Dynamic Average Consensus 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.

Prescribed-time multi-coalition Nash equilibrium seeking by event-triggered communication

This article investigates the event-triggered prescribed-time Nash equilibrium seeking problem among multiple coalitions of agents in noncooperative games. Each coalition acts as a virtual player in the noncooperative game, with decisions made by its member agents. Agents lack complete information about others’ decisions and instead estimate them through a communication graph. An event-triggered prescribed-time multi-coalition Nash equilibrium seeking method is developed based on the leader-following consensus protocol, dynamic average consensus protocol, and gradient play. This method ensures the Nash equilibrium of the multi-coalition game is reached within a prescribed time, even when communication between agents only occurs under specific triggering conditions—effectively conserving communication resources. Unlike existing approaches, the proposed algorithm allows precise settling time assignment without prior knowledge of system parameters. This algorithm also prevents Zeno behavior. Lastly, the efficiency of the designed algorithm is demonstrated through simulation experiments.

Three-dimensional free-will arbitrary time cooperative guidance law against moving target

A novel three-dimensional free-will arbitrary time cooperative guidance law based on biased proportional navigation is proposed for intercepting a high-value moving target. In contrast to existing research, the presented method does not require controlling the interceptors' axial speed or prediction of the interception point. First, the engagement plane is constructed so that a three-dimensional guidance problem can be formulated as a planar problem. Second, a new accurate time-to-go estimation algorithm against the moving target is deduced based on the formulated problem model. Third, a free-will arbitrary time cooperative guidance law is designed utilizing the leader-follower architecture. Multiple missiles can intercept a moving target simultaneously and the intercept time of each missile will converge within a free-will arbitrary time. Fourth, the proposed cooperative guidance law under different communication circumstances is analyzed. When the communication resources are abundant, missiles can reach dynamic average consensus. Meanwhile, the system is robust against the communication imperfection. Finally, numerical simulations are presented to verify the effectiveness of the time-to-go estimation algorithm and proposed cooperative guidance law.

Adaptive Dynamic Average Consensus Scheme With Preserving Privacy and Against False Data Injection Attacks: Dynamic Event-Triggered Mechanism

Adaptive Dynamic Average Consensus Scheme With Preserving Privacy and Against False Data Injection Attacks: Dynamic Event-Triggered Mechanism

Minimum loss optimization of flywheel energy storage systems via distributed adaptive dynamic programming

AbstractIn this article, a distributed controller based on adaptive dynamic programming is proposed to solve the minimum loss problem of flywheel energy storage systems (FESS). We first formulate a performance function aiming to reduce total losses of FESS in power distribution applications. Then we use the Hamilton–Jacobi–Bellman (HJB) equation to solve this optimal control problem. The solution of the HJB equation is approximated by neural networks. To achieve distributed control, we estimate the global variables in the HJB equation by using the dynamic average consensus algorithm. A barrier Lyapunov function and a saturation function are introduced to handle the issue of state and input constraints, respectively. Then the stability of the system is proved through the Lyapunov stability analysis. Finally the effectiveness of the proposed strategy is verified by simulations. Simulation results show that FESS can track the power command while minimizing total power losses by interacting with neighbors. The proposed algorithm leads to a loss reduction of compared to the equal power distribution strategy.

Distributed event-triggered estimation for dynamic average consensus: A perturbation-injected privacy-preservation scheme

Previous studies on the distributed estimation problem for dynamic average consensus of multi-agent networks are usually based on the assumption that each agent continuously and honestly shares information with its neighbors. To relax this assumption, this paper focuses on the distributed event-triggered private estimation problem. By injecting random perturbations into the original reference signal, an adaptive robust distributed privacy-preserving event-triggered estimation algorithm is proposed. With the proposed algorithm, the convergence of the estimation error is guaranteed under intermittent communication, while protecting the private reference signal information from disclosure. To determine the timing for communication, an adaptive distributed dynamic triggering mechanism with a dynamically updated internal triggering variable is designed. In addition, a dynamically updated adaptive gain instead of a static gain is employed in the estimation algorithm and triggering mechanism to eliminate the dependence on some global information. Finally, numerical simulation results are presented to illustrate the validity of the theoretical results.

Dynamic Average Consensus of Time-Varying Signals With Known Frequency Components

Dynamic Average Consensus of Time-Varying Signals With Known Frequency Components

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.

Distributed Nash Equilibrium Seeking for Multicluster Aggregative Game of Euler-Lagrange Systems With Coupled Constraints.

This article considers the distributed Nash equilibrium seeking problem of a multicluster aggregative game subject to local set constraints, consensus constraints in the same cluster, and coupled linear equality and nonlinear inequality constraints among all clusters. In the considered game, each cluster is composed of a group of players formulated by uncertain Euler-Lagrange (EL) dynamics, and its objective is to minimize its own cost function, which is the sum of the local functions of all players in the cluster. The local cost function of each player depends on its own decision and an aggregate of the decisions of all the players. An adaptive continuous-time distributed strategy is developed for uncertain EL systems to reach the generalized Nash equilibrium (GNE) of multicluster aggregative game. In particular, a new auxiliary system is synthesized using a projection operator, gradient descent, and dynamic average consensus to estimate the GNE. Based on the outputs of the auxiliary system, an adaptive tracking algorithm is developed for an EL system with uncertain parameters. Using the Lyapunov stability theory, it is shown that the developed distributed strategy achieves accurate convergence to the GNE. Finally, a numerical example is presented to demonstrate the theoretical results.

Convergence speed of dynamic consensus with delay compensation

A well-known drawback in distributed average consensus of multi-agent systems is that the exchanged information is usually delayed due to the time elapsed during the data transmission process. Using classical dynamic average consensus, delays may lead to poor performance or even instability. In this paper, we propose a novel dynamic consensus method that counteracts the negative effects of delays by means of delay compensation techniques. The interest of our dynamic consensus method with delay compensation is that it converges under mild conditions on graph connectivity and bounded reference signals, no matter how large the delays are, as long as delays are fixed and known. We also provide a formal characterization of the convergence speed of our method. Additionally, our results apply to fixed directed strongly connected, and undirected topologies.

Accurate consensus-based distributed secondary control with tolerance of communication delays for DC microgrids

Distributed secondary control is widely used in DC microgrids (MGs), which can achieve average voltage recovery and accurate power/current sharing among the distributed generators (DGs). In the distributed control architecture, a consensus-based average observer is usually desired to estimate the global average of the output voltage. However, the inevitable communication delay between DGs will cause the output average voltage to deviate from the rated. To tackle this problem, a novel dynamic average consensus observer based on bias compensation has been proposed in this paper, which can accurately converge to the average of the variables being tracked with tolerance of the bounded communication delay while getting rid of the harsh requirement for identical initial value of conventional distributed observer. Based on it, the proposed distributed secondary controller can ensure that the average output voltage converges to the rated without steady-state deviation and that the output currents are proportionally shared accurately. Instead of the conventional voltage and current dual secondary controller, the proposed secondary controller estimates the average of the voltage-current coupling variables and achieves the average voltage recovery and accurate current sharing simultaneously. Moreover, the communication delay margin is determined quantitatively. Finally, the performance of the proposed controller and the efficacy of the calculated communication delay margin is verified by real-time hardware-in-loop (HIL) tests.

Dynamic Average Consensus With Anti-Windup Applied to Interlinking Converters in AC/DC Microgrids Under Economic Dispatch and Delays

Dynamic Average Consensus With Anti-Windup Applied to Interlinking Converters in AC/DC Microgrids Under Economic Dispatch and Delays

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.

A voltage-shifting-based state-of-charge balancing control for distributed energy storage systems in islanded DC microgrids

This paper presents a distributed secondary level control strategy for battery energy units (BEUs) parallel in a DC microgrid. The control structure is divided into two layers. The primary control layer is implemented with a droop control. The voltage-shifting term is generated by the secondary control layer, where an information state factor λ is introduced to meet the bus voltage restoration, state-of-charge (SOC) balancing and accurate current sharing. A sigmoid function with a balancing adjustment factor is adopted to improve both SOC balancing accuracy and speed. When each information state factor in the system converges to the average value, accurate current sharing according to the SOC values of BEUs and capacities is attained, and the average output voltage is consistent with the nominal voltage of microgrid. Compared with existing methods, the proposed method has no requirement on a complex control structure and only two variables need to be transferred between adjacent converters, which reduces the information traffic and the communication burden. Moreover, the proposed nonlinear control strategy effectively avoids unnecessary cyclic charge or discharge between BEUs and inhibits circulating currents. The proposed method also has the ability of plug and play, since SOC balancing among BEUs with different capacities is considered, and, in the communication layer, the dynamic average consensus algorithm is utilized to obtain both average SOC and average λ. The performance of the proposed control method is confirmed in simulation and experiment.

A distributed event‐triggered dynamic average consensus scheme with a time‐varying threshold and its application in DC microgrid

AbstractWe propose a distributed event‐triggered dynamic average consensus (DAC) scheme with a time‐varying threshold for a multi‐agent system (MAS) in a directed graph. In this scheme, each agent is not required to monitor its neighbors in real time, and a threshold is chosen related to consensus performance directly in an MAS, where the threshold is adjusted adaptively according to average consensus performance. Also, we introduce a bounded and monotonically increasing function in a time‐varying threshold, and this function is for guaranteeing the value of a threshold to locate in an appropriate range. Stability analysis shows that the tracking error is eventually bounded and the MAS achieves DAC without Zeno behaviors. Furthermore, the proposed event‐triggered DAC scheme is applied to voltage restoration and adjustable current sharing in DC microgrid. The effectiveness of the proposed scheme is verified by two examples.

Dynamic average consensus control based on event-triggered cloud access

A dynamic average consensus (DAC) control scheme is proposed in the presence of constrained communication, where event-triggered cloud access is presented with a cloud repository for agents. With this framework, agents upload and download information from the cloud repository, in which they exchange information with neighbors indirectly. We first propose a triggered condition with a deviation of control signals for reduction of the frequency of communication with the cloud repository. Due to the fact that the neighbors’ information in the condition can’t be obtained in the cloud framework, cloud access scheduling rules, with an adaptive threshold for control signal updating, are then introduced via available information at current instants, and agents access the cloud repository in an asynchronous manner to avoid congestion. Available information from the cloud is employed, as well as their own, into the triggered condition for prediction of next access instants, and the triggered consequence is generated. Stability analysis presents that the control scheme in this paper steers the MAS to achieve DAC with an ultimately bounded tracking error and rules out Zeno behaviors. The effectiveness of the control scheme is verified via an example.

Privacy-Preserving Dynamic Average Consensus via Random Number Perturbation

This brief focuses on the study of privacy preservation of dynamic average consensus (DAC) in multi-agent networks. A privacy-preserving DAC (PP-DAC) algorithm is proposed based on a carefully designed random number perturbation mechanism. The PP-DAC algorithm is able to protect agents from the leakage of sensitive information without compromising their tracking accuracy. Furthermore, the privacy analysis for different scenarios is given to show that the PP-DAC algorithm works well unless all neighbors of the target agent collude with each other to attack this agent. Also, some numerical simulations are given to illustrate the validity of the proposed algorithm.

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

Accelerated Dual Averaging Methods for Decentralized Constrained Optimization

In this article, we study decentralized convex constrained optimization problems in networks. We focus on the dual averaging-based algorithmic framework that is well-documented to be superior in handling constraints and complex communication environments simultaneously. Two new decentralized dual averaging (DDA) algorithms are proposed. In the first one, a second-order dynamic average consensus protocol is tailored for DDA-type algorithms, which equips each agent with a provably more accurate estimate of the global dual variable than conventional schemes. We rigorously prove that the proposed algorithm attains <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1/t)$</tex-math></inline-formula> convergence for general convex and smooth problems, for which existing DDA methods were only known to converge at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1/\sqrt{t})$</tex-math></inline-formula> prior to our work. In the second one, we use the extrapolation technique to accelerate the convergence of DDA. Compared to existing accelerated algorithms, where typically two different variables are exchanged among agents at each time, the proposed algorithm only seeks consensus on local gradients. Then, the extrapolation is performed based on two sequences of primal variables, which are determined by the accumulations of gradients at two consecutive time instants, respectively. The algorithm is proved to converge at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(1)\left(\frac{1}{t^{2}}+\frac{1}{t(1-\beta)^{2}}\right)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\beta$</tex-math></inline-formula> denotes the second largest singular value of the mixing matrix. We remark that the condition for the algorithmic parameter to guarantee convergence does not rely on the spectrum of the mixing matrix, making itself easy to satisfy in practice. Finally, numerical results are presented to demonstrate the efficiency of the proposed methods.

Self-Disciplined Nonsmooth Coordination Control for Battery Energy Storage System in Autonomous DC Microgrids Toward Large-Signal Stability

For a Battery Energy Storage System (BESS)-based autonomous DC microgrid, owing to the coupling complexity between multiple control objectives under a hierarchical control framework, coordination control for large-signal stabilization is well-acknowledged as a non-trivial problem. This paper aims to present a self-disciplined nonsmooth coordination control strategy to address the multi-objective task within one framework. Firstly, a nonsmooth composite regulation law is designed to mitigate the increasing constant power loads (CPLs) by employing a feedforward compensation. Secondly, a dynamic droop strategy aiming for dynamic power allocation for state-of-charging (SOC) balancing of BESS is built based on a nonsmooth dynamic average consensus protocol with low communication cost. Then by utilizing a dynamic power allocation strategy and a large-signal stabilizer for each energy storage unit (ESU), both SOC dynamic balancing and system level large-signal stability can be ensured. Moreover, a fast performance recovery ability can be promised by bringing into two convergence rate coordination factors. Simulation and comparative experimental studies have demonstrated the efficacy of the proposed control strategy.