Time-varying Communication Topologies Research Articles

Event-Triggered Optimal Active Power Control in Islanded Microgrid With Variable Demand and Time-Varying Communication Topology

For islanded microgrids, traditional droop-based control leads to frequency deviation and low economic efficiency. To resolve this issue, a novel event-triggered optimal active power control strategy, which achieves frequency regulation and economic operation in a fully distributed way, is proposed in this paper. Frequency deviations are monitored and used to trigger the load estimation algorithm to track changes in power demand. Based on estimated demand values, a distributed economic dispatch (ED) algorithm, which only requires that the communication topology satisfies the jointly connected condition, is proposed to calculate the optimal generation references for the generators. The ED algorithm has the finite-time convergence property, which is rigorously proved by Lyapunov theory, LaSalle’s invariance principle and homogeneous property. Based on optimal generation references, the parameters of droop controller are reset in real time, which makes microgrid achieve frequency restoration and economic operation simultaneously. Finally, several case studies are presented to illustrate the effectiveness of the proposed control strategy.

Distributed Piecewise Approximation Economic Dispatch for Regional Power Systems Under Non-Ideal Communication

Appropriate distributed economic dispatch (DED) strategies are of great importance to manage wide-area controllable generators in wide-area regional power systems. Compared with existing works related to ED, where dispatch algorithms are carried out by a centralized controller, a practical DED scheme is proposed in this paper to achieve the optimal dispatch by appropriately allocating the load to generation units while guaranteeing consensus among incremental costs. The ED problem is decoupled into several parallel sub-problems by the primal-dual principle to address the computational issue of satisfying power balance between the demand and the supply from the distributed regional power system. The feasibility test and an innovative mechanism for unit commitment are then designed to handle extreme operation situations, such as low load level and surplus generation. In the designed mechanism, the on/off status of units is determined in a fully distributed framework, which is solved using the piecewise approximation method and the discrete consensus algorithm. In the algorithm, the push-sum protocol is proposed to increase the system adaptation on the time-varying communication topology. Moreover, consensus gain functions are designed to ensure the performance of the proposed DED under communication noise. Case studies on a standard IEEE 30-bus system demonstrate the effectiveness of our proposed methodology.

Distributed Anti-Disturbance Control Strategy for Multi-Aircraft Systems With Time-Varying Topology

This paper is concerned with the distributed consensus problems for second-order multi-aircraft systems in the presence of sensor data loss and time-varying communication topology. A novel model-based game strategy is proposed to handle the distributed problem regardless of the time-varying topology. An anti-disturbance sliding-mode controller is designed to realize the ability of disturbance rejection and state estimation. The extended state observer combines two methods together and finally produces an independent decision-making architecture for each individual such that better convergence is achievable. Theoretical analyses are given to guarantee both individual stability and distributed stability. The simulation and experimental results are presented to show the effectiveness of the proposed control scheme.

Consensus of Multi-Agent Systems With Piecewise Continuous Time-Varying Topology

This paper studies the consensus of multi-agent systems with piecewise continuous time-varying topology. The agents are assumed to have identical first-order linear dynamics, which their underlying communication topology is piecewise continuous time-varying. In the case of undirected time-varying communication topology, the consensus of the multi-agent system depends on the connectivity of its limit topology, and the states of all agents converge to the mean of their initial states. However, the consensus depends on the absolute integrability of the elements in the difference matrix between the Laplacian matrix and the limit matrix when the communication topology is directed and connected. Several simulation examples are presented to validate the proposed theories.

Distributed Finite-Time Consensus Control for Heterogeneous Battery Energy Storage Systems in Droop-Controlled Microgrids

This paper presents a novel distributed finite-time control scheme for heterogeneous battery energy storage systems (BESSs) in droop-controlled microgrids. In contrast to the existing centralized methods, the proposed control strategy is fully distributed so that each BESS only requires its own information and the information from its neighbors through a sparse communication network. Our novel consensus-based method is implemented to achieve energy level balancing, active/reactive power sharing, and voltage/frequency synchronization of energy storage devices by using inter-BESS communications, where both the heterogeneous nature of batteries and the hierarchical control structure are taken into consideration. Furthermore, the proposed design is shown to improve the synchronization performance and exhibit more accurate robustness against time-varying communication topologies and load changes. Simulation results on a modified IEEE 57-bus power system are provided to verify the effectiveness of the proposed consensus strategy.

Distributed control of cluster lag consensus for first-order multi-agent systems on QUAD vector fields

This paper addresses the problem of cluster lag consensus for first-order multi-agent systems which can be formulated as moving agents in a capacity-limited network. A distributed control protocol is developed based on local information, and the robustness of the protocol is analyzed by using tools of Frobenius norm, Lyapunov functional and matrix theory. It is shown that when the root agents of the clusters are influenced by the active leader and the intra-coupling among agents is stronger enough, the multi-agent system will reach cluster lag consensus. Moreover, cluster lag consensus for multi-agent systems with a time-varying communication topology and heterogeneous multi-agent systems with a directed topology are studied. Finally, the effectiveness of the proposed protocol is demonstrated by some numerical simulations.

Distributed Subgradient-Based Multiagent Optimization With More General Step Sizes

A wider selection of step sizes is explored for the distributed subgradient algorithm for multi-agent optimization problems, for both time-invariant and time-varying communication topologies. The square summable requirement of the step sizes commonly adopted in the literature is removed. The step sizes are only required to be positive, vanishing and non-summable. It is proved that in both unconstrained and constrained optimization problems, the agents' estimates reach consensus and converge to the optimal solution with the more general choice of step sizes. The idea is to show that a weighted average of the agents' estimates approaches the optimal solution, but with different approaches. In the unconstrained case, the optimal convergence of the weighted average of the agents' estimates is proved by analyzing the distance change from the weighted average to the optimal solution and showing that the weighted average is arbitrarily close to the optimal solution. In the constrained case, this is achieved by analyzing the distance change from the agents' estimates to the optimal solution and utilizing the boundedness of the constraints. Then the optimal convergence of the agents' estimates follows because consensus is reached in both cases. These results are valid for both a strongly connected time-invariant graph and time-varying balanced graphs that are jointly strongly connected.

Avoiding Congestion in Cluster Consensus of the Second-Order Nonlinear Multiagent Systems.

In order to avoid congestion in the second-order nonlinear leader-following multiagent systems over capacity-limited paths, an approach called cluster lag consensus is proposed, which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times. Lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus. It is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold, the cluster lag consensus can be achieved. Furthermore, the cluster lag consensus with a time-varying communication topology is investigated. Finally, an illustrative example is presented to demonstrate the effectiveness of the theoretical results. In particular, when the physical sizes of the agents are taken into consideration, it is shown that with a rearrangement and a position transformation, the multiagent system will reach cluster lag consensus in the new coordinate system. This means that all agents in the same cluster will reach consensus on the velocity, but their positions may be different and yet their relative positions converge to a constant asymptotically.

Stable control of a heterogeneous platoon of vehicles with switched interaction topology, time-varying communication delay and lag of actuator

This paper is devoted to the study of longitudinal control of heterogeneous vehicular platoons with constant spacing policy between successive vehicles. In order to provide a more precise model, communication delays are assumed to be non-uniform and time-varying. A linear control based on relative measurements by considering communication delay and lag is used as the upper level control of each vehicle. In a vehicular platoon, the time-varying communication topology may be a source of instability of the closed-loop dynamics. Therefore, to perform the stability analysis using common Lyapunov function, three new methods based on Lyapunov–Razumikhin and Lyapunov–Krasovskii theorems are introduced. The results of these methods prove the global asymptotic stability of the resultant switched linear time-varying delay systems. A comparison between the proposed methods indicates that the Krasovskii-based approach is more robust against communication delay and lag than the Razumikhin-based approaches. Several simulation studies are provided to show the effectiveness of the proposed methods.

DRHC synthesis for simultaneous tracking and formation of nonhomogeneous multi-agents with time-varying communication topology

The synthesis approach of distributed receding horizon control is studied for the simultaneous tracking and formation problem of nonhomogeneous multi-agents. Different from the existing works, the communication topology between multi-agents is allowed to be time-varying in this article, which meets miscellaneous conditions in practice. To accommodate the time-varying communication topology, we refresh at each sampling instant the individual cost function for each agent, according to the real-time neighbourhood. Moreover, to guarantee the exponential stability of the overall closed-loop system, we design an auxiliary constraint and impose it in the individual optimization problem. The recursive feasibility of the auxiliary constraint can be guaranteed by updating the formation weighting scalars in real time. By solving the individual optimization problem (with respect to the input, state and auxiliary constraints) at each sampling instant, each agent can obtain its optimal control input sequence. The implementation of the first control input among the sequence for each agent can steer the overall multi-agent system to cooperatively achieve the desired tracking and formation objective. The effectiveness and practicability of our results are demonstrated through the illustrative examples.

Exponential Synchronization for Second-Order Nodes in Complex Dynamical Network with Communication Time Delays and Switching Topologies

This paper is devoted to the study of exponential synchronization problem for second-order nodes in dynamical network with time-varying communication delays and switching communication topologies. Firstly, a decomposition approach is employed to incorporate the nodes’ inertial effects into the distributed control design. Secondly, the sufficient conditions are provided to guarantee the exponential synchronization of second-order nodes in the case that the information transmission is delayed and the communication topology is balanced and arbitrarily switched. Finally, to demonstrate the effectiveness of the proposed theoretical results, it is applied to the typical second-order nodes in dynamical network, as a case study. Simulation results indicate that the proposed method has a high performance in synchronization of such network.

Containment control of continuous-time multi-agent systems with general linear dynamics under time-varying communication topologies

This paper devotes itself to the containment tracking problem of general linear high-order multiagent systems (MASs) under time-varying communications. For general linear MASs with time-varying weightunbalanced digraph, the containment control problem is difficult and challenging, because the Lyapunov method is not an effective approach in this case. Under the assumption that the graph topology uniformly and jointly has a directed spanning forest, we show that when the exponentially unstable mode associated with each agent’s self-dynamics is weak enough, the followers can asymptotically tend to the dynamical convex hull spanned by the leaders, i.e. the containment can be achieved. Moreover, the least convergence rate is explicitly specified. Simulations are also provided to demonstrate the effectiveness of our result.

Leader-Following Coordination of Nonlinear Agents Under Time-Varying Communication Topologies

This paper deals with the problem of synchronizing the outputs of a set of nonlinear agents that exchange information through a time-varying communication network in a leader-follower configuration. The dynamics of the individual followers may differ from each other and from that of the leader. The information exchange between the leader and (a limited fraction of) the followers as well as between neighboring followers only consists of the relative values of the output variables that are to be synchronized. The theory of output regulation for nonlinear systems is used to design decentralized controllers embedding an internal model of the leader dynamics. Then, under mild connectivity hypotheses, it is shown how synchronization between the local control loops can be achieved.

Quantized Subgradient Algorithm and Data-Rate Analysis for Distributed Optimization

In this paper, we consider quantized distributed optimization problems with limited communication capacity and time-varying communication topology. A distributed quantized subgradient algorithm is presented with quantized information exchange between agents. Based on a proposed encoder-decoder scheme and a zooming-in technique, the optimal solution can be obtained without any quantization errors. Moreover, we explore how to minimize the quantization level number for quantized distributed optimization problems. In fact, the optimization problem can be solved with five-level quantizers in the switching topology case, while it can be solved with three-level quantizers in the fixed topology case.

A new game model for distributed optimization problems with directed communication topologies

Abstract In this paper, the distributed optimization problems of multi-agent systems with directed communication topologies are investigated by using the game theory. In particular, a new general non-cooperative game model, termed state based weakly acyclic game, is provided to solve the problem. Based on this approach, the desired global objective is achieved by designing local objective function for individual agent to make coordination decisions. It is worth noting that all the obtained equilibria are thus solutions to the proposed distributed optimization problems with directed and time-varying communication topologies. Simulations on consensus problem in multi-agent systems are provided to verify the validness of the proposed methodology.

Modeling and distributed gain scheduling strategy for load frequency control in smart grids with communication topology changes

In this paper, we investigate the modeling and distributed control problems for the load frequency control (LFC) in a smart grid. In contrast with existing works, we consider more practical and real scenarios, where the communication topology of the smart grid changes because of either link failures or packet losses. These topology changes are modeled as a time-varying communication topology matrix. By using this matrix, a new closed-loop power system model is proposed to integrate the communication topology changes into the dynamics of a physical power system. The globally asymptotical stability of this closed-loop power system is analyzed. A distributed gain scheduling LFC strategy is proposed to compensate for the potential degradation of dynamic performance (mean square errors of state vectors) of the power system under communication topology changes. In comparison to conventional centralized control approaches, the proposed method can improve the robustness of the smart grid to the variation of the communication network as well as to reduce computation load. Simulation results show that the proposed distributed gain scheduling approach is capable to improve the robustness of the smart grid to communication topology changes.

Consensus with quantized relative state measurements

In this paper, cooperative control of multi-agent systems under limited communication between neighboring agents is investigated. In particular, quantized values of the relative states are used as the control parameters. By taking advantage of tools from nonsmooth analysis, explicit convergence results are derived for both uniform and logarithmic quantizers under static and time-varying communication topologies. Compared with our previous work, less conservative conditions that ensure global convergence are provided. Moreover, second order dynamical systems under similar constraints are taken into account. Computer simulations are provided to demonstrate the validity of the derived results.

Chebyshev Polynomials in Distributed Consensus Applications

In this paper we analyze the use of Chebyshev polynomials in distributed consensus applications. It is well known that the use of polynomials speeds up the convergence to the consensus in a significant way. However, existing solutions only work for low degree polynomials and require the topology of the network to be fixed and known. We propose a distributed algorithm based on the second order difference equation that describes the Chebyshev polynomials of first kind. The contributions of our algorithm are three: (i) Since the evaluation of Chebyshev polynomials is stable, there is no limitation in the degree of the polynomial. (ii) Instead of the knowledge of the whole network topology, it only requires a partial knowledge or an approximation to it. (iii) It can be applied to time varying topologies. In the paper we characterize the main properties of the algorithm for both fixed and time-varying communication topologies. Theoretical results, as well as experiments with synthetic data, show the benefits of using our algorithm compared to existing methods.

Quantized Data--Based Distributed Consensus under Directed Time-Varying Communication Topology

Distributed average consensus (DAC) is investigated for multiagent systems (MASs) with directed time-varying communication topology and quantized communication data. We propose a communication feedback--based distributed consensus protocol suitable for directed time-varying topologies to deal with the inconsistency between the internal state of each agent's encoder and the output of its neighbors' decoder, and give rigorous analysis for the consensus of the MAS. The consensus protocols are designed based on uniform quantizers with scaling. A finite lower bound of the communication data rate between each pair of adjacent agents is obtained to ensure the exponential consensus by properly choosing system parameters. In addition, the lower bound is proved to be merely 1-bit for the directed fixed topology case, no matter how large the agent number is. A numerical example is presented to demonstrate the results obtained.

Robust Stability of a Multi-Agent System Under Arbitrary and Time-Varying Communication Topologies and Communication Delays

This technical note considers formation control of a group of identical agents that can communicate with each other. A necessary and sufficient condition for robust stability in the case of arbitrary time-invariant communication topologies and sufficient conditions in the case of arbitrary time-varying topology and communication delays are derived, that reduce the stability analysis and controller design problems to analysis or synthesis, respectively, for a single agent.