structure for the average estimator which can embed the internal model of inputs is proposed and conditions which result in the zero estimation error in the steady state are derived. We present constructive design procedures for the cases of constant inputs and time-varying inputs employing the root locus for the former and LQR-based design for the latter. The theory is validated through numerical simulations.

Tutorial on Dynamic Average Consensus: The Problem, Its Applications, and the Algorithms

Technological advances in ad hoc networking and the availability of low-cost reliable computing, data storage, and sensing devices have made scenarios possible where the coordination of many subsystems extends the range of human capabilities. Smart grid operations, smart transportation, smart health care, and sensing networks for environmental monitoring and exploration in hazardous situations are just a few examples of such network operations. In these applications, the ability of a network system to (in a decentralized fashion) fuse information, compute common estimates of unknown quantities, and agree on a common view of the world is critical. These problems can be formulated as agreement problems on linear combinations of dynamically changing reference signals or local parameters. This dynamic agreement problem corresponds to dynamic average consensus, which, as discussed in Summary, is the problem of interest of this article. The dynamic average consensus problem is for a group of agents to cooperate to track the average of locally available time-varying reference signals, where each agent is capable only of local computations and communicating with local neighbors.

Distributed Control of Active–Passive Networked Multiagent Systems

An active–passive networked multiagent system framework is introduced and analyzed, which consists of agents subject to exogenous inputs (active agents) and agents without any inputs (passive agents). Specifically, we propose an integral action-based distributed control approach and establish its transient time and steady-state performance characteristics using results from graph theory, matrix mathematics, Lyapunov stability, and ${\mathcal L}$ stability. Apart from the existing relevant literature, where either none of the agents are subject to exogenous inputs (i.e., average consensus problem) or all agents are subject to these inputs (i.e., dynamic average consensus problem), the key feature of our approach is that the states of all agents converge to the average of the exogenous inputs applied only to the active agents. We further discuss the conditions when the performance of the proposed distributed controller specializes to the performance of standard distributed controllers used for average consensus and dynamic average consensus of leaderless networks, and draw connections between pinning control and containment control of leader–follower networks. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed distributed control approach.

Dynamic average consensus via nonlinear protocols

This paper addresses the dynamic average consensus problem under nonlinear protocols for networks of dynamic agents. In this problem, each agent aims to track the average of time-varying reference inputs of all the agents in the network by local communication with neighbors. We propose a class of continuous-time nonlinear protocols for this problem, and theoretical analyses for two cases are provided: (1) undirected networks with switching topologies and (2) balanced directed networks with switching topologies. Based upon the analysis results, design procedures for nonlinear protocols are presented. Simulations are also provided to demonstrate the effectiveness of the proposed design procedures.

Synthesis and analysis of robust dynamic linear protocols for dynamic average consensus estimators

The dynamic average consensus problem in multi-agent networks is considered. Each agent residing on the network establishes a dynamic average consensus estimator whose output tracks the average of time-varying inputs to all the agents in the network. The authors propose a systematic methodology to construct any dynamic linear protocol for the dynamic average consensus having desired stability and performance properties. Our aim is to reduce the design problem of the dynamic average consensus protocols to the design problem of a simple system constructed of a simple integrator with a disturbance rejection controller as a feedback control. The authors rigorously analyse the input-to-state stability and some important performance properties of the dynamic linear protocol. The important case of switching topology is precisely analysed and therefore sufficient conditions for the uniform-input-to-state stability of the switched dynamic average consensus estimators are identified. Also the cases of initialisation errors and uniform time delays are well addressed. The case of addition/deletion of the agents is also pointed out. A design example of the dynamic linear protocol and its simulation results is presented demonstrating the efficiency of the proposed method.