Multi-agent Consensus Research Articles

Multiple Lyapunov Functions Approach for Consensus of One-Sided Lipschitz Multi-Agents Over Switching Topologies and Input Saturation

This brief investigates the leader-based consensus of one-sided Lipschitz (OSL) multi-agents under switching graphs and input saturation. By using the local design approach and multiple Lyapunov functions (MLFs), a novel condition for the consensus in nonlinear agents is provided by accomplishing guaranteed local stability. The notion of the average dwell time (ADT) has been applied for dealing with the switching topologies, which relaxes the classical dwell time restriction for switching instances. In contrast to the classical methods, both input saturation and switching topologies, representing a complicated and more meaningful consensus control scenario, are considered for nonlinear agents. The conservatism in existing methods for OSL agents has been overcome owing to the utilization of MLFs and ADT. Simulation results for eight mobile agents are provided to show the effectiveness of our consensus protocol.

Consensus of One-Sided Lipschitz Multi-Agents Under Input Saturation

This brief investigates a new consensus control methodology for nonlinear one-sided Lipschitz (OSL) multi-agents by considering the input saturation nonlinearity for each agent. Local design approaches are followed for dealing with the constrained consensus control of nonlinear agents by using the OSL dynamics, saturation nonlinearity, and quadratic inner-boundedness property. A region of initial conditions based on the consensus error is revealed, for which the proposed control approach guarantees the consensus error’s convergence to the origin. A new design condition for computation of the consensus protocol gain is developed for the leader-following consensus. Then, simulation results on synchronization of mobile OSL are provided by considering input saturation.

Event-based bipartite multi-agent consensus with partial information transmission and communication delays under antagonistic interactions

This paper mainly concentrates on the event-based bipartite consensus (BCs) in multi-agent networks (MANs) with partial information transmission (PIT) and communication delays. Two types of communication constraints, i.e., time delays and partial information transmission, makethe BCs problem in MANs more challenging andpractical.A distributed event-triggered scheme (ETS) isproposed for the considered MANs. Based on the proposed ETS, it is observed that the addressed MANs reaches BCs provided that the network is balanced.A numerical example is presented to demonstrate the effectiveness of the theoretical results.

Distributed Economic Dispatch for Energy Internet Based on Multiagent Consensus Control

We consider the economic dispatch (ED) for an Energy Internet composed of energy routers (ERs), interconnected microgrids, and main grid. The microgrid consists of several bus nodes associated with distributed generators (DGs) and intelligent control units (ICUs). We propose a distributed ED algorithm for the grid-connected microgrid, where each ICU iterates the estimated electricity price of the distribution system and the estimation for the average power mismatch of the whole microgrid by leader-following and average-consensus algorithms, respectively. The ER iterates the incremental power exchanged with the distribution system. By constructing an auxiliary consensus system, we prove that if the communication topology of the Energy Internet contains a spanning tree with the ER as the root and there is a path from each ICU to the ER, then the estimated electricity price of the distribution system converges to its real value, the power supply and demand achieves balance and the ED achieves optimal asymptotically. Furthermore, we propose an autonomous distributed ED algorithm covering both grid-connected and isolated modes of the microgrid by feeding back the estimated average power mismatch for updating the incremental costs with penalty factor. It is proved that if the communication topology of the microgrid is connected and there exists an ICU bidirectionally neighboring the ER, then the microgrid can switch between the two modes reliably. The simulation results demonstrate the effectiveness of the proposed algorithms.

Distributed Clustering Algorithm in Sensor Networks via Normalized Information Measures

Distributed data clustering in sensor networks is receiving increasing attention with the development of network technology. A variety of algorithms for distributed data clustering have been proposed recently. However, most of these algorithms have trouble with either non-Gaussian shaped data clustering or model order selection problem. In order to address such two problems simultaneously, we propose a novel discriminative clustering algorithm with rigorous convergence analysis via normalized information measures and then extend it to a distributed one by borrowing consensus algorithms from the multi-agent consensus community. More specifically, we first select the normalized information distance (NID) between cluster data and cluster labels as the objective function, by minimizing which, a Minimum Normalized Information Distance-based (MNID) algorithm with capabilities of non-Gaussian data clustering and model selection is then proposed. Next, to further implement the MNID algorithm in a distributed manner, we employ some finite-time multi-agent consensus algorithms over the sensor networks to calculate the global model parameters, where only local intermediate variables are exchanged between one-hop neighbors. Both the centralized and the distributed MNID algorithms are proved to converge rigorously. Finally, the validity of the proposed algorithms is demonstrated through numerical tests on both synthetic and real data.

An Optimization Approach to Verifying and Synthesizing K-cooperative Systems

Differential positivity and K-cooperativity, a special case of differential positivity, extend differential approaches to control to nonlinear systems with multiple equilibria, such as switches or multi-agent consensus. To apply this theory, we reframe conditions for strict K-cooperativity as an optimization problem. Geometrically, the conditions correspond to finding a cone that a set of linear operators leave invariant. Even though solving the optimization problem is hard, we combine the optimization perspective with the geometric intuition to construct a heuristic cone-finding algorithm centered around Linear Programming (LP). The algorithm we obtain is unique in that it modifies existing rays of a candidate cone instead of adding new ones. This enables us to also take a first step in tackling the synthesis problem for K-cooperative systems. We demonstrate our approach on some examples, including one in which we repurpose our algorithm to obtain a novel alternative tool for computing polyhedral Lyapunov functions of bounded complexity.

An Event-Based Interaction Sampled-Control for Consensus of Multi-Agents With Multiple Time-Varying Delays

An event-based consensus filtering control scheme for multi-agents with multiple mixing delays is proposed in the paper. Firstly, a piece-wise sampling model with transmission delay defined from sensors to controllers is built, and the effect of time-varying delay on sampling is analyzed. Secondly, a self-triggered scheme is proposed to take into consideration of reducing redundant data and complexity. Thirdly, to fully utilize the available information, by employing an improved generalized free-weighting matrix inequality, a novel Lyapunov-Krasovskii functional approach is proposed to achieve global asymptotically synchronization. At last, an example of multiple unmanned aerial vehicles is offered to show the effectiveness of proposed method.

Dynamic Quantized Consensus of General Linear Multi-agent Systems under Denial-of-Service Attacks

In this paper, we study a multi-agent consensus problem under Denial-of-Service (DoS) attacks with data rate constraints. We consider leaderless consensus under an undirected communication graph and assume that the graph is connected in the absence of DoS. The dynamics of the agents take general forms modeled as homogeneous linear time-invariant systems. In our analysis, we derive specific bounds on the data rate for the multi-agent system to achieve consensus even in the presence of DoS attacks. The main contribution of the paper is the characterization of the trade-off between the tolerable DoS attack level and the required data rates for the communication among the agents. To avoid quantizer saturation under DoS attacks, we employ dynamic quantization with zoom-in and zoom-out capabilities.

Coherent Plug-and-Play: Digital Holographic Imaging Through Atmospheric Turbulence Using Model-Based Iterative Reconstruction and Convolutional Neural Networks

In order to image a distant object through atmospheric turbulence, it is necessary to correct for the phase errors that would otherwise cause rapidly varying spatial blur in a conventionally focused image. One approach to solving this problem is to illuminate an object with coherent light and to use a digital holography (DH) receiver to form a coherent measurement. The associated amplitude and phase can then be used with model-based iterative reconstruction (MBIR) frameworks to estimate and correct for atmospheric phase errors from single-shot DH data (i.e., one sensor measurement). In this work, we present a new approach for the reconstruction of optically-coherent images from single-shot DH data in the presence of atmospheric turbulence, referred to as Coherent Plug-and-Play (C-PnP). Our algorithm integrates a convolutional neural network (CNN) image model with physics-based models for image reconstruction from DH data corrupted by atmospheric phase errors. C-PnP combines the modeling power of deep neural networks with the accuracy of existing physics models. Based on an extension of the plug-and-play framework, C-PnP uses multi-agent consensus equilibrium to balance the influence of these models. When compared with an existing approach using a simple image model, C-PnP improves image quality by a factor of $2.2\times$ and phase-error correction by a factor of $2.9\times$ , on average. We obtain these results by considering a wide range of images, signal levels, and phase-error strengths.

Distributed Iterative CT Reconstruction Using Multi-Agent Consensus Equilibrium

Model-Based Image Reconstruction (MBIR) methods significantly enhance the quality of computed tomographic (CT) reconstructions relative to analytical techniques, but are limited by high computational cost. In this article, we propose a multi-agent consensus equilibrium (MACE) algorithm for distributing both the computation and memory of MBIR reconstruction across a large number of parallel nodes. In MACE, each node stores only a sparse subset of views and a small portion of the system matrix, and each parallel node performs a local sparse-view reconstruction, which based on repeated feedback from other nodes, converges to the global optimum. Our distributed approach can also incorporate advanced denoisers as priors to enhance reconstruction quality. In this case, we obtain a parallel solution to the serial framework of Plug-n-play (PnP) priors, which we call MACE-PnP. In order to make MACE practical, we introduce a partial update method that eliminates nested iterations and prove that it converges to the same global solution. Finally, we validate our approach on a distributed memory system with real CT data. We also demonstrate an implementation of our approach on a massive supercomputer that can perform large-scale reconstruction in real-time.

Push-Pull Finite-Time Convergence Distributed Optimization Algorithm

With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.

Optimal Control Points Problem in Domination Game on Large Scale Multi-Agent Systems

In this paper, we deal with large scale multi-agent consensus systems in which some agents are assumed to be weakly controlled with feedback and consider a domination game between several players. We assume that each player can choose a set of controlled agents and input signals to control the states of all the agents to its own desired reference state. The reference states of the players are assumed to be different from each other, therefore, a conflict occurs between the players. The problem for each player is to choose a set of controlled agents to dominate the whole system as possible and we call this as a domination game. To find the optimal set of the controlled agents is essentially a complex combination problem, however, in this paper, we show that the optimal set can be given by small calculations. This result provides a strategy to the players for the domination game and we discuss the relationship between the structure of networks and monopolistic/equally domination games.

Dynamic Resilient Graph Games for State-Dependent Jamming Attacks Analysis on Multi-Agent Systems

A cybersecurity problem for a multi-agent consensus problem is investigated through a dynamic game formulation. Specifically, we consider a game repeatedly played between a jamming attacker and a defender. The attacker attempts to jam the links between a number of agents to delay their consensus. On the other hand, the defender tries to maintain the connection between agents by attempting to recover some of the jammed links with the goal of achieving faster consensus. In each game, the players decide which links to attack/recover and for how long to continue doing so based on a Lyapunov-like function representing the largest difference between the states of the agents. We analyze the subgame perfect equilibrium of the game and obtain an upper bound of the consensus time that is influenced by the strategies of the players. The results are illustrated with a numerical example.

A distributed control strategy of microgrid based on multi-agent consensus algorithm

In an islanded microgrid with distributed generators (DGs), on account of the influence of feeder impedance, load and other factors, it is difficult to dispatch output power reasonably by means of droop control, therefore the secondary control is employed to solve this problem. However, the convention methods may fail to achieve the expected effect. In this context, an improved distributed control strategy based on multi-agent consensus algorithm is proposed in this paper. A virtual leader is set to track the balance of power. Through the mutual communication between DGs, it can realize the flexible distribution of load power and has good convergence. By introducing the integral controller on the basis of conventional droop control, the droop curve can move adaptively to maintain frequency and voltage stable. Finally, the effectiveness of the proposed scheme and the performance of anti-communication failure are verified in MATLAB/Simulink simulation platform.

Average Consensus by Graph Filtering: New Approach, Explicit Convergence Rate, and Optimal Design

This paper revisits the problem of multi-agent consensus from a graph signal processing perspective. Describing a consensus protocol as a graph spectrum filter, we present an effective new approach to the analysis and design of consensus protocols in the graph spectrum domain for the uncertain networks, which are difficult to handle by the existing time-domain methods. This novel approach has led to the following new results in this paper: 1) New necessary and sufficient conditions for both finite-time and asymptotic average consensus of multi-agent systems. 2) Direct link between the consensus convergence rate and the periodic consensus protocols. 3) Conversion of the fast consensus problem to the problem of polynomial design of graph spectrum filter. 4) A Lagrange polynomial interpolation method and a worst-case optimal interpolation method for the design of periodic consensus protocols for the MASs on uncertain graphs. 5) Explicit formulas for the convergence rate of the designed protocols. Several numerical examples are given to demonstrate the validity, effectiveness and advantages of these results.

An event‐triggered approach to quantized resilient consensus

SummaryWe consider an event‐triggered update scheme for the problem of multiagent consensus in the presence of faulty and malicious agents within the network. In particular, we focus on the case where the agents take integer (or quantized) values. To keep the regular agents from being affected by the behavior of faulty agents, algorithms of the mean subsequence reduced type are employed, where neighbors taking extreme values are ignored in the updates. Different from the real‐valued case, the quantized version requires the update rule to be randomized. We characterize the error bound on the achievable level of consensus among the agents as well as the necessary structure for the network in terms of the notion of robust graphs. We verify via a numerical example the effectiveness of the proposed algorithms.

Optimal planning and operation of dispatchable active power resources for islanded multi‐microgrids under decentralised collaborative dispatch framework

As an islanded multi-microgrid (IMMG) receives little support from the main network, it is necessary to develop new dispatch frameworks to fulfil its real-time dispatch requirement. Hence, a decentralised collaborative dispatch framework of IMMG based on multi-agent consensus algorithm is proposed. In the framework, the ttal power command of IMMG can be optimally allocated among all the microgrids (MGs) based on consensus algorithm. Then the power command of each MG can be efficiently allocated among all the dispatchable units based on the proposed priority-based collaborative dispatch strategy. Based on the decentralised collaborative dispatch framework, in order to optimise the planning and operation of dispatchable active power resources (DAPRs), on one hand, a bi-level model that couples the planning and operation problems of an IMMG is established to optimise the configuration of DAPR; on the other hand, more detailed models are proposed for the regulation costs of various dispatchable units, which is an improvement over the existing regulation cost model. By considering the two aspects, the consensus algorithm is embedded in multiple population genetic algorithm to solve the bi-level model. Case studies are conducted on an IMMG consisting of three MGs to examine the effectiveness of the proposed planning and dispatch model.

Event-based discrete-time multi-agent consensus over signed digraphs with communication delays

The ability to ensure the desired performance of the cooperative-antagonistic multi-agent networks (MANs) in the presence of communication constraints is an important task in many applications of real systems. In this paper, under the proposed event-triggered condition (ETC), different types of consensus are obtained under different network topology. We concentrates on the event-based bipartite consensus. It is shown that under the proposed ETC (i) the addressed cooperative-antagonistic network with arbitrary communication delays reaches bipartite consensus provided that the network is balanced; (ii) the network model reaches zero if the network is unbalanced. Further, to avoid the continuously verifying the triggering condition, a self-triggered algorithm is proposed for realizing the bipartite consensus of the network model. A numerical example is given to illustrate the effectiveness of the theoretical results.

Multi-Agent Consensus Algorithm-Based Optimal Power Dispatch for Islanded Multi-Microgrids

Islanded multi-microgrids formed by interconnections of microgrids will be conducive to the improvement of system economic efficiency and supply reliability. Due to the lack of support from a main grid, the requirement of real-time power balance of the islanded multi-microgrid is relatively high. In order to solve real-time dispatch problems in an island multi-microgrid system, a real-time cooperative power dispatch framework is proposed by using the multi-agent consensus algorithm. On this basis, a regulation cost model for the microgrid is developed. Then a consensus algorithm of power dispatch is designed by selecting the regulation cost of each microgrid as the consensus variable to make all microgrids share the power unbalance, thus reducing the total regulation cost. Simulation results show that the proposed consensus algorithm can effectively solve the real-time power dispatch problem for islanded multi-microgrids.

QUAD-Condition, Synchronization, Consensus of Multiagents, and Anti-Synchronization of Complex Networks.

In this article, we discuss quadratic condition (QUAD-condition) for general models of synchronization of complex networks and consensus of multiagents with or without pinning controller in detail. Synchronization analysis consists of two parts. One is connection structure, which is described with coupling matrix. The other one is the intrinsic property of the uncoupled system. QUAD-conditions play a key role in describing the intrinsic property of the uncoupled system. With QUAD-conditions, we unify synchronization and consensus of multiagents in a framework. It is interesting that anti-synchronization can be easily transformed to synchronization by introducing suitable QUAD-condition.