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.     

Global Robust Stabilization via Sampled‐Data Output Feedback for Nonlinear Systems with Uncertain Measurement and Control Gains

This paper studies the problem of using a sampled‐data output feedback controller to globally stabilize a class of nonlinear systems with uncertain measurement and control gains. A reduced‐order observer and a linear output control law, both in the sampled‐data form, are designed without the precise knowledge of the measurement and control gains except for their bounds. The observer gains are chosen recursively in a delicate manner by utilizing the output feedback domination approach. The allowable sampling period is determined by estimating and restraining the growth of the system states under a zero‐order‐hold input with the help of the Gronwall–Bellman Inequality. A DC–DC buck power converter as a real‐life example will be shown by numerical simulations to demonstrate the effectiveness of the proposed control method.     

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.     

A decoupled designing approach for sampling consensus of multi‐agent systems

This paper introduces the motion‐planning approaches to solve the distributed consensus problems via sampling measurements. First, for first‐order multiagent systems, a class of sampled‐data–based algorithms are developed with arbitrary sampling periods, which solve the asymptotic consensus problem under both directed fixed and random switching topologies. Then, a new kind of distributed consensus algorithms is designed based on sampling measurements for second‐order multiagent systems. Under both the directed fixed and periodical switching topologies, asymptotic consensus problems of second‐order multiagent systems can be solved by using the proposed algorithms. Compared with existing continuous‐time consensus algorithms, one of remarkable advantages of proposed algorithms is that the sampling periods, communication topologies, and control gains are decoupled and can be separately designed, which relaxes many restrictions in controller designs. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.     

Distributed Observer‐based Stabilization of Nonlinear Multi‐agent Systems with Sampled‐data Control

In this paper, the distributed observer‐based stabilization problem of multi‐agent systems under a directed graph is investigated. Distributed observer‐based control protocol with sampled‐data information is proposed. The dynamics of each agent contain a nonlinear part, which is supposed to be general Lipschitz. In order to stabilize the states of the whole network, all the nodes utilize the relative output estimation error at sampling instants and only a small fraction of nodes use the absolute output estimation error additionally. By virtue of the input‐to‐state stability (ISS) property and the Lyapunov stability theory, an algorithm to design the control gain matrix, observer gain matrix, coupling strength as well as the allowable sampling period are derived. The conditions are in the form of LMIs and algebraic inequality, which are simple in form and easy to verify. Some further discussions about the solvability of obtained linear matrix inequalities (LMIs) are also given. Lastly, an example is simulated to further validate the obtained results.     

Consensus of linear multi‐agent systems with stochastic noises and binary‐valued communications

This article studies consensus problems of discrete‐time linear multi‐agent systems with stochastic noises and binary‐valued communications. Different from quantized consensus of first‐order systems with binary‐valued observations, the quantized consensus of linear multi‐agent systems requires that each agent observes its neighbors' states dynamically. Unlike the existing quantized consensus of linear multi‐agent systems, the information that each agent in this article gets from its neighbors is only binary‐valued. To estimate its neighbors' states dynamically by using the binary‐valued observations, we construct a two‐step estimation algorithm. Based on the estimates, a stochastic approximation‐based distributed control is proposed. The estimation and control are analyzed together in the closed‐loop system, since they are strongly coupled. Finally, it is proved that the estimates can converge to the true states in mean square sense and the states can achieve consensus at the same time by properly selecting the coefficient in the estimation algorithm. Moreover, the convergence rate of the estimation and the consensus speed are both given by O(1/t). The theoretical results are illustrated by simulations.     

On the general consensus protocol in multi‐agent networks with second‐order dynamics and sampled data

This paper considers the problem of the convergence of the consensus for multiple agents in a directed network. A general distributed consensus protocol is designed, the advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. Necessary and sufficient conditions are established for reaching consensus of the system by choosing the appropriate sampling period, the control parameters and the spectra of the Laplacian matrix. It is found that second‐order consensus cannot be reached for a sufficiently large sampling period while it can be reached for a sufficiently small one. Furthermore, the coupling gains can be carefully designed under the given network structure and the sampling period. Finally, a simulation example is given to verify and illustrate the theoretical analysis.     

Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data

This paper addresses the distributed observer‐based consensus problem of second‐order multi‐agent systems via sampled data. Firstly, for the case of fixed topology, a velocity‐independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.     

Global decentralized sampled‐data output feedback stabilization for a class of large‐scale nonlinear systems with sensor and actuator failures

In this paper, we investigate global decentralized sampled‐data output feedback stabilization problem for a class of large‐scale nonlinear systems with time‐varying sensor and actuator failures. The considered systems include unknown time‐varying control coefficients and inherently nonlinear terms. Firstly, coordinate transformations are introduced with suitable scaling gains. Next, a reduced‐order observer is designed to estimate unmeasured states. Then, a decentralized sampled‐data fault‐tolerant control scheme is developed with an allowable sampling period. By constructing an appropriate Lyapunov function, it can be shown that all states of the resulting closed‐loop system are globally uniformly ultimately bounded. Finally, the validity of the proposed control approach is verified by using two examples.     

Second-order consensus in multi-agent dynamical systems with sampled position data

This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.     

Impulsive consensus algorithms for second-order multi-agent networks with sampled information

In this paper, the distributed consensus problem for second-order continuous-time multi-agent networks with sampled-data communication is investigated. Motivated by impulsive control strategy, two kinds of impulsive distributed consensus algorithm are proposed. These algorithms only utilize the sampled information and are implemented at sampled times. By using the stability theory of impulsive systems and properties of the Laplacian matrix, necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks. It is shown that the control gains, the sampling period and the eigenvalues of the Laplacian matrix of the communication graph play key roles in achieving the consensus. A numerical example is given to illustrate the results.     

Asynchronous sampled-data consensus of singular multi-agent systems based on event-triggered strategy

This paper is concerned with sampled-data consensus for multi-agent systems with singular dynamics. It is assumed that the sampling period of each agent is independent of the other's. Based on event-triggered sampled-data transmission strategy, a distributed consensus protocol is presented. The consensus of singular multi-agent system is transformed into the stability of singular systems with multiple time-varying delays. By employing the Lyapunov-Krasovskii functional method, a sufficient condition on the consensus of multi-agent singular system is derived. Based on the obtained condition, an algorithm to design consensus controller gains is presented in terms of linear matrix inequalities. Two numerical examples are given to show the effectiveness of the proposed method.     

Stochastic consensus of single‐integrator multi‐agent systems under relative state‐dependent measurement noises and time delays

This paper proposes a consensus algorithm for continuous‐time single‐integrator multi‐agent systems with relative state‐dependent measurement noises and time delays in directed fixed and switching topologies. Each agent's control input relies on its own information state and its neighbors' information states, which are delayed and corrupted by measurement noises whose intensities are considered a function of the agents' relative states. The time delays are considered time‐varying and uniform. For directed fixed topologies, condition to ensure mean square linear χ‐consensus (average consensus, respectively) are derived for digraphs having spanning tree (balanced digraphs having spanning tree, respectively). For directed switching topologies, conditions on both time delays and dwell time have been given to extend the mean square linear χ‐consensus (average consensus, respectively) of fixed topologies to switching topologies. Copyright © 2016 John Wiley & Sons, Ltd.     

Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

This paper considers global output feedback stabilization via sampled‐data control for a general class of nonlinear systems, which admit unknown control coefficients and nonderivable output function. A sector region of the output function is given by utilizing a technical lemma, and a sampled‐data controller is designed by combining a robust state stabilizer and a reduced‐order sampled‐data observer. By carefully choosing an appropriate sampling period, the proposed controller guarantees the globally asymptotical stability of the closed‐loop systems.     

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

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

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

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

Output Consensus of Heterogeneous Linear Multi‐agent Systems Subject to Different Disturbances

This paper investigates the output consensus problem of heterogeneous linear multi‐agent systems with individual agents subject to different disturbances. A distributed control law based on internal reference models and dynamic output feedback is presented for output consensus. It is shown that the embedded internal reference models of agents can achieve consensus to a common trajectory which is determined by the underlying system topology and the initial states of the internal reference models. Then a necessary and sufficient condition is presented for output consensus of heterogeneous linear multi‐agent systems. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control laws.     

Distributed Consensus of Third‐order Multi‐agent Systems with Communication Delay

This paper studies the consensus problem for a class of general third‐order multi‐agent systems on an undirected connected network. By employing a variables transformation, the consensus control problem can be turned into a asymptotical stability problem. Then we present a necessary and sufficient condition for guaranteeing consensus by using Routh‐Hurwitz stability criterion. And this result can be applied to a special case of third‐order integrator systems. Also we will present a tolerable communication time delay for third‐order integrator systems under the assumption that multi‐agent systems can reach consensus without communication delay.     

Semiglobal stabilization of linearly uncontrollable and unobservable nonlinear systems via sampled‐data control

This article investigates the problem of using sampled‐data state/output feedback to semiglobally stabilize a class of uncertain nonlinear systems whose linearization around the origin is neither controllable nor observable. For any arbitrarily large bound of initial states, by employing homogeneous domination approach and a homogeneous version of Gronwall‐Bellman inequality, a sampled‐data state feedback controller with appropriate sampling period and scaling gain is constructed to semiglobally stabilize the system. In the case when not all states are available, a reduced‐order sampled‐data observer is constructed to provide estimates for the control law, which can guarantee semiglobal stability of the closed‐loop system with carefully selected sampling period and scaling gain.     

Consensus of second‐order multi‐agent systems with exogenous disturbances

In this paper, the consensus of second‐order multi‐agent dynamical systems with exogenous disturbances is studied. A pinning control strategy is designed for a part of agents of the multi‐agent systems without disturbances, and this pinning control can bring multiple agents' states to reaching an expected consensus track. Under the influence of the disturbances, disturbance observers‐based control (DOBC) is developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi‐agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi‐agent systems with switching topologies and exogenous disturbances, the consensus of multi‐agent systems is reached under the DOBC with the designed parameters. Copyright © 2010 John Wiley & Sons, Ltd.