基于部分稳定性方法的离散时间多智能体系统的一致性

研究有向信息拓扑下离散时间线性多智能体系统的一致性分析与设计问题.利用提出的线性变换,将一致性问题转换为相应线性系统的部分变元渐近稳定性问题.基于部分变元稳定性理论,得到有向信息拓扑下离散时间线性多智能体系统达到渐近一致的基于矩阵Schur稳定性的充要条件和状态一致函数的解析表达式.同时设计了反馈增益矩阵.最后数值实例验证了所得理论的有效性.     

Consensus of Multi-agent Systems with Feedforward Nonlinear Dynamics and Digraph

This paper considers a high-order consensus problem of multi-agent system with feedforward nonlinear and time-varying input delay in a directed network. In order to achieve the consensus, we propose a low gain distributed protocol which can get rid of impacts of feedforward nonlinearity and an arbitrarily bounded input delay on the consensus problem. Moreover, for any upper bound time-varying delay and strongly connected diagraph, the proposed controller can solve the consensus problem of multi-agent systems with feedforward nonlinearity if the designed parameter θ is great than the threshold value. Finally, several numerical simulations are presented to demonstrate the validity of the theoretical results.     

Consensus of feedforward nonlinear systems with a time-varying communication delay

The consensus problem of feedforward nonlinear systems under an undirected network with a time-varying communication delay is studied. In order to solve this problem, new consensus controller with an additional design parameter that can eliminate the effect of a feedforward nonlinearity and a time-varying communication delay on the consensus problem is proposed. Also, it is proved that if an upper bound of time-varying delay is known, the proposed consensus controller can always solve the consensus problem of multi-agent systems even in the presence of feedforward nonlinearity and an arbitrarily large communication delay. A numerical example is given to illustrate the validness of the proposed approach.     

Passivity‐based state synchronization of homogeneous multiagent systems via static protocol in the presence of input saturation

This paper studies semiglobal and global state synchronization of homogeneous multiagent systems with partial‐state coupling (ie, agents are coupled through part of their states) via a static protocol. We consider 2 classes of agents, ie, G‐passive and G‐passifiable via input feedforward, which are subjected to input saturation. The proposed static protocol is purely decentralized, ie, without an additional channel for the exchange of controller states. For semiglobal synchronization, a static protocol is designed for an a priori given set of network graphs with a directed spanning tree. In other words, the static protocol only needs rough information on the network graph, ie, a lower bound for the real part and an upper bound for the modulus, of the nonzero eigenvalues of the corresponding Laplacian matrix. Whereas for global synchronization, only strongly connected and detailed balanced network graphs are considered. In this case, for G‐passive agents, the static protocol does not need any network information, whereas for G‐passifiable agents via input feedforward, the static protocol only needs an upper bound for the modulus of the eigenvalues of the corresponding Laplacian matrix.     

Asymptotic stabilization of high‐order feedforward systems with delays in the input

This paper deals with the state feedback controller design for a class of high‐order feedforward (upper‐triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher‐order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time‐delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust ℒ︁2‐gain feedforward control of uncertain systems using dynamic IQCs

We consider the problem of robust ??₂‐gain disturbance feedforward control for uncertain systems described in the standard LFT form. We use integral quadratic constraints (IQCs) for describing the uncertainty blocks in the system. For technical reasons related to the feedforward problem, throughout the paper, we work with the duals of the constraints involved in robustness analysis using IQCs. We obtain a convex solution to the problem using a state‐space characterization of nominal stability that we have developed recently. Specifically, our solution consists of LMI conditions for the existence of a feedforward controller that guarantees a given ??₂‐gain for the closed‐loop system. We demonstrate the effectiveness of using dynamic IQCs in robust feedforward design through a numerical example. Copyright © 2008 John Wiley & Sons, Ltd.     

Design and Experimental Evaluation of a Discrete‐time ASPR‐based Adaptive Output Feedback Control System Using FRIT

This paper describes the design of an adaptive output feedback control system in discrete‐time, based on almost strictly positive real (ASPR)‐ness with a feedforward input. It is well‐known that an adaptive output feedback control system based on ASPR conditions can achieve asymptotic stability via a constant feedback gain. Unfortunately, most realistic systems are not ASPR because of the severe conditions. The introduction of a parallel feedforward compensator (PFC) is an efficient way to alleviate such restrictions. However, the problem remains that there exists a steady state error between the output of the augmented system and the output of the original system. The proposed scheme provides a strategy wherein the feedforward input is utilized such that the steady state error is removed. Furthermore, the fictitious reference iterative tuning (FRIT) approach is employed to determine the control parameters using one‐shot input/output experimental data directly, without prior information about the control system. This paper explains how the FRIT approach is applied in designing an adaptive output feedback control system. The effectiveness of the proposed scheme is confirmed experimentally, by using a motor application.     

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.     

Bounded control of feedforward nonlinear systems subject to input time‐delay

This article is concerned with the global stabilization problem of a family of feedforward nonlinear time‐delay systems whose linearized system consists of multiple distinct oscillators. To fully utilize the delayed information and maintain the state decoupling property in the controller design, the considered nonlinear feedforward system is first transformed into a new system which contains time delays in both its input and states based on a novel model transformation containing time delays, and then the stabilizing saturated controller for the transformed system is designed based on the recursive design method. Meanwhile, explicit stability conditions are also provided. When the linearized system is a cascade of multiple oscillators and multiple integrators, a modified saturated feedback control utilizing not only the current state but also the delayed state is also established for the corresponding global stabilization problem. Two examples, including a practical one, are given to show the effectiveness and superiority of the proposed approaches.     

Average consensus of continuous‐time multi‐agent systems with quantized communication

This paper focuses on the average consensus problem of first‐order and second‐order continuous‐time multi‐agent systems with logarithmic quantized information transmission. The balanced and strongly connected digraphs are utilized to characterize the interaction topologies between agents. Based on the state estimation, distributed state updating mechanisms are introduced for every agent such that all agents’ states achieve average consensus asymptotically. By means of differential inclusion theory, we discuss the existence and convergence property of the Krasovskii solutions to the closed‐loop system models. By designing the proper control gain parameters and quantizer accuracy, two sufficient conditions are established to guarantee the achievement of average consensus. Finally, two numerical simulations are provided to illustrate the effectiveness of theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Consensus of multiple double‐integrator agents with intermittent measurement

This paper is concerned with consensus problems in directed networks of multiple agents with double‐integrator dynamics. It is assumed that each agent adjusts its state based on the information of its states relative to its neighbors at discrete times and the interaction topology among agents is time‐varying. Both synchronous and asynchronous cases are considered. The synchrony means that each agent's update times, at which it obtains new control signals, are the same as the others', and the asynchrony implies that each agent's update times are independent of the others'. In the synchronous case, the consensus problem is proved to be equivalent to the asymptotic stability problem of a discrete‐time switched system. By analyzing the asymptotic stability of the discrete‐time switched system, it is shown that consensus can be reached if the update time intervals are small sufficiently, and an allowable upper bound of update time intervals is obtained. In the asynchronous case, the consensus problem is transformed into the global asymptotic stability problem of a continuous‐time switched system with time‐varying delays. In virtue of a linear matrix inequality method, it is proved that consensus can be reached if the delays are small enough, and an admissible upper bound of delays is derived. Simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Squared‐down passivity–based state synchronization of homogeneous continuous‐time multiagent systems via static protocol in the presence of time‐varying topology

This paper studies state synchronization of homogeneous multiagent systems (MAS) via a static protocol with partial‐state coupling in the presence of a time‐varying communication topology, which includes general time‐varying graphs as well as switching graphs. If the agents are squared‐down passive or squared‐down passifiable (via static output feedback or static input feedforward), then a static protocol can be designed for balanced, time‐varying graphs. Moreover, this static protocol works for arbitrary switching directed graphs if the agents are squared‐down minimum phase with relative degree one. The static protocol is designed for each agent such that state synchronization is achieved without requiring exact knowledge about the time‐varying network.     

Second‐order consensus for directed multi‐agent systems with sampled data

This paper deals with the consensus problem of second‐order multi‐agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi‐agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time‐varying piecewise‐continuous delay and proposing a novel time‐dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.     

关于二元延迟3步前馈逆有限自动机的结构

前馈逆有限自动机的结构是有限自动机可逆性理论中的基本问题.对延迟步数≥3的前馈逆结构的刻划,则是一个长期的未解决问题.研究了二元延迟3步前馈逆有限自动机的结构.对于自治有限自动机M_a的状态图为圈的二元延迟3步弱可逆半输入存储有限自动机C(M_af ),给出了其长3极小输出权分别为1,2,8三种情形下结构的一种刻画.由于C(M_af )延迟3步弱可逆当且仅当它是延迟3步弱逆,因此,得到了二元延迟3步前馈逆有限自动机结构的一种部分刻画.     

Leader‐following consensus for nonlinear agents with measurement feedback

The leader‐following consensus problem is investigated for large classes of nonlinear identical agents. Sufficient conditions are provided for achieving consensus via state and measurement feedback laws based on a local (ie, among neighbors) information exchange. The leader's trajectories are assumed bounded without knowledge of the containing compact set and the agents' trajectories possibly unbounded under the action of a bounded input. Generalizations to heterogeneous agents and robustness are also discussed.     

Further results on finite‐time consensus of second‐order multi‐agent systems without velocity measurements

This paper investigates the problem of finite‐time consensus (FTC) for second‐order nonlinear multi‐agent systems when the velocity information is unavailable. Based on the global finite‐time stability theory and homogeneity with dilation, a class of novel finite‐time consensus protocols are proposed for the multi‐agent systems. The protocol design is divided into two parts. First, when all the state information of the agents are measurable, a new continuous state feedback is designed to achieve FTC. Then, when the velocity information is unmeasurable, two finite‐time convergent discontinuous observers are presented to estimate the velocities of the followers and the leader, respectively, which further ensure the final FTC for the multi‐agent systems. Finally, one example is given to demonstrate the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed consensus of discrete‐time multi‐agent systems with multiplicative noises

In this paper, we consider the consensus problem of discrete‐time multi‐agent systems with multiplicative communication noises. Each agent can only receive information corrupted by noises from its neighbors and/or a reference node. The intensities of these noises are dependent on the relative states of agents. Under some mild assumptions of the noises and the structure of network, consensus is analyzed under a fixed topology, dynamically switching topologies and randomly switching topologies, respectively. By combining algebraic graph theory and martingale convergence theorem, sufficient conditions for mean square and almost sure consensus are given. Further, when the consensus is achieved without a reference, it is shown that the consensus point is a random variable with its expectation being the average of the initial states of the agents and its variance being bounded. If the multi‐agent system has access to the state of the reference, the state of each agent can asymptotically converge to the reference. Numerical examples are given to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.     

Output feedback regulation of a class of high‐order feedforward nonlinear systems with unknown time‐varying delay in the input under measurement sensitivity

An output feedback regulation problem is considered for a class of high‐order feedforward nonlinear systems with delay in the input under measurement sensitivity. The key features are that the considered systems have uncertain high‐order feedforward nonlinearity and unknown time‐varying delay in the input. Then, the controller is supposed to be engaged where the output feedback information is distorted by measurement sensitivity. Our proposed controller has two gains—fixed and adaptive gains. The fixed gain is first designed to compensate for measurement sensitivity, and the adaptive gain is next utilized to dominate both unknown input delay and uncertain high‐order feedforward nonlinearity. Simulation examples are given to highlight the advantage of our control scheme.     

Optimal disturbance rejection control for singularly perturbed composite systems with time‐delay

The optimal control problem for a class of singularly perturbed time‐delay composite systems affected by external disturbances is investigated. The system is decomposed into a fast linear subsystem and a slow time‐delay subsystem with disturbances. For the slow subsystem, the feedforward compensation technique is proposed to reject the disturbances, and the successive approximation approach (SAA) is applied to decompose it into decoupled subsystems and solve the two‐point boundary value (TPBV) problem. By combining with the optimal control law of the fast subsystem, the feedforward and feedback composite control (FFCC) law of the original composite system is obtained. The FFCC law consists of analytic state feedback and feedforward terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. Simulation results are employed to test the validity of the proposed design algorithm. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A robust model predictive control algorithm for incrementally conic uncertain/nonlinear systems

This paper presents a robustly stabilizing model predictive control algorithm for systems with incrementally conic uncertain/nonlinear terms and bounded disturbances. The resulting control input consists of feedforward and feedback components. The feedforward control generates a nominal trajectory from online solution of a finite‐horizon constrained optimal control problem for a nominal system model. The feedback control policy is designed off‐line by utilizing a model of the uncertainty/nonlinearity and establishes invariant ‘state tubes’ around the nominal system trajectories. The entire controller is shown to be robustly stabilizing with a region of attraction composed of the initial states for which the finite‐horizon constrained optimal control problem is feasible for the nominal system. Synthesis of the feedback control policy involves solution of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the control design and the resulting closed‐loop system performance. Copyright © 2010 John Wiley & Sons, Ltd.