离散多智能体切换系统的二阶分组一致性研究

针对随机切换拓扑下离散多智能体系统的二阶分组一致性问题进行了研究。 设计了一种新颖的分组一致性协议,该协议不依赖于保守的假设条件,能全面反映系统中智能体在分组内与分组间的相互影响。引入马尔科夫链来模拟系统的随机拓扑变化, 基于矩阵理论和图论得到了在马尔科夫切换拓扑条件下,应用新协议使系统达到分组一致的充分条件。 在证明过程的结尾部分,使用线性不等式 (LMI) 工具给出了获取协议中控制参数的算法。最后,通过数字仿真实例证明了理论结果的有效性。     

H ∞ consensus control of multi-agent systems with switching topology: a dynamic output feedback protocol

This article is devoted to the consensus control for switching networks of multiple agents with linear coupling dynamics and subject to external disturbances, which is transformed into an H _∞ control problem by defining an appropriate controlled output. On this basis, a distributed dynamic output feedback protocol is proposed with an undetermined system matrix, and a condition in terms of linear matrix inequalities (LMIs) is derived to ensure consensus of the multi-agent system with a prescribed H _∞ level. Furthermore, system matrix of the protocol is designed by solving two LMIs. A numerical example is included to illustrate the effectiveness of the proposed consensus protocol.     

Fixed‐time sliding mode cooperative control for multiagent networks via event‐triggered strategy

In this article, the problem of event‐triggered‐based fixed‐time sliding mode cooperative control is addressed for a class of leader‐follower multiagent networks with bounded perturbation. First, a terminal integral sliding mode manifold with fast convergent speed is designed. Then, a distributed consensus tracking control strategy based on event‐triggered and sliding mode control is developed that guarantees the multiagent networks achieve consensus within a fixed time which is independent of initial states of agents in comparison with the finite‐time convergence. Furthermore, the update frequency of control law can be considerably reduced and Zeno behavior can be removed by utilizing the proposed event‐triggered control algorithm. Simulation examples are used to show the effectiveness of the new control protocol.     

Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach

This paper is devoted to the output consensus problem of directed networks of multiple high‐order agents with external disturbances, and proposes a distributed protocol using the neighbors' measured outputs. By defining an appropriate controlled output and conducting a model transformation in two steps, consensus performance analysis of the multi‐agent system under the proposed protocol is transformed into a normal H_∞ problem. Then using H_∞ theory of linear systems, conditions are derived to ensure the consensus performance with a prescribed H_∞ index for networks with fixed and switching topologies, respectively. A numerical example of the formation control application is included to validate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive consensus protocol for networks of multiple agents with nonlinear dynamics using neural networks

In this paper, an adaptive protocol is proposed to solve the consensus problem of multi‐agent systems with high‐order nonlinear dynamics by using neural networks (NNs) to approximate the unknown nonlinear system functions. It is derived that all agents achieve consensus if the undirected interaction graph is connected, and the transient performance of the multi‐agent system is also investigated. It shows that the adaptive protocol and the consensus analysis can be easily extended to switching networks by the existing LaSalle's Invariance Principle of switched systems. A numerical simulation illustrates the effectiveness of the proposed consensus protocol. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Non-linear protocols for optimal distributed consensus in networks of dynamic agents

We consider stationary consensus protocols for networks of dynamic agents with fixed topologies. At each time instant, each agent knows only its and its neighbors’ state, but must reach consensus on a group decision value that is function of all the agents’ initial state. We show that the agents can reach consensus if the value of such a function is time-invariant when computed over the agents’ state trajectories. We use this basic result to introduce a non-linear protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents’ initial states. As a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value. We use a Lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time-invariant undirected network. Finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles.     

Distributed adaptive consensus protocol with decaying gains

This article brings a distributed adaptive protocol for consensus and synchronization in multiagent systems on directed communication networks. Agents are modeled as general linear time‐invariant systems. The proposed protocol introduces a novel adaptation scheme allowing control coupling gains to decay to their reference values. This approach improves upon existing adaptive consensus protocols which may result in overly large or even unbounded coupling gains. The protocol design in this article does not rely on any centralized information; hence it is distributed. Nevertheless, the price to pay for this is the need to estimate those reference values. Convergence of the overall network dynamics is guaranteed for correctly estimated references; otherwise, the trajectory of the system is only uniformly ultimately bounded. Two estimation algorithms are proposed: one based on the interval‐halving method and the other based on a distributed estimation of Laplacian eigenvalues. Numerical simulations validate the proposed approach.     

Distributed Average Consensus in Multi-agent Networks with Limited Bandwidth and Time-delays

This paper studies the distributed average consensus problem of multi-agent digital networks with time-delays. For the network, each agent can only exchange symbolic data with its neighbours. We provide a distributed average consensus protocol which uses the quantized and time-delay information. We consider two types of dynamic encoders/decoders in our protocol. One uses inverse proportion function as scaling function, while the other uses exponential function as scaling function. All agents can reach average consensus asymptotically with our protocol. Furthermore, we show that the average consensus protocol is robust to finite symmetric time-delays, but is sensitive to asymmetric time-delays that will destroy the average consensus of the networks. Finally, simulations are presented to illustrate validity of our theoretical results.      

Consensus of multi-agent systems based on sampled-data control

This article studies the consensus problem in directed networks, assuming that each agent is with double-integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants. We propose a protocol based on sampled-data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol. In virtue of this equivalent characterisation, we further consider two cases: fixed topology and switching topology. For the first case, we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem. For the second case, we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals, respectively. Finally, simulations are provided to illustrate the effectiveness of the theoretical results.     

基于nRF2401软件跳频协议的设计与实现

为解决射频收发器NRF2401在ISM频段内同频干扰,提高无线通信系统的通信质量和可靠性,提出了一种软件自适应跳频扩频协议。该协议充分利用nRF2401射频芯片多频点特性,使用软件程序设计将125个间隔为1 MHz的频道分成低、中、高三个频段,在无线信道受阻或同频干扰时,依据"低频-中频-高频"的循环顺序进行频道跳变。实验结果表明,工程机械仪表无线显示系统采用这种软件扩频协议设计,可以有效避免同频干扰和多点传输干扰,提高系统传输可靠性。     

Event- and self-triggered consensus for double-integrator networks with relative state measurements

ABSTRACT

This paper addresses the consensus problem of double-integrator networks via event- and self-triggered control approaches. In the proposed control protocol, only relative state information is utilised to synchronise all agents. First, an event-triggering algorithm with periodic event detection is designed to determine the event times of each agent. Then, a self-triggered control algorithm is provided to further reduce resource consumption. Two numerical simulations are conducted to illustrate the effectiveness of the results.     

Robust L 2 − L ∞ consensus control for uncertain high-order multi-agent systems with time-delay

This article studies that the robust consensus problem for high-order multi-agent systems with time-delay, which are subjected to external disturbances and communication uncertainties. An approach based on the weighting matrix is introduced to meet the requirement that the peak value of controlled output is often required into a certain range. Then, a dynamic model of high-order multi-agent systems is established. Using a feedback controller and interactions from the neighbours including uncertainties, a linear control protocol is proposed for the systems with networks under fixed or switching topologies. Sufficient conditions in terms of linear matrix inequalities are derived to make all the agents reach robust consensus with the prescribed L ₂???L _∞ performance. A numerical simulation is provided to demonstrate the effectiveness of the proposed protocol.     

Consensus Of Identical Linear Systems with Communication Delays by Using the Information of Second‐Order Neighbors

This paper studies the consensus protocol using the information of second‐order neighbors in undirected and connected networks of linear systems with communication delays. The feedback matrix which guarantees consensus under both the proposed and the traditional protocol is given; it is shown that with this matrix, the networks under the proposed protocol converge faster than the traditional protocol. Based on this result, the delay sensitivity of the proposed protocol is considered under an assumption about the communication topology. The maximum allowable upper bound of the delays is obtained by solving certain linear matrix inequalities. Two simulation examples are presented to illustrate the effectiveness of the theoretical results.     

Necessary and sufficient conditions for solving consensus problems of double‐integrator dynamics via sampled control

In this paper, consensus problems of double‐integrator dynamics via sampled control are investigated. The sampled control protocol is induced from continuous‐time linear consensus protocol by using periodic sampling technology and zero‐order hold circuit. With the obtained sampled control protocol, the continuous‐time multi‐agent system is equivalently transformed into a linear discrete‐time system. Necessary and sufficient conditions are given to guarantee that all the agents asymptotically travel with zero relative positions and common velocities. Furthermore, consensus problem with continuous‐time consensus protocol is re‐analyzed. A necessary and sufficient condition is also obtained which is consistent with the special case when the sampling period tends to zero. The effectiveness of these algorithms is demonstrated through simulations. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H ∞ consensus control concerning second-order multi-agent systems with time-varying delays on dynamic topologies

Robust H _∞ consensus control for second-order multi-agent systems is addressed. Considering the delayed directed networks with disturbances and uncertainty parameters on dynamic topologies, the consensus protocols are proposed and analysed. By constructing the common Lyapunov–Krasovkii functional, applying the Lyapunov–Krasovkii theory and integral inequality approach, the sufficient condition of consensus protocol convergence is derived, guaranteeing robust H _∞ consensus for given second-order multi-agent systems. Finally, numerical examples are provided to demonstrate the effectiveness of the main results.     

Adaptive tuning to frequency response specifications

The paper describes a procedure to design adpative controllers when the specifications are given in terms of a number of points of a desired closed-loop frequency response. The key idea is the use of a bank of ‘band-compensators’, each one of which is intended to act on its corresponding frequency band. The compensator parameters are updated based on a finite impulse response on-line interpolation of the plant frequency response. The latter is carried out using a bank of filters and independent processing of the complex valued gain of each band. This frequency-domain approach obviates the need of parametric representations for both, plant and reference model, and inherits the robustness properties of frequency response designs.     

Consensus problems in networks of agents with switching topology and time-delays

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.     

Scalable robust stability for nonsymmetric heterogeneous networks

Scalable decentralized stability certificates in networks i.e. decentralized stability guarantees for an arbitrary interconnection of heterogeneous dynamical systems, are often based on certain symmetry assumptions in the way the systems are interconnected. Such structure simplifies the mathematical analysis significantly, nevertheless a potential pitfall needs to be addressed: the stability proof might offer no robustness guarantees to deviations from protocol symmetry. This is, for example, the case for Internet congestion control stability results for arbitrary networks i.e. the stability proofs break down with an arbitrarily small deviation from protocol symmetry. We propose in the paper conditions that can guarantee scalable robust stability in a nonsymmetric interconnection setting for a class of networks that includes Internet congestion control models and consensus protocols. The certificates derived are decentralized and scale with the degree of nonsymmetry.     

H∞ Consensus of Directed Lur'e Networks with Incremental Nonlinearities

This paper considers robust consensus problem for Lur'e networks with incrementally nonlinearity and unknown disturbance, under a given directed communication topology. Both incrementally sector bounded nonlinearities and incrementally passive nonlinearities are investigated. A distributed protocol is proposed to achieve global consensus. In the design of consensus protocol, H_∞ technique is used to attenuate the effect of disturbance. Moreover, the design conditions for robust H_∞ consensus are formulated into linear matrix inequalities. Finally, numerical simulations are used to demonstrate the effectiveness and superiority of the proposed method.     

Adaptive finite-time consensus in multi-agent networks

This paper is concerned with the finite-time consensus problem of distributed agents having non-identical unknown nonlinear dynamics, to a leader agent that also has unknown nonlinear control input signal. By parameterization of unknown nonlinear dynamics, a Lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite-time consensus control protocol in undirected networks. Homogeneous Lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous. Theoretical analysis shows that leader-following consensus can be achieved in finite-time, meanwhile, finite-time parameter convergence can be also guaranteed under the proposed control scheme. An example is given to validate the theoretical results.