Multi-agent Consensus Research Articles

Centralized and Collective Neurodynamic Optimization Approaches for Sparse Signal Reconstruction via L₁-Minimization.

This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction by solving the L1 -minimization problem. First, two centralized neurodynamic approaches are designed based on the augmented Lagrange method and the Lagrange method with derivative feedback and projection operator. Then, the optimality and global convergence of them are derived. In addition, considering that the collective neurodynamic approaches have the function of information protection and distributed information processing, first, under mild conditions, we transform the L1 -minimization problem into two network optimization problems. Later, two collective neurodynamic approaches based on the above centralized neurodynamic approaches and multiagent consensus theory are proposed to address the obtained network optimization problems. As far as we know, this is the first attempt to use the collective neurodynamic approaches to deal with the L1 -minimization problem in a distributed manner. Finally, several comparative experiments on sparse signal and image reconstruction demonstrate that our proposed centralized and collective neurodynamic approaches are efficient and effective.

Secure Consensus via Objective Coding: Robustness Analysis to Channel Tampering

This work mainly addresses continuous-time multiagent consensus networks where an adverse attacker affects the convergence performances of said protocol. In particular, we develop a novel secure-by-design approach in which the presence of a network manager monitors the system and broadcasts encrypted tasks (i.e., hidden edge weight assignments) to the agents involved. Each agent is then expected to decode the received codeword containing data on the task through appropriate decoding functions by leveraging advanced security principles, such as objective coding and information localization. Within this framework, a stability analysis is conducted for showing the robustness to channel tampering in the scenario where part of the codeword corresponding to a single link in the system is corrupted. A tradeoff between objective coding capability and network robustness is also pointed out. To support these novelties, an application example on decentralized estimation is provided. Moreover, an investigation of the robust agreement is as well extended in the discrete-time domain. Further numerical simulations are given to validate the theoretical results in both the time domains.

Cloud-based self-triggered coordination for nonlinear multi-agent consensus

This paper addresses the practical tracking consensus problem for first-orderheterogeneous nonlinear multi-agent systems in presence of external disturbances under directed graphs. Agents with limited communication capability interact with each other through a cloud repository, where the information exchange is asynchronous and indirect. The system model is more general than the ones in existing results, moreover, locally Lipschitz nonlinearities and adaptive control schemes are taken into account. It is proven that under the designed self-triggered protocol, agents can track a virtual leader with bounded error and Zeno behaviour is excluded for real implementation. Finally, a numerical simulation demonstrates the effectiveness of the theoretical results.

Distributed dynamic event-triggered communication and control for multi-agent consensus: A hybrid system approach

This paper investigates the output-based event-triggered communication and control for linear multi-agent consensus under a directed graph based on a co-design method. The communication among the agents, as well as the controller updates, are determined by some new event-triggering mechanisms, in order to reduce the use of the network resources. To simultaneously guarantee the significant properties including the asymptotic consensus, and strong Zeno-freeness (strictly positive inter-event times), a novel distributed dynamic event-triggered protocol is proposed. Unlike the most-existing emulation-based approaches in which the control gain is previously decided, a systematic co-design procedure is proposed to design the controller gain, the observer gain, and the event-triggering mechanisms altogether in terms of solving a linear matrix inequality optimization problem. Based on the resulting hybrid system framework, a hybrid model is established for the distributed closed-loop system and the asymptotic consensus is achieved. Finally, a numerical example is presented to verify our systematic design methodology.

Game-based coordination control of multi-agent systems

In this paper, we are interested in how agents interact with each other in multi-agent systems. First, we model the interactions among agents in multi-agent systems as a multi-player game. The topology of the interactions among agents is a directed graph. We design cost functions for the game and assume that each agent in the systems tends to minimize its own cost. Then, the unique Nash equilibrium solution to the proposed multi-player game is obtained as the next state of the agent. A necessary and sufficient condition for achieving multi-agent consensus is established using the system transformation method and graph theory. Furthermore, we extend the result to the problem of containment control in the presence of leaders. The criterion for solving the containment control is also given in this paper. Finally, several simulation examples are given to verify the effectiveness of the theoretical results.

A Decentralized Primal-Dual Method for Constrained Minimization of a Strongly Convex Function

We propose decentralized primal-dual methods for cooperative multiagent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific convex functions over conic constraint sets defined by agent-specific nonlinear functions; hence, the optimal consensus decision should lie in the intersection of these private sets. Under the strong convexity assumption, we provide convergence rates for suboptimality, infeasibility, and consensus violation in terms of the number of communications required; examine the effect of underlying network topology on the convergence rates.

An edge-based augmented system approach for second-order nodal consensus

Many works on multi-agent consensus protocol designs rely on the full states of nodes or the node- observer-based procedures, under both of which the nodal information plays a key role in the consensus design. In this paper, we propose an edge-based augmented system approach for second-order nodal consensus, based on the edge loop transfer matrix of the closed-loop multi-agent system, which is defined by cutting the loop at the inputs of the edges. Each agent is allowed to be of single-output and additional poles and zeros are introduced into edges to construct the channel filter with previous data stored in the memories. We firstly focus on the consensus design by reserving two terms of the non-recursive filter and then propose a simplified design approach exploiting a single parameter, which is of low complexity and can be readily implemented. We also discuss the consensus design by using the non-recursive channel filter with higher-order realizations. Finally, as an extension, we discuss the consensus design based on the first-order recursive channel filter. The effectiveness of the proposed method is verified by the illustrative simulations.

Special issue on PID control in the information age: Theoretical advances and applications

Special issue on PID control in the information age: Theoretical advances and applications

Consensus of multiagent with interaction distortions via echo control

This paper studies the discrete-time multiagent consensus problem with kinds of diverse interaction distortions which are related to the states of agents, and a novel dual switching control strategy is proposed, named echo control, to make the system achieve state consensus. The main feature of the echo control strategy is that agents resend the information flows (received from neighbors) to the corresponding neighbor, just like the reflecting of sound waves. In other words, every individual under the echo control strategy is not only the sender and receiver of the information flows, but also the reflector of its neighbors’ messages. In this way, a negative feedback loop is constructed between every two agents, which is designed to ensure the stability of the multiagent system (MAS), and then the agents’ states will converge to a common value. The effectiveness of the echo control protocol is theoretically analyzed, and numerical simulations validate the correctness of the relevant results.

Neurodynamic approaches for sparse recovery problem with linear inequality constraints

This paper develops two neurodynamic approaches for solving the L1-minimization problem with the linear inequality constraints. First, a centralized neurodynamic approach is proposed based on projection operator and nonnegative quadrant. The stability and global convergence of the centralized neurodynamic approach are analyzed by the Lyapunov method in detail. Considering that the distributed optimization problem has the advantages of information protection and scalability, the L1-minimization problem with linear inequality constraints is transformed into a distributed sparse optimization problem under mild conditions. Then, using the centralized neurodynamic approach and multi-agent consensus theory, a distributed neurodynamic approach is proposed for the distributed optimization problem. Furthermore, relevant theories show that each agent globally converges to an optimal solution of the distributed optimization problem. Finally, the presented centralized neurodynamic approach is applied to sparse recovery problem with L∞-norm noise constraints and the effectiveness of distributed approach is shown by several experiments on sparse signal recovery.

Event-triggered consensus for delayed second-order leader-following heterogeneous multi-agent systems under input saturated condition

The event-triggered consensus problem for observer-based second-order leader-following heterogeneous multi-agent systems with nonlinear term delay under input saturation conditions is investigated in this study. For a class of second-order leader-following heterogeneous multi-agent system models, the situation of agents with nonlinear delay terms in the system is considered. The observer is designed to reconstruct the state of the system. The structural state replaces the real state of the system to achieve the required state feedback, and the difference between the output quantities is inputted into the system as a feedback quantity (deviation) to achieve a better simulation. Considering the phenomenon of saturation control in many control systems, multi-agent consensus is achieved by combining saturation control and event-triggered pinning control in the controller. On the premise that each agent is affected by input saturation, an event-triggered pinning control protocol is designed to achieve the purpose of control by pinning down some key agents. The sufficient conditions for the second-order multi-agent system to achieve consensus are obtained by using the Lyapunov stability theory, algebraic Riccati equation, matrix theory, and other analytical techniques. The proposed event-triggered function can avoid Zeno behavior. The feasibility of the results is verified by numerical simulation.

Hierarchical Cooperative Control Strategy for Battery Storage System in Islanded DC Microgrid

This paper presents a novel hierarchical cooperative control strategy to solve the problems of unbalanced State of Charge (SoC), unreasonable load current sharing, and unstable bus voltage for battery storage system (BSS) in islanded DC microgrid. In the communication layer, a neighbor-to-neighbor communication network architecture is constructed in which each battery storage unit (BSU) only communicates information with neighboring nodes, and a multi-agent consensus algorithm is used to iteratively estimate the relevant average global variables. In the main control layer, the droop coefficient is dynamically adjusted by constructing a fast SoC convergence function to ensure that the load current is reasonably distributed based on the rated capacity of each BSU. In the secondary control layer, a virtual voltage drop equalization controller and an average bus voltage compensation controller are designed to eliminate the impact of line impedance mismatch and compensate the average bus voltage. Furthermore, an optimized factor is designed to accelerate the later stage of SoC convergence. Finally, a DC microgrid experimental platform based on StarSim HIL is built, and the results demonstrate that the proposed strategy can achieve the control objectives of fast SoC balance, proportional load current sharing, and bus voltage stability.

Consensus Control of Highway On-Ramp Merging With Communication Delays

In the environment of intelligent and connected vehicles, the information sharing level among vehicles and infrastructure get comprehensively improved. Aiming at the cooperative merging control at highway ramp, we present a two-stage hybrid cooperative control framework considering communication time delays including centralized decision-making for grouping with sequencing and distributed consensus control. The centralized controller is based on a grouping strategy and a cost function for minimizing total travel time and delays and determining the optimal vehicle passage order. Then we model the merging vehicles formation as a multi-agent system, which also could be viewed as a distributed controlling system. Combining with the multi-agent consensus method, it could achieve the desired inter-vehicle distance and speed. The proof tool is the Lyapunov-Krasovskii stability theorem in terms of convergence and formation stability. Finally, we design three simulation scenarios through varying the number of vehicles. Meanwhile, in order to verify the resistance of the algorithm to communication time delays, three conditions with respect to no time delays, heterogeneous time delays, and homogeneous time delays are considered. Simulation result verifies the advantage of the proposed method compared with the Hamilton control method. The efficiency of the proposed method is impervious in three different types of communication time delays and has approximately 30%, 25%, 15% improvement over that of the Hamiltonian method, respectively. Furthermore, the adaptation and effectiveness of the proposed method is demonstrated under different volumes of traffic flow and communication delays.

Optimized Leader-Follower Consensus Control Using Reinforcement Learning for a Class of Second-Order Nonlinear Multiagent Systems

In this article, an optimized leader-follower consensus control is proposed for a class of second-order unknown nonlinear dynamical multiagent system. Different with the first-order multiagent consensus, the second-order case needs to achieve the agreement not only on position but also on velocity, therefore this optimized control is more challenging and interesting. To derive the control, reinforcement learning (RL) can be a natural consideration because it can overcome the difficulty of solving the Hamilton–Jacobi–Bellman (HJB) equation. To implement RL, it needs to iterate both adaptive critic and actor networks each other. However, if this optimized control learns RL from most existing optimal methods that derives the critic and actor adaptive laws from the negative gradient of square of the approximating function of the HJB equation, this control algorithm will be very intricate, because the HJB equation correlated to a second-order nonlinear multiagent system will become very complex due to strong state coupling and nonlinearity. In this work, since the two RL adaptive laws are derived via implementing the gradient descent method to a simple positive function, which is obtained on the basis of a partial derivative of the HJB equation, this optimized control is significantly simple. Meanwhile, it not merely can avoid the requirement of known dynamic acknowledge, but also can release the condition of persistent excitation, which is demanded in most RL optimization methods for training the adaptive parameter more sufficiently. Finally, the proposed control is demonstrated by both theory and computer simulation.

A Two-Layer Distributed Algorithm Using Neurodynamic System for Solving L 1-Minimization

This brief considers a distributed algorithm for solving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L_{1}}$ </tex-math></inline-formula> -minimization problem based on nonlinear neurodynamic system. Compared with centralized algorithms, distributed algorithms have great potential in data privacy protection, distributed storage and processing of data. In this brief, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L_{1}}$ </tex-math></inline-formula> -minimization problem is transformed into a distributed problem by using multiagent consensus theory. For the distributed optimization problem, a two-layer distributed algorithm is designed by utilizing neurodynamic system, projection matrix and derivative feedback technique. Compared with the existing distributed neurodynamic algorithm, the proposed algorithm has a simpler structure and has fewer neurons on the premise that the calculation error does not increase. Besides, the proposed algorithm converges to a minimal point of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L_{1}}$ </tex-math></inline-formula> -minimization problem and is Lyapunov stable. Finally, the comparative examples of sparse signal reconstruction show that the proposed distributed algorithm is effective and superior.

Polymorphic Distributed Energy Management for Low-Carbon Port Microgrid With Carbon Capture and Carbon Storage Devices

In order to reduce the carbon emission of the port and build a green port, a polymorphic distributed energy management method for the low carbon port microgrid with carbon capture and carbon storage device is proposed. Firstly, this paper presents a low carbon port microgrid in a polymorphic network environment to realize the information interaction among energy subjects in different modes and improve network communication performance among port power generation device, main grid, carbon capture and carbon storage device. Secondly, the energy management model of low-carbon port microgrid is constructed considering the additional carbon capture device and carbon storage device in the port. Then, based on the multi-agent consensus algorithm, a distributed energy management method is proposed, which is respectively oriented to the grid-connected operation mode, island operation mode and switching operation mode of the port microgrid, so as to achieve the economic, low carbon and reliable operation of the port microgrid. Finally, the simulation results of Matlab verify the effectiveness of the proposed method.

Generalized demand-side resource hierarchical control strategy based on multi-agent consensus of historical data online transfer

To achieve large-scale generalized demand-side resources to participate in the “peak-shaving and valley-filling” of the power system, a distributed cooperative control strategy for discrete-time linear multi-agents considering historical data is proposed, which comprehensive consider the changes in load commands, topology, multi-objective function coefficients, communication delays and input delays. This paper combines the distributed multi-agent system with the hierarchical architecture to solve the problems of extensive data calculations in centralized control, which may easily cause communication channel blockage and delay. Considering the cost of changing the generalized demand-side resources and the user’s comfort, the pre-learning historical data storage strategy based on K-means clustering is adopted before the actual task, and the idea of transfer learning is introduced into the consensus algorithm. Finally, through experimental statistics, the number of iteration steps of the consensus algorithm is reduced and the effectiveness of the proposed algorithm is proved.

Multiagent Consensus Subject to Communication and Privacy Constraints

We consider a multi-agent consensus problem in the presence of adversarial agents. The adversaries are able to listen to the inter-agent communications and try to estimate the state of the agents. The agents have a limited bit-rate for communication and are required to quantize the transmitted signal in order to meet the bit-rate constraint of the communication channel. We propose a consensus protocol that is protected against the adversaries, i.e., the expected mean-square error of the adversary state estimate is lower bounded. In order to deal with the bit-rate constraint, we propose a dynamic quantization scheme that guarantees protected consensus.

Dynamic Quantized Consensus of General Linear Multiagent Systems Under Denial-of-Service Attacks

In this article, we study multiagent consensus problems under Denial-of-Service (DoS) attacks with data rate constraints. We first consider the leaderless consensus problem and after that we briefly present the analysis of leader–follower consensus. The dynamics of the agents take general forms modeled as homogeneous linear time-invariant systems. In our analysis, we derive lower bounds on the data rate for the multiagent systems to achieve leaderless and leader–follower consensus in the presence of DoS attacks, under which the issue of overflow of quantizer is prevented. The main contribution of the article is the characterization of the tradeoff between the tolerable DoS attack levels for leaderless and leader–follower consensus and the required data rates for the quantizers during the communication attempts among the agents. To mitigate the influence of DoS attacks, we employ dynamic quantization with zooming-in and zooming-out capabilities for avoiding quantizer saturation.

Distributed Fixed-Time Resource Allocation Algorithm for the General Linear Multi-Agent Systems

This brief focuses on the distributed resource allocation problem (RAP) for a general linear heterogeneous multi-agent system (MAS), in which each agent adopts different structure parameters. By means of multi-agent consensus approach and symbolic-function-based fixed-time control theory, an initialization-free distributed resource allocation algorithm is designed. Moreover, the equality constraint is solved based on the proportional-integral (PI) control idea and the output of all agents tracks to the optimal solution within fixed-time. Finally, we reveal the effectiveness and fast convergence performance of our proposed algorithm by a simulation example.