Distributed event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus of nonlinear multi-agent systems with observer-based protocols

This paper is concerned with distributed pinning consensus problem for a class of nonlinear multi-agent system with observer-based protocols. Two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents. According to the state information observed, a distributed pinning observer-based protocol is proposed for the leader-following consensus of the multi-agent system. Furthermore, two multi-step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively. It is shown that under the condition that the pinning joint communication topology contains a directed spanning tree, the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable, but also guarantee the consensus of the multi-agent system to be solved asymptotically. Finally, two numerical examples are provided to demonstrate the effectiveness of the observer-based protocols.     

Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Observer-based distributed adaptive iterative learning control for linear multi-agent systems

This paper investigates the consensus problem for linear multi-agent systems from the viewpoint of two-dimensional systems when the state information of each agent is not available. Observer-based fully distributed adaptive iterative learning protocol is designed in this paper. A local observer is designed for each agent and it is shown that without using any global information about the communication graph, all agents achieve consensus perfectly for all undirected connected communication graph when the number of iterations tends to infinity. The Lyapunov-like energy function is employed to facilitate the learning protocol design and property analysis. Finally, simulation example is given to illustrate the theoretical analysis.     

Cooperative observers and regulators for discrete‐time multiagent systems

This paper investigates the design of distributed observers for agents with identical linear discrete‐time state‐space dynamics networked on a directed graph interaction topology. The digraph is assumed to have fixed topology and contain a spanning tree. Cooperative observer design guaranteeing convergence of the estimates of all agents to their actual states is proposed. The notion of convergence region for distributed observers on graphs is introduced. It is shown that the proposed cooperative observer design has a robustness property. Application of cooperative observers is made to the synchronization problem. A command trajectory generator and pinning control are employed for synchronizing all the agents to a desired trajectory. Complete knowledge about the agent's state is not assumed. A duality principle is shown for observers and state feedback for distributed discrete‐time systems on graph topologies. Three different observer/controller architectures are proposed for dynamic output feedback regulator design, and they are shown to guarantee convergence of the estimate to the true state and synchronization of all the agents' states to the command state trajectory. This provides design methods for cooperative regulators based on a separation principle. It is shown that the observer convergence region and feedback control synchronizing region for discrete‐time systems are inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than the results for the continuous‐time counterparts. This is in part remedied by using weighting of different feedback coupling gains for every agent. Copyright © 2012 John Wiley & Sons, Ltd.     

Average Consensus for Multi‐Agent System with Measurement Noise and Binary‐Valued Communication

This paper considers the average consensus problems of a class of multi‐agent systems (MAS) with binary‐valued communication. Each agent can only obtain its neighbor's binary‐valued information under measurement noise because of limited bandwidth in communication channels. To seek consensus, we propose a two‐scale multi‐agent consensus algorithm with distributed strategy by combining state estimation and control design alternately. An exponential step size is chosen in the state estimation process and the estimation method can be proved to be asymptotically efficient. Additionally, by utilizing a distributed control law designed based on the estimates of the neighbors' states with a constant gain, we further prove that the proposed average consensus algorithm is convergent. Furthermore, the proposed average consensus algorithm is given and proved. Finally, some simulation results, which illustrate the effectiveness of the obtained results, are also given in the paper.     

Distributed adaptive leader-following tracking control of networked Lagrangian systems with unknown control directions under undirected/directed graphs

This paper addresses the leader-following consensus problem of networked Lagrangian systems with unknown control directions and uncertain dynamics. For undirected graphs and directed graphs, two types of distributed control protocols are proposed without assuming that the leader's position information is linearly parameterised. It is proven that all signals in the closed-loop system are bounded, and a leader-following consensus can be achieved with the proposed corresponding protocols. These protocols are distributed in the sense that the control input for each Lagrangian system is solely based on local relative position and velocity information from its neighbourhood set and does not require additional information, e.g. acceleration or observer information of its neighbours, thus avoiding the dead-loop problem and reducing the communication burden. Simulations on networked two-link revolute joint arms are given to validate the theoretical findings.     

Adaptive consensus control for stochastic nonlinear multiagent systems with full state constraints

In this paper, the consensus tracking problem is investigated for stochastic nonlinear multiagent systems with full state constraints and time delays. The barrier Lyapunov functions proposed for single‐agent constrained systems are constructively extended to solve the consensus problem for multiagent systems with the full state constraints. Some Lyapunov‐Krasovskii functionals are introduced to compensate for state time delays, which are inherent in the complicated nonlinear systems. Based on the variable separation technique, the difficulty arising from the nonstrict‐feedback structure is overcome. Under a directed communication topology, the distributed neuroadaptive control protocols are proposed to guarantee that all the follower agents follow the trajectory of the leader agent and the full state constraints are not violated. The effectiveness of the proposed distributed adaptive control approach is verified via simulation examples.     

Observer‐based leaderless and leader‐following consensus for multiagent systems: A modified integral‐type event‐triggered design

This article aims to solve leaderless and leader‐following consensus problems for general linear systems by integral‐type event‐triggered control method. Different from the existing integral‐type event‐triggered controllers for multiagent systems (MASs), a modified distributed integral‐type event‐triggered scheme is designed via defining a measurement error without continuous communication. Then, distributed event‐triggered protocols are proposed for MASs to achieve the leaderless and leader‐following consensus. Moreover, for the case that all the agents' states are not available, distributed observers are given to estimate the full states. Meanwhile, leaderless and leader‐following consensus problems are investigated based on the observer‐based event‐triggered schemes. In addition, no agent will exhibit Zeno behavior. Finally, simulations are given to verify the effectiveness of our results.     

Distributed event-triggered consensus control for multiple Lur'e nonlinear systems under directed graph

This article addresses the distributed consensus problem of multi-agent systems with Lur'e nonlinear dynamics under directed graphs based on event-triggered strategy. With the state-dependent event-triggered thresholds, a novel distributed event-triggered consensus controller is designed, under which the consensus can be achieved with zero final consensus error. The proposed strategy has several distinguishing features, including the fact that individual agent does not require continuous, or even periodic, communication with their neighbours to update the controller or monitor the triggering condition, and all the required parameters can be locally determined by the agent. Furthermore, we also prove that there is no Zeno behaviour existed. Finally, the simulation example about Chua’s circuit is given to illustrate the theoretical analysis.     

Distributed observer‐based leader‐follower attitude consensus control for multiple rigid bodies using rotation matrices

This paper addresses the distributed observer‐based leader‐follower attitude consensus control problem for multiple rigid bodies. An intrinsic distributed observer is proposed for each follower to estimate the leader's trajectory, which is only available to a subset of followers. The proposed observer can guarantee that the estimated attitude evolves on rotation matrices all the time, and it provides us with a simple way to design the attitude consensus control law. The dynamics of rigid bodies and distributed observer are both modeled directly on rotation matrices, so that the singularity and ambiguity can be avoided. Furthermore, adopting the idea of disturbance observer on vector space, a gyro bias observer on the rotation matrices is proposed. Based on the distributed observer, three types of attitude consensus control law are proposed, which are respectively on the basis of full‐state, biased angular velocity, and external disturbance combined with biased angular velocity. Finally, the SimMechanics experiments are provided to illustrate effectiveness of the proposed theoretical results.     

Finite-time distributed consensus via binary control protocols

This paper investigates the finite-time distributed consensus problem for multi-agent systems using a binary consensus protocol and the pinning control scheme. Compared with other consensus algorithms which need the complete state or output information of neighbors, the proposed algorithm only requires sign information of the relative state measurements, that is, the differences between a node’s state and that of its neighbors. This corresponds to only requiring a single-bit quantization error relative to each neighbor. This signum protocol is realistic in terms of observed behavior in animal groups, where relative motion is determined not by full time-signal measurements, but by coarse estimates of relative heading differences between neighbors. The signum protocol does not require explicit measurement of time signals from neighbors, and hence has the potential to significantly reduce the requirements for both computation and sensing. Analysis of discontinuous dynamical systems is used, including the Filippov solutions and set-valued Lie derivative. Based on the second-order information on the evolution of Lyapunov functions, the conditions that guarantee the finite-time consensus for the systems are identified. Numerical examples are given to illustrate the theoretical results.     

Time averaged consensus in a direct coupled coherent quantum observer network

This paper considers the problem of constructing a direct coupling quantum observer for a closed linear quantum system. The proposed distributed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network converges to a consensus in a time averaged sense in which each element of the observer estimates the specified output of the quantum plant. An example and simulations are included to illustrate the properties of the observer network.     

Fixed-time Consensus Tracking for Second-order Leader-follower Multi-agent Systems with Nonlinear Dynamics Under Directed Topology

In this paper, we address the fixed-time consensus tracking problem of second-order leader-follower multi-agent systems with nonlinear dynamics under directed topology. The consensus tracking algorithm consists of distributed observer and observer-based decentralized controller. The fixed-time distributed observer guarantees that each follower estimates the leader’s state under directed topology within a fixed time, where the upper bound of convergence time is independent on the initial conditions. The fixed-time decentralized controller makes each follower converge to the leader’s state in fixed time via tracking the distributed observer’s state and overcome the nonlinear dynamics without adding linear control terms. Finally, the numerical example is provided to illustrate the effectiveness of the results.

     

Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

This paper investigates the problem of distributed reliable H_∞ consensus control for high‐order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi‐agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time‐varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology‐based average dwell time approach is introduced to deal with switching jumps. By applying topology‐based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H_∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite-time weighted average consensus with respect to a monotonic function and its application

The consensus state is an important and fundamental quantity for consensus problems of multi-agent systems, which indicates where all the dynamical agents reach. In this paper, weighted average consensus with respect to a monotonic function, which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values, is studied for a group of kinematic agents with time-varying topology. By constructing a continuous nonlinear distributed protocol, such a consensus problem can be solved in finite time even though the time-varying topology involves unconnected graphs. Then the distributed protocol is employed to compute the maximum-likelihood estimation of unknown parameters over sensor networks. Compared with the existing results, the estimate scheme proposed here may reduce the costs of data communication, storage memory, book-keeping and computational overheads.     

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under a directed graph. We propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter‐event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.     

Cooperative Target-centric Formation Control without Relative Velocity Measurements under Heterogeneous Networks

This paper proposes distributed control laws for a group of unmanned aerial vehicles (UAVs) to make and maintain a circular formation around a maneuvering target. The work considers usage of heterogeneous communication networks to achieve the desired formation. Two different scenarios are considered on velocity information. In both scenarios, it is assumed that each UAV has its own position and velocity measurements available to itself. However, the team is unable to exchange velocity information among themselves. In the first scenario, each agent uses its own position and velocity information in the consensus algorithm. In the second scenario, agents need only position information for the consensus algorithm. For both the approaches, each agent calculates a virtual estimate of target’s velocity from the received information and exchanges the estimate with its neighbors. The control algorithms are developed using heterogeneous communication networks to satisfy a communication bandwidth constraint. Three different communication networks are used to circulate position information, virtual estimates, and its time derivatives. The graphs representing communication networks are undirected and connected. Further, it is considered that there is at least one UAV (agent) receiving position, velocity, and acceleration information of the target. The agent receiving target’s position need not be the same agent which receives velocity and/or acceleration information of the maneuvering target. However, the target does not receive any information from any agent. Using Barbalat’s lemma, the stability of the target-centric formation of a group of UAVs is analyzed. The performance of the proposed laws are illustrated through numerical simulations.     

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

The consensus problem is investigated in this paper for a class of multi‐agent systems with general linear node dynamics and directed communication topologies. A new distributed observer‐type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer‐type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi‐agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low‐Earth‐orbit satellite formation flying are provided to illustrate the theoretical results.