09 Jan 09:27
by Lin Wang, Xiaofan Wang, Xiaoming Hu
Summary
In this paper, we develop a set of decentralized control laws with bounded potential functions. The basic control law is a combination of attractive, repulsive, and alignment forces, which can keep connectivity, avoid collision, synchronize all agents, and further track a constant moving leader. Furthermore, we investigate the distributed tracking problem with a varying-velocity leader, where the acceleration of the leader can not be measured. Two cases are considered; the acceleration of the leader is bounded, and the acceleration function satisfies Lipschitz condition. In the first case, the relative velocities of neighbors are integrated and transmitted as a new variable to account for the uncertain time-varying acceleration. In the second case, two distributed estimators are added for the leader's position and velocity. Finally, some simulations are presented to show the effectiveness of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd.
09 Jan 08:28
Maintaining the connectivity of an underlying robot network during a rendezvous task in the presence of obstacles is a challenge in control systems technology. In this brief, a navigation-function-based potential field approach is developed to address this challenging problem. A concept called connectivity constraint is used to establish a navigation function. A new potential field that simultaneously integrates rendezvous requirement, connectivity maintenance, and obstacle avoidance is also developed. On the basis of this potential field, we design a bounded control input for multirobot control. The proposed controller can drive multiple robots to an agreement state while maintaining connectivity of the underlying network provided that the initial configurations of the robots are connected. Simulations and experiments are performed to verify the effectiveness of the proposed approach.
09 Jan 08:27
In this paper, performance analysis of generalized extended state observer (ESO) in handling fast-varying sinusoidal disturbances is presented. It is shown that the higher order ESO offers improvement in the tracking of fast-varying sinusoidal disturbances, if the ESO bandwidth is chosen significantly larger than the frequency of the disturbance and ensuring that it is sufficiently smaller than unmodeled high frequency dynamics. The frequency and time-domain analysis results are presented, and the findings are verified through numerical simulations and experimentation on Quanser's motion control module.
09 Jan 08:20
by Shengyuan Xu, James Lam, Baoyong Zhang, Yun Zou
Summary
This paper presents a new insight into the delay-dependent stability for time-delay systems. Because of the key observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices in the Lyapunov–Krasovskii functional to be positive definite, an improved delay-dependent asymptotic stability condition is presented in terms of a set of LMIs. This fact has been overlooked in the development of previous stability results. The importance of the present method is that a vast number of existing delay-dependent results on analysis and synthesis of time-delay systems derived by the Lyapunov–Krasovskii stability theorem can be improved by using this observation without introducing additional variables. The reduction of conservatism of the proposed result is both theoretically and numerically demonstrated. It is believed that the proposed method provides a new direction to improve delay-dependent results on time-delay systems. Copyright © 2013 John Wiley & Sons, Ltd.
09 Jan 08:19
by Qian Ma, Frank L. Lewis, Shengyuan Xu
Summary
This paper investigates the cooperative containment control problem for discrete-time multi-agent systems with general linear dynamics. Distributed containment control protocols on the basis of state feedback design and output feedback design are proposed. Necessary and sufficient conditions are presented for both the state feedback and output feedback cases, which are less conservative than those in the literature. These conditions depend on the spectral properties of the topology matrix. Then, effective algorithms are proposed to obtain control gain matrices for both cases based on H ∞ type Riccati design. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.
09 Jan 08:07
Publication date: January 2014
Source:Systems & Control Letters, Volume 63
Author(s): Antonio Barreiro , Alfonso Baños , Sebastián Dormido , José A. González-Prieto
Reset controllers provide a simple way to improve performance when controlling strongly traded-off plants. A reset controller operates most of the time as a linear system, but when some condition holds, it performs a zero resetting action on its state. Recently, some generalizations have been proposed, for example, the anticipation of the reset condition with the so-called reset band. There is a lack of analysis tools for reset systems with reset band. In this paper we address this problem by means of Poincaré maps (PM). It is shown how PM can predict the existence and stability of limit cycles, and give also information on pathologies such as Zenoness, and provide parameter ranges where the system is guarded against those behaviors and thus global asymptotical stability (GAS) is guaranteed.
09 Jan 08:06
Publication date: February 2014
Source:Systems & Control Letters, Volume 64
Author(s): Daniel E. Miller , Edward J. Davison
In the decentralized control of linear time-invariant (LTI) systems, a decentralized fixed mode (DFM) is a system mode which is immoveable using an LTI controller, while a quotient DFM (QDFM) is one which is immoveable using any form of nonlinear time-varying compensation. If a system has no unstable DFMs, there are well-known procedures for designing an LTI stabilizing controller; for systems which have unstable DFMs but no unstable QDFMs, we provide a simple design algorithm which yields a linear periodic sampled-data stabilizing controller.
09 Jan 07:55
Publication date: February 2014
Source:Automatica, Volume 50, Issue 2
Author(s): Yingbo Zhao , Paolo Minero , Vijay Gupta
This paper studies the problem of disturbance propagation in a string of vehicles aiming to proceed along a given trajectory while keeping a constant distance between each vehicle and its successor. It is assumed that each vehicle can control its position based on the spacing error with respect to the preceding vehicle in the string, as well as on coded information transmitted by the lead vehicle. Using information-theoretic techniques, this paper establishes a lower bound to the integral of the sensitivity function of spacing errors with respect to a stochastic disturbance acting on the lead vehicle. The derived bound depends on the open-loop poles and zeros of the vehicles’ dynamics as well as on the (possibly nonlinear) controller used at each vehicle. The lower bound is shown to be tight for a specific class of systems and controllers.
09 Jan 07:51
Publication date: March 2014
Source:Automatica, Volume 50, Issue 3
Author(s): Attilio Priolo , Andrea Gasparri , Eduardo Montijano , Carlos Sagues
In this work we propose a distributed algorithm to solve the discrete-time average consensus problem on strongly connected weighted digraphs (SCWDs). The key idea is to couple the computation of the average with the estimation of the left eigenvector associated with the zero eigenvalue of the Laplacian matrix according to the protocol described in Qu et al. (2012). The major contribution is the removal of the requirement of the knowledge of the out-neighborhood of an agent, thus paving the way for a simple implementation based on a pure broadcast-based communication scheme.
19 Dec 08:12
Publication date: October 2013
Source:Systems & Control Letters, Volume 62, Issue 10
Author(s): Hui Yu , Yanjun Shen , Xiaohua Xia
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.
19 Dec 08:11
Publication date: October 2013
Source:Systems & Control Letters, Volume 62, Issue 10
Author(s): D.L. Gaudette , D.E. Miller
Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of stabilizing (in a bounded-input–bounded-output sense) a first order linear time invariant plant with an arbitrarily large time varying delay and an arbitrarily large uncertain gain; we propose the use of a mildly non-linear, periodic controller, which is simple to implement. We will derive a clear, simple formula relating the maximum delay duration, the location of the unstable plant pole and the bounds on the derivative of the delay for which our controller stabilizes the system.
19 Dec 08:06
Publication date: November 2013
Source:Systems & Control Letters, Volume 62, Issue 11
Author(s): Amir Ajorlou , Amir G. Aghdam
This paper presents a bounded connectivity preserving control strategy for the aggregation of multi-agent systems. The problem is investigated for two cases of single-integrator agents and unicycles. Under the proposed control strategy, if two agents are in the connectivity range at some point in time, they will stay connected thereafter. The agents finally aggregate while avoiding collision in such a way that the average of the distances between every pair of neighboring agents is bounded by a pre-specified positive real number, which can be chosen arbitrarily small. The results are developed based on some important characteristics of the positive limit set of the closed-loop system under the proposed control strategy and a fundamental property of convex real functions. The theoretical results are verified by simulation.
19 Dec 08:04
Publication date: December 2013
Source:Systems & Control Letters, Volume 62, Issue 12
Author(s): Hong-xiang Hu , Andong Liu , Qi Xuan , Li Yu , Guangming Xie
This paper investigates the consensus problem of second-order multi-agent systems with switching topologies by designing a time-delayed impulsive consensus control scheme. All the agents are governed by the same nonlinear intrinsic dynamics. In this study, agents can cooperate or compete with each other, i.e., the elements in the weight matrix of the coupling graph can be either positive or negative. By establishing a comparison system, a new comparison principle method is successfully applied to study such consensus problem. Then, several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree. Meanwhile, the exponential consensus rate is also obtained. Finally, simulation results are presented to validate the effectiveness of the theoretical analysis.
19 Dec 08:03
Publication date: December 2013
Source:Systems & Control Letters, Volume 62, Issue 12
Author(s): Guanghui Wen , Guoqiang Hu , Wenwu Yu , Jinde Cao , Guanrong Chen
This paper studies the distributed consensus tracking problem of linear higher-order multi-agent systems with switching directed topologies and occasionally missing control inputs. In this framework, the underlying topology of dynamic agents may switch among several directed graphs, each having a directed spanning tree rooted at the leader. Furthermore, the control inputs to the followers may be temporally missed due to actuator failures and network-induced packet loss. To guarantee asymptotic consensus tracking in such a multi-agent system, several distributed controllers are constructed based only on the relative state information of neighboring agents. By appropriately constructing a switching Lyapunov function and using tools from the M-matrix theory, some sufficient conditions for achieving distributed consensus tracking are provided. Finally, some numerical simulations are given to illustrate the theoretical analysis.
19 Dec 08:03
Publication date: February 2014
Source:Systems & Control Letters, Volume 64
Author(s): Yuan Liu , Haibo Min , Shicheng Wang , Zhiguo Liu , Shouyi Liao
This paper studies the adaptive consensus problem of networked mechanical systems with time-varying delay and jointly-connected topologies. Two different consensus protocols are proposed. First, we present an adaptive consensus protocol for the connected switching topologies. Based on graph theory, Lyapunov stability theory and switching control theory, the stability of the proposed algorithm is demonstrated. Then we investigate the problem under the more general jointly-connected topologies, and with concurrent time-varying communication delay. The proposed consensus protocol consists of two parts: one is for the connected agents which contains the current states disagreement among them and the other is designed for the isolated agents which contains the states difference between the current and past. A distinctive feature of this work is to address the consensus control problem of mechanical systems with unknown parameters, time-varying delay and switching topologies in a unified theoretical framework. Numerical simulation is provided to demonstrate the effectiveness of the obtained results.
19 Dec 07:53
Publication date: October 2013
Source:Automatica, Volume 49, Issue 10
Author(s): Håvard Fjær Grip , Ali Saberi , Anton A. Stoorvogel
When dealing with heterogeneous networks, where the agents are governed by non-identical models, interesting questions arise regarding the ability of the network to synchronize to a common non-trivial output trajectory, as well as the nature of such a trajectory. On this topic, Wieland, Allgöwer, and Sepulchre have recently derived results showing that for a class of heterogeneous networks of dynamically controlled linear agents, non-trivial output synchronization implies the existence of an observable virtual exosystem for which the regulator equations are solvable for each agent. Moreover, this virtual exosystem defines the output trajectories on the agreement manifold and is contained within each agent as an internal model. In this paper, we shed further light on this topic by showing that, under a more general set of assumptions, non-trivial output synchronization can occur in the absence of such a virtual exosystem. We propose a modified result for this case that specifies the existence of a possibly unobservable virtual exosystem for which the regulator equations are solvable, and for which the observable part defines the output trajectories on the agreement manifold. We also show that a variation of the virtual exosystem is contained within each agent as an internal model.
19 Dec 07:52
Publication date: October 2013
Source:Automatica, Volume 49, Issue 10
Author(s): Keyou You , Zhongkui Li , Lihua Xie
This paper studies both continuous and discrete time consensus problems for multi-agent systems with linear time-invariant agent dynamics over randomly switching topologies. The switching is governed by a time-homogeneous Markov process, whose state corresponds to a possible interaction topology among agents. Necessary and sufficient conditions are derived for achieving consensus under a common control protocol, respectively. It is shown that the effect of switching topologies on consensus is determined by the union of topologies associated with the positive recurrent states of the Markov process. Moreover, the effect of random link failures on discrete time consensus is investigated. The implications and relationships with the existing results are discussed. Finally, the theoretical results are validated via simulations.
19 Dec 07:50
Publication date: November 2013
Source:Automatica, Volume 49, Issue 11
Author(s): Andrey Polyakov , Denis Efimov , Wilfrid Perruquetti , Jean-Pierre Richard
The output stabilization problem for a linear system with an unknown bounded time-varying input delay is considered. The interval observation technique is applied in order to obtain guaranteed interval estimate of the system state. The procedure of the interval observer synthesis uses lower and upper estimates of the unknown delay and requires to solve a special Silvester’s equation. The interval predictor is introduced in order to design a linear stabilizing feedback. The control design procedure is based on Linear Matrix Inequalities (LMI). The theoretical results are supported by numerical simulations and compared with a control design scheme based on a Luenberger-like observer.
19 Dec 07:45
Publication date: November 2013
Source:Automatica, Volume 49, Issue 11
Author(s): Paresh Deshpande , Prathyush P. Menon , Christopher Edwards
This paper considers a network of vehicles moving in a two dimensional plane. The overall network, described by a collection of double integrator dynamics, is controlled by a novel distributed static output feedback methodology to maintain a desired formation. The distributed control architecture stabilizes the network using static output feedback of position information only, by exploiting delays in communication of the relative information. An optimization algorithm, based on Linear Matrix Inequalities together with the DIRECT search algorithm, is used to synthesize the controller gains and the delay.
19 Dec 07:33
Publication date: November 2013
Source:Automatica, Volume 49, Issue 11
Author(s): Frédéric Mazenc , Thach Ngoc Dinh , Silviu-Iulian Niculescu
For a family of nonlinear discrete-time systems with input, output and uncertain terms, a new interval observer is designed. Its main feature is that it is composed of two copies of classical observers. This interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback. An illustrative example completes the presentation.
19 Dec 07:25
Publication date: January 2014
Source:Automatica, Volume 50, Issue 1
Author(s): Andrés A. Peters , Richard H. Middleton , Oliver Mason
For vehicle platoons, the leader following control architecture is known to be capable of achieving string stability while maintaining tight formations. In this paper, we study a variety of schemes where the leader state is available to the other members of the platoon. We show that in some cases it is possible to achieve string stability in the presence of certain amounts of time delay in the leader state reception. We also compare other properties of the different schemes and discuss some of their advantages and disadvantages.
19 Dec 07:24
Publication date: December 2013
Source:Automatica, Volume 49, Issue 12
Author(s): Houria Kheloufi , Ali Zemouche , Fazia Bedouhene , Mohamed Boutayeb
This paper deals with the problem of observer-based stabilization for linear systems with parameter inequality. A new design methodology is proposed thanks to a judicious use of the famous Young relation. This latter leads to a less restrictive synthesis condition, expressed in term of Linear Matrix Inequality (LMI), than those available in the literature. Numerical comparisons are provided in order to show the validity and superiority of the proposed method.
19 Dec 07:20
Publication date: January 2014
Source:Automatica, Volume 50, Issue 1
Author(s): Greg Foderaro , Silvia Ferrari , Thomas A. Wettergren
This paper presents a novel optimal control problem, referred to as distributed optimal control, that is applicable to multiscale dynamical systems comprised of numerous interacting agents. The system performance is represented by an integral cost function of the macroscopic state that is optimized subject to a hyperbolic partial differential equation known as the advection equation. The microscopic control laws are derived from the optimal macroscopic description using a potential function approach. The optimality conditions of the distributed optimal control problem are first derived analytically and, then, demonstrated numerically through a multi-agent trajectory optimization problem.
19 Dec 07:19
Publication date: February 2014
Source:Automatica, Volume 50, Issue 2
Author(s): Tao Yang , Ziyang Meng , Dimos V. Dimarogonas , Karl H. Johansson
In this paper, we consider the global consensus problem for discrete-time multi-agent systems with input saturation constraints under fixed undirected topologies. We first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents. We then focus on two special cases, where the agent model is either neutrally stable or a double integrator. For the neutrally stable case, any linear protocol of a particular form, which solves the consensus problem for the case without input saturation constraints, also solves the global consensus problem for the case with input saturation constraints. For the double integrator case, we show that a subset of linear protocols, which solve the consensus problem for the case without saturation constraints, also solve the global consensus problem for the case with input saturation constraints. The results are illustrated by numerical simulations.
19 Dec 07:19
Publication date: Available online 2 December 2013
Source:Automatica
Author(s): Deyuan Meng , Yingmin Jia , Junping Du , Jun Zhang
This paper deals with formation control problems for multi-agent systems with nonlinear dynamics and switching network topologies. Using the nearest neighbor knowledge, a distributed algorithm is constructed by employing the iterative learning control approach. Sufficient conditions are given to obtain the desired relative formations of agents, which benefits from the strict positiveness of products of stochastic matrices. It is shown that the derived results can effectively work, although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees. Such result is also illustrated via numerical simulations.
19 Dec 07:16
Publication date: February 2014
Source:Automatica, Volume 50, Issue 2
Author(s): Bin Zhou , Zongli Lin
We study in this paper the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays in both the communication network and inputs. Provided that the open-loop dynamics of the agents is not exponentially unstable, but may be polynomially unstable, and the communication topology contains a directed spanning tree, a truncated predictor feedback approach is established to solve the consensus problem. It is shown that, if the delays are constant and exactly known, the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays. If it is further assumed that the open-loop dynamics of the agents only contains zero eigenvalues, the delays are allowed to be time-varying and unknown. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches.
19 Dec 07:15
Publication date: March 2014
Source:Automatica, Volume 50, Issue 3
Author(s): Zhongkui Li , Zhisheng Duan , Frank L. Lewis
This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, based on the local state information of neighboring agents, a fully distributed continuous adaptive consensus protocol is designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable bounded set. For the case where there exists a leader whose control input is unknown and bounded, a distributed adaptive consensus protocol is proposed to ensure the boundedness of the consensus error. A sufficient condition for the existence of the proposed protocols is that each agent is stabilizable.
19 Dec 07:15
Publication date: February 2014
Source:Automatica, Volume 50, Issue 2
Author(s): Wei Zhu , Zhong-Ping Jiang , Gang Feng
In this paper, the event-based consensus problem of general linear multi-agent systems is considered. Two sufficient conditions with or without continuous communication between neighboring agents are presented to guarantee the consensus. The advantage of the event-based strategy is the significant decrease of the number of controller updates for cooperative tasks of multi-agent systems involving embedded microprocessors with limited on-board resources. The controller updates of each agent are driven by properly defined events, which depend on the measurement error, the states of its neighboring agents and an arbitrarily small threshold. It is shown that the controller updates for each agent only trigger at its own event time instants. A simulation example is presented to illustrate the theoretical results.
11 Oct 04:46
by Yuanzhen Feng, Shengyuan Xu, Frank L. Lewis, Baoyong Zhang
Summary
In this paper, we consider the consensus problem for heterogeneous multi-agent systems composed of some first-order and some second-order dynamic agents in directed communication graphs. Consensus protocols are proposed for the second- and first-order dynamic agents, respectively. Under certain assumptions on the control parameters, for fixed communication topologies, necessary and sufficient conditions for consensus are given, and the consensus values of all agents are established. For switching topologies, sufficient conditions are given for all agents to reach consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.