Finite-time Average Consensus Research Articles

A novel finite-time average consensus protocol for multi-agent systems with switching topology

Multi-agent consensus has been widely applied in engineering. A novel protocol that can achieve an average state consensus for multi-agent systems in finite time is presented in this paper. The proposed protocol contains a non-linear and a linear term. The state consensus is achieved in finite time by the non-linear term and convergence performance is improved by the linear term to some degree. The protocol can be applied to systems with a switching topology as long as the communication graph is always undirected and connected. The upper bound of convergence time is obtained. The relationship between convergence time and protocol parameter, communication topology and initial state is analysed. Lastly, simulations are conducted to verify the effectiveness of the results.

Distributed Economic Dispatch for Smart Grids With Random Wind Power

In this paper, we present a distributed economic dispatch (ED) strategy based on projected gradient and finite-time average consensus algorithms for smart grid systems. Both conventional thermal generators and wind turbines are taken into account in the ED model. By decomposing the centralized optimization into optimizations at local agents, a scheme is proposed for each agent to iteratively estimate a solution of the optimization problem in a distributed manner with limited communication among neighbors. It is theoretically shown that the estimated solutions of all the agents reach consensus of the optimal solution asymptomatically. This scheme also brings some advantages, such as plug-and-play property. Different from most existing distributed methods, the private confidential information, such as gradient or incremental cost of each generator, is not required for the information exchange, which makes more sense in real applications. Besides, the proposed method not only handles quadratic, but also nonquadratic convex cost functions with arbitrary initial values. Several case studies implemented on six-bus power system, as well as the IEEE 30-bus power system, are discussed and tested to validate the proposed method.

Distributed Finite-Time Average Consensus in Digraphs in the Presence of Time Delays

Most algorithms for distributed averaging only guarantee asymptotic convergence. This paper introduces a distributed protocol that allows nodes to find the exact average of the initial values in a finite and minimum number of steps on interconnection topologies described by strongly connected directed graphs (digraphs). More specifically, under the assumption that each component has knowledge of the number of its outgoing links (i.e., the number of components to which it sends information), we show that the average value can be computed based on local observations over a finite time interval. The average can be obtained in a finite number of steps even when the information exchange is subject to delays. The proposed algorithm is the first in the literature that allows for distributed computation of the exact average in digraphs in finite time, with and without delays.

Distributed Cooperative Secondary Control for Voltage Unbalance Compensation in an Islanded Microgrid

This paper presents a distributed cooperative control scheme for voltage unbalance compensation (VUC) in an islanded microgrid (MG). By letting each distributed generator (DG) share the compensation effort cooperatively, unbalanced voltage in sensitive load bus (SLB) can be compensated. The concept of contribution level (CL) for compensation is first proposed for each local DG to indicate its compensation ability. A two-layer secondary compensation architecture consisting of a communication layer and a compensation layer is designed for each local DG. A totally distributed strategy involving information sharing and exchange is proposed, which is based on finite-time average consensus and newly developed graph discovery algorithm. This strategy does not require the whole system structure as a prior and can detect the structure automatically. The proposed scheme not only achieves similar VUC performance to the centralized one, but also brings some advantages, such as communication fault tolerance and plug-and-play property. Case studies including communication failure, CL variation, and DG plug-and-play are discussed and tested to validate the proposed method.

Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs

In this paper, finite-time multi-agent consensus problems are considered under networks associated with signed graphs whose edge weights can be not only positive but also negative. A nonlinear consensus protocol is proposed to guarantee the states of all agents to converge in a finite time. If the signed graph is structurally balanced, then the final consensus states of all agents are the same in modulus but not in sign. Otherwise, if the signed graph is structurally unbalanced, then the states of all agents converge to zero. Moreover, the final consensus states of agents can be provided uniformly regarding a signed-average quantity that depends on both the initial states of agents and the topology structure of the whole multi-agent network. Numerical simulations illustrate that the protocol is effective in achieving the finite-time consensus of agents under signed graphs and can particularly solve the finite-time average consensus problem of agents when their associated graph has all positive edge weights.

Finite-Time Consensus Using Stochastic Matrices With Positive Diagonals

We discuss the possibility of reaching consensus in finite time using only linear iterations, with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure. We show that finite-time average consensus can always be achieved for connected undirected graphs. For directed graphs, we show some necessary conditions for finite-time consensus, including strong connectivity and the presence of a simple cycle of even length.

Revisiting Finite-Time Distributed Algorithms via Successive Nulling of Eigenvalues

In this letter, we characterize the finite-time behavior on arbitrary undirected graphs. In particular, we derive distributed iterations that are a function of a linear operator on the underlying graph and show that any arbitrary initial condition can be forced to lie on a particular subspace in a finite time. This subspace can be chosen to have the same dimension as the algebraic multiplicity of any (arbitrarily chosen) eigenvalue of the underlying linear operator and is spanned by the eigenvectors corresponding to the chosen eigenvalue. In other words, finite-time behavior is completely characterized by the algebraic multiplicity of the eigenvalues and the corresponding eigenvectors of the underlying linear operator. We show that finite-time average-consensus can be cast naturally in this setup for which we further develop the necessary and sufficient conditions.

Step-size sequence design for finite-time average consensus in secure wireless sensor networks

This paper concerns the study of average consensus in wireless sensor networks with aim of providing a way to reach consensus in a finite number of steps. In particular, we investigate the design of consensus protocols when, for security reasons for instance, the underlying graph is constrained to be strongly regular or distance regular. The proposed design method is based on parameters of the intersection array characterizing the underlying graph. With this protocol, at execution time, average consensus is achieved in a number of steps equal to the diameter of the graph, i.e. the smallest possible number of steps to achieve consensus.

Distributed Design of Finite-time Average Consensus Protocols

In this paper, we are interested in the finite-time average consensus problem for multi-agent systems or wireless sensor networks. This issue is formulated in a discrete-time framework by utilizing a linear iteration scheme, where each node repeatedly updates its value as a weighted linear combination of its own value and those of its neighbors. Unlike most of research in literature, this work deals with the foremost step, called configuration step, during which the consensus protocol is to be set up in each agent. Designing consensus protocols can be viewed as a matrix factorization problem. For connected undirected graphs, we propose a learning method for solving such matrix factorization problem in a distributed way. More precisely, we first show how solving this problem for the particular case of strongly regular graphs. Then, a distributed gradient back-propagation algorithm is derived for the general case. The performance of the proposed algorithm is evaluated by means of simulation results.