Consensus Control For Multi-agent Systems Research Articles

Consensus control for multi-agent systems with quasi-one-sided Lipschitz nonlinear dynamics via iterative learning algorithm

This paper deals with the problem of iterative learning control algorithm for consensus of a class of multi-agent systems, and all the agents in the considered systems are governed by the nonlinear dynamics with quasi-one-sided Lipschitz condition. Based on the framework of network topologies, distributed consensus-based iterative learning control protocols are designed by using the nearest neighbor knowledge. Under the action of the iterative learning control law, consensus on the finite time interval along the iteration axis can be reached for all the directed communication graphs with spanning trees. A simulation example is finally used to illustrate the effectiveness of the proposed approach.

Adaptive H Consensus Control for Distributed Parameter Systems of Hyperbolic Type on Directed Graph

Abstract A design method of adaptive H∞ consensus control of multi-agent systems composed of a class of infinite-dimensional systems on directed network graphs, is presented in this paper. The proposed control scheme is derived as a solution of certain H∞ control problems, where the effects of neglected infinite-dimensional modes are regarded as external disturbances to the process. It is shown that the desirable consensus tracking is achieved approximately via the finite dimensional adaptive controller.

Dynamic Pinning Consensus Control of Multi-Agent Systems

In this letter, consensus pinning control for a single agent in a multi-agent system is discussed. The consensus speed by static pinning control is bounded in general. We propose dynamic pinning control using a minimum order observer and an integrator to increase the consensus speed. Furthermore, we show that the consensus speed using dynamic pinning control increases up to the absolute value of the largest real part of all canceled pole-zero pairs of the reducible transfer function. We show that dynamic pinning control achieves faster consensus than static pinning control if a network structure is a complete ${k}$ -partite graph. It is shown, however, that an overshoot occurs at a pinning agent and increases as the consensus speed increases.

Distributed event-based consensus control of multi-agent system with matching nonlinear uncertainties

Event-triggered scheme for multi-agent system is motivated by the network systems with limited communication and energy resources. In our paper, the event-triggered consensus problem of multi-agent system with heterogeneous matching uncertainties is considered. An event-based distributed adaptive controller and a novel event-triggered rule without continuous communication among agents are proposed, with which the consensus errors are uniformly bounded and all the agents could converge to an adjustable small bounded set exponentially. Meanwhile, the Zeno behavior is excluded with the designed control strategy. Finally, numerical examples are given to illustrate the effectiveness of the theoretical analysis.

Finite-horizon H∞-consensus control for multi-agent systems with random parameters: The local condition case

This paper is concerned with the distributed H∞-consensus control problem over the finite horizon for a class of discrete time-varying multi-agent systems with random parameters. First, by utilizing the proposed information matrix, a new formula is established to calculate the weighted covariance matrix of random matrix. Next, by allowing every agent to track the average of the neighbor agents, a novel local H∞-consensus performance constraint is presented to cater to the local performance analysis. Then, by means of the proposed definition of the stochastic vector dissipativity-like over the finite horizon, a set of sufficient conditions for every agent is obtained such that the controlled outputs of the closed-loop multi-agent systems satisfy the proposed H∞-consensus performance constraint. As a result, the proposed consensus control algorithm can be executed on each agent in an indeed distributed manner. Finally, a simulation example is employed to verify the effectiveness of the proposed algorithm.

Stability of Sampled-data Systems with Uncertain Time-varying Delays and Its Application to Consensus Control of Multi-agent Systems

In this paper, we propose a new stability condition for sampled-data systems with uncertain time-varying delays less than a sampling interval. The derivation is based on the robustness of the corresponding discrete-time systems subject to perturbation caused by an uncertain time-varying delay. Then, we apply the proposed stability condition to a consensus control problem of two-wheeled robots. Numerical simulations and experiments show the validity and usefulness of the derived condition.

Distributed Optimal Consensus Control for Multiagent Systems With Input Delay.

This paper addresses the problem of distributed optimal consensus control for a continuous-time heterogeneous linear multiagent system subject to time varying input delays. First, by discretization and model transformation, the continuous-time input-delayed system is converted into a discrete-time delay-free system. Two delicate performance index functions are defined for these two systems. It is shown that the performance index functions are equivalent and the optimal consensus control problem of the input-delayed system can be cast into that of the delay-free system. Second, by virtue of the Hamilton-Jacobi-Bellman (HJB) equations, an optimal control policy for each agent is designed based on the delay-free system and a novel value iteration algorithm is proposed to learn the solutions to the HJB equations online. The proposed adaptive dynamic programming algorithm is implemented on the basis of a critic-action neural network (NN) structure. Third, it is proved that local consensus errors of the two systems and weight estimation errors of the critic-action NNs are uniformly ultimately bounded while the approximated control policies converge to their target values. Finally, two simulation examples are presented to illustrate the effectiveness of the developed method.

Fixed-time event-triggered consensus control for multi-agent systems with nonlinear uncertainties

This paper investigates the fixed-time event-triggered consensus control problem for multi-agent systems with nonlinear uncertainties. The fixed-time consensus protocols are presented based on event-triggered strategies which can significantly reduce energy consumption and the frequency of the controller updates. Both the centralized and the distributed consensus control strategies are considered. It is proved that under the proposed event-triggered consensus control strategies the Zeno behavior is avoided. Compared with the finite-time consensus, the fixed-time consensus can be achieved within a fixed settling time with arbitrary initial states of the agents. Finally, two examples are presented to show the effectiveness of the fixed-time event-triggered consensus protocols.

Data-Driven Optimal Consensus Control for Discrete-Time Multi-Agent Systems With Unknown Dynamics Using Reinforcement Learning Method

This paper investigates the optimal consensus control problem for discrete-time multi-agent systems with completely unknown dynamics by utilizing a data-driven reinforcement learning method. It is known that the optimal consensus control for multi-agent systems relies on the solution of the coupled Hamilton–Jacobi–Bellman equation, which is generally impossible to be solved analytically. Even worse, most real-world systems are too complicated to obtain accurate mathematical models. To overcome these deficiencies, a data-based adaptive dynamic programming method is presented using the current and past system data rather than the accurate system models also instead of the traditional identification scheme which would cause the approximation residual errors. First, we establish a discounted performance index and formulate the optimal consensus problem via Bellman optimality principle. Then, we introduce the policy iteration algorithm which motivates this paper. To implement the proposed online action-dependent heuristic dynamic programming method, two neural networks (NNs), 1) critic NN and 2) actor NN, are employed to approximate the iterative performance index functions and control policies, respectively, in real time. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed method.

Edge event-triggered control for multi-agent systems under directed communication topologies

ABSTRACTThe edge event-triggered consensus control for multi-agent systems with single- or double-integrator dynamics under directed communication topologies is investigated in this paper. With the edge event-triggered sampling strategies, a class of novel consensus protocols is proposed to reduce control update frequency. The main features of the proposed edge event-triggered control include three aspects: (i) measurement errors are defined based on directed information flow and thus they allow that the communication topology is directed, (ii) each individual controller updates its output only when the associated edge event occurs and the control actions are independent of other agents, and (iii) the proposed edge event-triggered control does not exhibit Zeno behaviour and it is shown that the inter-event intervals are lower bounded by a positive constant. In the consensus analysis, matrix transformation techniques are used to convert the high-dimensional system into a low-dimensional system, and some sufficient consensus conditions are derived for the multi-agent systems with single- or double-integrator dynamics. Finally, the effectiveness of the edge event-triggered sampling strategies is illustrated by simulations.

Output consensus control of multi-agent systems with nonlinear non-minimum phase dynamics

ABSTRACTThis paper considers the output consensus problem in non-minimum phase nonlinear multi-agent systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, a consensus protocol consisting of two terms is proposed. The first term is a linear function of the states of each agent employed in order to overcome the non-minimum phase dynamics, and the second term is a function of the output of neighbouring agents which provides coupling among agents and guarantees output consensus in the network. The asymptotic stability of output consensus errors and the boundedness of the states of agents are also studied. A numerical example is presented to show the effectiveness of the proposed approach.

Reduced-Order Distributed Consensus Controller Design via Edge Dynamics

This paper proposes a novel approach to design reduced-order distributed consensus controllers for multi-agent systems (MASs) with identical linear dynamics of agents. A new model namely edge dynamics representing the differences on agents' states is first presented. Then the distributed consensus controller design is shown to be equivalent to the synthesis of a distributed stabilizing controller for this edge dynamics. Consequently, based on LQR approach, the globally optimal and locally optimal distributed stabilizing controller designs are proposed, of which the locally distributed stabilizing controller for the edge dynamics results in a distributed consensus controller for the MAS with no conservative bound on the coupling strength. This approach is next further developed to obtain reduced-order distributed consensus controllers for linear MASs. Several numerical examples are introduced to illustrate the theoretical results.

Inverse Optimal and Asymptotically Stable Adaptive Consensus Control of Multi-Agent Systems Based on H∞ Control Criterion

Design methods of asymptotically stable adaptive consensus control of multi-agent systems composed of the first-order and the second-order regression models are presented based on inverse optimal c...

Leader-Follower Fixed-Time Group Consensus Control of Multiagent Systems under Directed Topology

This paper investigates the fixed-time group consensus problem for a leader-follower network of integrators with directed topology. A nonlinear distributed control protocol, based on local information, is proposed such that the follower agents in each subgroup are able to track their corresponding leaders in a prescribed convergence time regardless of the initial conditions. Simulation examples are presented to demonstrate the availability of our theoretical results.

Secure consensus control for multiagent systems with attacks and communication delays

This paper addresses the consensus problem for nonlinear multi-agent systems suffering from attacks and communication delays. The network studied in this paper consists of two types of agents, namely, loyal agents and attack agents. The loyal agents update their states based on delayed state information exchanged with their neighbors. Meanwhile, the attack agents can strategically send messages with wrong values, or collude with other attack agents to disrupt the correct operation of the system. We design a novel delay robust secure consensus U+0028 DRSC U+0029 algorithm according to the neighboring nodes U+02BC delayed information. Convergence analysis of the system under the protocol designed is provided by using Lyapunov-Krasovskii stability theory and Barbalat-like argument approach. Finally, an example and simulation results are presented to demonstrate the effectiveness of the algorithm.

Output Consensus Control of Multiagent Systems With Unknown Nonlinear Dead Zone

This paper investigates the output consensus control problem of uncertain second-order nonlinear multiagent systems with unknown nonlinear dead zone, where the communication networks can be described as a directed graph with a fixed topology. The control input in each follower is assumed to be subject to unknown nonlinear dead zone. By the function approximation capability of neural networks (NNs), a distributed adaptive NN-based controller is designed for each follower in the graph such that all the outputs of the followers can asymptotically synchronize to the output of the leader with synchronization errors being semiglobally uniformly ultimately bounded. Based on Lyapunov stability theory and algebraic graph theory, analysis is conducted on stability and parameter convergence of the proposed algorithm. Finally, an example is provided to validate the theoretical results.

Observer-Based Event-Triggering Consensus Control for Multiagent Systems With Lossy Sensors and Cyber-Attacks.

In this paper, the observer-based event-triggering consensus control problem is investigated for a class of discrete-time multiagent systems with lossy sensors and cyber-attacks. A novel distributed observer is proposed to estimate the relative full states and the estimated states are then used in the feedback protocol in order to achieve the overall consensus. An event-triggered mechanism with state-independent threshold is adopted to update the control input signals so as to reduce unnecessary data communications. The success ratio of the launched attacks is taken into account to reflect the probabilistic failures of the attacks passing through the protection devices subject to limited resources and network fluctuations. The purpose of the address problem is to design an observer-based distributed controller such that the closed-loop multiagent system achieves the prescribed consensus in spite of the lossy sensors and cyber-attacks. By making use of eigenvalues and eigenvectors of the Laplacian matrix, the closed-loop system is transformed into an easy-to-analyze setting and then a sufficient condition is derived to guarantee the desired consensus. Furthermore, the controller gain is obtained in terms of the solution to certain matrix inequality which is independent of the number of agents. An algorithm is provided to optimize the consensus bound. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.

Distributed adaptive consensus control for multi-agent systems with Lipschitz nonlinear dynamics

In this paper, the observer-based consensus problem for nonlinear multi-agent systems is considered. The dynamics of each agent is given in general form of Lipschitz nonlinear system, and the communication topology among the agents is assumed to be undirected and connected. The leader-following case and leaderless case are discussed. In the former, it is assumed that the leader’s input is possibly nonzero and time-varying and only a subset of the following agents can access the state information of the leader. To track the active leader, a distributed adaptive consensus protocol, based on the relative-output information with its neighbouring agents, is proposed for each following agent. It is shown that under suitable conditions, all the following agents can track the leader under the designed adaptive controllers and observers. Following that, the leaderless case is probed. Finally, a numerical example is given to illustrate our obtained result.

Observer-based robust consensus control for multi-agent systems with noises

This study deals with the problem of consensus error calculation for linear multi-agent systems (MASs) with system noises and measurement noises. It is supposed that there exist communication noises when the information exchanges among distinct agents. The agents cannot reach consensus due to the existence of the system noises. We aim to design proper distributed control protocol to calculate the consensus error for the MASs. The states of each agent and its neighbors are estimated by applying Kalman-filtering theory. The distributed control protocol is designed by employing the estimated state information. Then the consensus error is calculated via the unique solution of a Lyapunov equation. Finally, a simulation example is presented to verify the correctness of the proposed results.

Distributed adaptive consensus control of Lipschitz nonlinear multi-agent systems using output feedback

ABSTRACTThis paper addresses output-feedback-based distributed adaptive consensus control of multi-agent systems having Lipschitz nonlinear dynamics. Distributed dynamic protocols are designed based on the relative outputs of neighbouring agents and the adaptive coupling weights, under which consensus is reached between the nonlinear systems for all undirected connected communication topologies. Extension to the case of Lipschitz nonlinear multi-agent systems subjected to external disturbances is further studied, and a robust adaptive fully distributed consensus protocol is suggested. By application of a decoupling technique, necessary and sufficient conditions for the existence of these consensus protocols are provided in terms of linear matrix inequalities. Finally, numerical simulation results are demonstrated to validate the effectiveness of the theoretical results.