Showing papers on "Consensus published in 2017"

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

Abstract: 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.

On the Bipartite Consensus for Generic Linear Multiagent Systems With Input Saturation

Abstract: The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.

Output Consensus of Heterogeneous Linear Multi-Agent Systems by Distributed Event-Triggered/Self-Triggered Strategy

Abstract: This paper addresses the output consensus problem of heterogeneous linear multi-agent systems. We first propose a novel distributed event-triggered control scheme. It is shown that, with the proposed control scheme, the output consensus problem can be solved if two matrix equations are satisfied. Then, we further propose a novel self-triggered control scheme, with which continuous monitoring is avoided. By introducing a fixed timer into both event- and self-triggered control schemes, Zeno behavior can be ruled out for each agent. The effectiveness of the event- and self-triggered control schemes is illustrated by an example.

Leader-Following Consensus of Nonlinear Multiagent Systems With Stochastic Sampling

Abstract: This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master–slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

Fixed-Time Leader-Following Consensus for Second-Order Multiagent Systems With Input Delay

Abstract: This paper studies fixed-time leader-following lag consensus problem of second-order multiagent systems with input delay. Using fixed-time distributed observer, we obtain the leader's states for each followers. An extension of the Artstein's reducing transformation is employed to transform the delayed error system into a second-order system without time delay and a novel nonsingular terminal sliding mode protocol is proposed to achieve fixed-time consensus. The presented sliding mode controller can avoid singularity, eliminate chattering, and achieve exact convergence. It is mathematically proved that the presented protocol can achieve exact fixed-time leader-following lag consensus. Moreover, the upper bound of convergence time only depends on observer parameters, controller parameters, network parameters, and delay time, which makes it possible to determine the convergence time offline regardless of initial condition. The presented protocol is applied to coordinated lag tracking control of single-link robotic manipulators and the results validate the effectiveness of the proposed fixed-time protocol.

Distributed Robust Fixed-Time Consensus for Nonlinear and Disturbed Multiagent Systems

Abstract: In this paper, the robust fixed-time consensus problem for multiagent systems with nonlinear dynamics and uncertain disturbances under a weighted undirected topology is investigated. Some nonlinear control protocols are proposed under which fixed-time consensus in the considered multiagent systems can be ensured. Compared with the initial-condition based finite-time consensus, it is theoretically shown that any prescribed convergence time for the achievement of consensus can be guaranteed within fixed time regardless of the initial conditions. Furthermore, the achievement of consensus is shown to be robust against bounded uncertain disturbances affecting the agents. Finally, some numerical examples are provided to illustrate the performance and effectiveness of the theoretical results.

Sampled-Data Consensus of Linear Multi-agent Systems With Packet Losses

Abstract: In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

Consensus of Multiagent Systems Subject to Partially Accessible and Overlapping Markovian Network Topologies

Abstract: This paper addresses the consensus problem for a continuous-time multiagent system (MAS) with Markovian network topologies and external disturbance. Different from some existing results, global jumping modes of the Markovian network topologies are not required to be completely available for consensus protocol design. A network topology mode regulator (NTMR) is first developed to decompose unavailable global modes into several overlapping groups, where overlapping groups refer to the scenario that there exist commonly shared local modes between any two distinct groups. The NTMR schedules which group modes each agent may access at every time step. Then a new group mode-dependent distributed consensus protocol on the basis of relative measurement outputs of neighboring agents is delicately constructed. In this sense, the proposed consensus protocol relies only on group and partial modes and eliminates the need for complete knowledge of global modes. Sufficient conditions on the existence of desired distributed consensus protocols are derived to ensure consensus of the MAS with a prescribed $H_{\infty }$ performance level. Two examples are provided to show the effectiveness of the proposed consensus protocol.

Distributed Tracking of Nonlinear Multiagent Systems Under Directed Switching Topology: An Observer-Based Protocol

Abstract: This paper deals with a consensus tracking problem for multiagent systems (MASs) with Lipschitz-type nonlinear dynamics and directed switching topology. Unlike most existing works where the relative full state measurements of neighboring agents are utilized, it is assumed that only the relative output measurements of neighboring agents are available for coordination. To achieve consensus tracking in the considered MASs, a new class of observer-based protocols is proposed. By appropriately constructing some topology-dependent multiple Lyapunov functions, it is theoretically shown that distributed consensus tracking in the closed-loop MASs equipped with the designed protocols can be ensured if each possible topology contains a directed spanning tree rooted at the leader and the dwell time for the switchings among different topology is less than a derived positive quantity. Interestingly, it is found that the communication topology for observers’ states may be independent with that of the feedback signals. The derived results are further extended to the case of directed switching topology with only average dwell time constraints. Finally, the effectiveness of the analytical results is demonstrated via numerical simulations.

Distributed Active Anti-Disturbance Consensus for Leader-Follower Higher-Order Multi-Agent Systems With Mismatched Disturbances

Abstract: This technical note studies the finite-time consensus problem of leader-follower higher-order multi-agent systems with mismatched disturbances. To solve such a problem, by combining the non-singular terminal sliding-mode control (NTSMC) and disturbance observer based control (DOBC) methods together, a distributed active anti-disturbance cooperative control scheme is proposed. Firstly, to estimate the matched/mismatched disturbances of each follower, a finite-time disturbance observer is constructed. Secondly, by distributedly employing the mismatched disturbances estimates, integral-type non-singular terminal sliding-mode surfaces are designed for followers. Thirdly, distributed protocols are proposed based on the surfaces. In the presence of mismatched disturbances, these protocols achieve finite-time output consensus for the agents. Simulations validate the correctness and effectiveness of the proposed control scheme.

Fully Distributed Event-Triggered Semiglobal Consensus of Multi-agent Systems With Input Saturation

Abstract: In this paper, the event-triggered semiglobal consensus problem is investigated for general linear multi-agent systems subjected to input saturation, by utilizing the algebraic Riccati equation-based low-gain feedback technique. Two scenarios for systems with or without updating delays are considered, and fully distributed event-triggered control schemes are proposed to guarantee the semiglobal consensus of the connected systems, in which each agent is asymptotically null controllable with bounded controls. Strictly positive lower bounds for both the sampling intervals and the updating delays are captured for each agent to eliminate the Zeno behaviors in these two event-triggered processes. Finally, the effectiveness of these event-triggered control schemes are verified by simulations.

Distributed MPC-Based Secondary Voltage Control Scheme for Autonomous Droop-Controlled Microgrids

Abstract: In this study, we propose a novel distributed secondary control scheme for both voltage and frequency in autonomous microgrids. By incorporating predictive mechanisms into distributed generations, the secondary voltage control is converted to a tracker consensus problem of distributed model predictive control, with the synchronous convergence procedure for voltage magnitudes to the reference value drastically accelerated at a low communication cost. A sufficient local stability condition with the parameter analysis is established. Thus, a distributed proportional integral method combined with a finite-time observer to estimate the global reference information is presented in the frequency restoration while maintaining accurate active power sharing. Our approach accommodates model uncertainty, plug-and-play capability, and especially robustness against information update intervals, which is essential when the conventional method probably yields toward a poor performance. Meanwhile, the distributed architecture implemented on the local and neighboring information allows for a sparse communication network and eliminates the requirement for a centralized controller. Simulation results are provided to verify the effectiveness of the proposed control methodology.

Consensus control of stochastic multi-agent systems: a survey

Abstract: In this article, we provide a review of the consensus controlproblem for stochastic multi-agent systems (MASs). Recent advancesare surveyed according to the method of occurrence of the stochasticity of the MASs. First, the consensus problem is discussed for MASs, whereinindividual agents are corrupted by random noises, i.e., thedynamics of agents involve stochasticity in process and/ormeasurement equations. Both additive noises and multiplicativenoises are surveyed in detail and special attention is paid to theMASs whose dynamics are governed by Itodifferential equations.Moreover, particular effort is devoted to presenting the latestprogress on the consensus problem for a special type of stochasticMAS with Markovian jump parameters. Subsequently, the relevant research issummarized for MASs with noisy communication environments andstochastic sampling. Further, we provide a systematic review ofthe consensus problems for MASs whose communication topologyvaries randomly in the process of data propagation among agents.Finally, conclusions are drawn and several potential future researchdirections are outlined.

Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots

Abstract: The consensus problem of multiple nonholonomic mobile robots in the form of high-order chained structure is considered in this paper. Based on the model features and the finite-time control technique, a finite-time cooperative controller is explicitly constructed which guarantees that the states consensus is achieved in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader

Abstract: This paper is concerned with the distributed consensus tracking problem of uncertain multiagent systems with directed communication topology and a single high-dimensional leader. Compared with existing related works, the dynamics of each follower in the present framework are subject to unmodeled dynamics and unknown external disturbances, which is more practical in various applications. Furthermore, the dimensions of leader’s dynamics may be different with those of the followers’ dynamics. Under the mild assumption that each follower can directly or indirectly sense the output information of the leader, a distributed robust adaptive neural network controller together with a local observer are designed to each follower to ensure that the states of each follower ultimately synchronize to the leader’s output with bounded residual errors under a fixed topology. By appropriately constructing some multiple Lyapunov functions, the derived results are further extended to consensus tracking with switching directed communication topologies. The effectiveness of the analytical results is demonstrated via numerical simulations.

Event-Triggered Control of Multiagent Systems for Fixed and Time-Varying Network Topologies

Abstract: A decentralized controller that uses event-triggered communication scheduling is developed for the leader-follower consensus problem under fixed and switching communication topologies. To eliminate continuous interagent communication, state estimates of neighboring agents are designed for control feedback and are updated via communication to reset growing estimate errors. The communication times are based on an event-triggered approach and are adapted based on the trade-off between the control system performance and the desire to minimize the amount of communication. An important aspect of the developed event trigger strategy is that communication is not required to determine when a state update is needed. Since the control strategy produces switched dynamics, analysis is provided to show that Zeno behavior is avoided by developing a positive constant lower bound on the minimum inter-event interval. A Lyapunov-based convergence analysis is also provided to indicate bounded convergence of the developed control methodology.

Observer-based leader-following consensus of uncertain nonlinear multi-agent systems

Abstract: Summary In this paper, the leader-following consensus problem of uncertain high-order nonlinear multi-agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer-based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi-globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed-loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.

Observer design for tracking consensus in second-order multi-agent systems: Fractional order less than two

Abstract: This technical note studies the leader-following tracking consensus problem of a class of multi-agent systems where the dynamics of the leader is described by second-order systems. In order to track the states of the leader, observers for the followers are designed by fractional-order multi-agent systems where the relative velocity information is unavailable. It is interestingly found that the followers can track the leader with second-order dynamics even if the fractional order is less than two by only using the position information of the local neighbors, which is different from the existing results. A novel fractional-order observer is first proposed, whose order is surprisingly less than the original leader system. It is also shown that leader-following consensus can be ensured if some carefully selected followers are informed and the relative position-based protocols are appropriately designed with fractional order being between one and two. A necessary and sufficient condition for the leader-following consensus in multi-agent systems without control-input delay is proposed. The results are then extended to the case with constant control-input delay. It is found that, in both cases, the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix of the topology play an important role in achieving consensus.

Distributed Velocity-Constrained Consensus of Discrete-Time Multi-Agent Systems With Nonconvex Constraints, Switching Topologies, and Delays

Abstract: In this technical note, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information. The gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors' information. It is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval. The analysis approach is based on multiple novel model transformations, proper control parameter selections, boundedness analysis of state-dependent stochastic matrices1, exploitation of the convexity of stochastic matrices, and the joint connectivity of the communication graphs. Numerical examples are included to illustrate the theoretical results.

Observer-Based Consensus Tracking of Nonlinear Agents in Hybrid Varying Directed Topology

Abstract: The problem of leader-following consensus of nonlinear agents in hybrid varying directed topology is considering not only the agent but also that the directed edges can have a time-varying nonlinear dynamics with jump discontinuity, which contains the switching topology as its special case. This paper has the following contributions toward this problem. The leader-following consensus problem in hybrid varying directed topology is first addressed, and an online leader switching method is proposed, which reduces the dependence on some global conditions and the connectivity assumptions on the selection of leaders. Second, we generalize the Lipschitz condition and the combined condition of one-sided Lipschitz and quadratically inner-boundedness conditions to a new generalized linear incremental condition, which gives us a more generalized result in the Lyapunov proof and better performance in simulation. Third, an observer-based consensus protocol is constructed with two sufficient observability and controllability conditions and two optimal control design algorithms. Finally, an example of teleoperating multirobotic manipulator joint network is provided to illustrate the performance improvement by comparing with the existing results.

Leader-Following Consensus for Linear and Lipschitz Nonlinear Multiagent Systems With Quantized Communication

Abstract: This paper studies the leader-following consensus problem for linear and Lipschitz nonlinear multiagent systems where the communication topology has a directed spanning tree with the leader as the root. Due to the constraints of communication bandwidth and storage space, agents can only receive uniform quantized information. We first consider the leader-following consensus problem for linear multiagent systems via quantized control. Then, in order to reduce the communication load, an event-triggered control strategy is investigated to solve the consensus problem for linear multiagent systems with uniform quantization. It is shown that leader-following practical consensus can be achieved and no Zeno behavior occurs in this case. Furthermore, the proposed control strategies are extended to investigate the leader-following consensus problem for multiagent systems with Lipschitz nonlinear dynamics. Simulation results are given to demonstrate the feasibility and effectiveness of the theoretical analysis.

Robust Consensus of Linear Feedback Protocols Over Uncertain Network Graphs

Abstract: In this paper, we study the robust consensus problem for a group of linear discrete-time or continuous-time agents to coordinate over an uncertain communication network, which is to achieve consensus against transmission errors and noises. We model the network by communication links subject to deterministic uncertainties, which can be additive perturbations described by either some unknown transfer functions or norm bounded matrices. We show that the robust consensus problem can generally be solved by solving a simultaneous $H_\infty$ control problem for a set of low-dimensional subsystems. We also derive necessary conditions for the existence of a protocol achieving robust consensus. The results show that for discrete-time agents the uncertainty size must not exceed the inverse of the Mahler measure of the agents, while for continuous-time agents it must be less than the unity. Sufficient conditions in terms of linear matrix inequalities are further presented to design the robust consensus protocols.

Stabilization of Positive Switched Linear Systems and Its Application in Consensus of Multiagent Systems

Abstract: In this note, we study the stabilization problem of positive switched linear system (PSLS) with disturbance. By introducing a class of weak common linear copositive Lyapunov functions, we design time-dependent switching rules under which the system is asymptotically stable. Both continuous-time and discrete-time PSLS are taken into consideration, and the obtained results are also extended to nonpositive switched systems. Finally, the theoretical results are applied to consensus problem of multiagent systems with switching topologies and disturbance.

Event-Triggered Communication and Control of Network Systems for Multi-Agent Consensus

Abstract: This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for algorithm synthesis, the technical challenges involved in establishing desirable properties of the resulting implementations, and their applications in distributed control. We pay special attention to the assumptions on the capabilities of the network agents and the resulting features of the algorithm execution, including the interconnection topology, the evaluation of triggers, and the role of imperfect information. The issues raised in our discussion transcend the specific consensus problem and are indeed characteristic of cooperative algorithms for networked systems that solve other coordination tasks. As our discussion progresses, we make these connections clear, highlighting general challenges and tools to address them widespread in the event-triggered control of networked systems.

Adaptive Fuzzy Leader-Following Consensus Control for Stochastic Multiagent Systems with Heterogeneous Nonlinear Dynamics

Abstract: This paper focuses on the leader-following consensus control problem of multiagent systems in random vibration environment. The Ito stochastic systems with heterogeneous unknown dynamics and external disturbances are established to describe the agents in random vibration environment. The fuzzy logic systems are applied to approximate the unknown nonlinear dynamics, and one adaptive parameter is designed to decay the effect of external disturbances. We present a new distributed consensus controller for each follower agent only based on local information that is measured or received from its neighbors and itself. Under the consensus controller, we prove that all the follower agents can keep consensus with the leader, even though only a very small part of follower agents can measure or receive the state information of the leader. Furthermore, the states of all the follower agents are bounded in probability. Finally, the simulation results are provided to illustrate the effectiveness of the designed algorithm.

Network-Based Practical Consensus of Heterogeneous Nonlinear Multiagent Systems

Abstract: This paper studies network-based practical leader-following consensus problem of heterogeneous multiagent systems with Lipschitz nonlinear dynamics under both fixed and switching topologies. Considering the effect of network-induced delay, a network-based leader-following consensus protocol with heterogeneous gain matrix is proposed for each follower agent. By employing Lyapunov–Krasovskii method, a sufficient condition for designing the network-based consensus controller gain is derived such that the leader-following consensus error exponentially converges to a bounded region under a fixed topology. Correspondingly, the proposed design approach is then extended to the case of switching topology. Two numerical examples with networked Chua’s circuits are given to show the efficiency of the design method proposed in this paper.