Bounded consensus tracking for sampled‐data second‐order multi‐agent systems with fixed and Markovian switching topology

This paper studies the bounded consensus tracking problems of second‐order multi‐agent systems with fixed and Markovian switching topology in a sampling setting. It is assumed that all the agents can only obtain the approximative value of the leader's acceleration instead of the actual value. Moreover, only a portion of agents can have the access to the leader and obtain the leader's position and velocity directly. By virtue of matrix analysis and perturbation theory, we present necessary and sufficient conditions for boundedness of tracking error system and show the ultimate bound of tracking errors under fixed and Markovian switching topology, respectively. Finally, a simulation example is given to illustrate the effectiveness of the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Consensus analysis of continuous‐time second‐order multi‐agent systems with nonuniform time‐delays and switching topologies

In this study, consensus problems for second‐order multi‐agent systems with nonuniform and switching topologies are investigated. Each agent has a self‐delay, and each delay is independent of the others. As a measure of the disagreement dynamics, a class of positive semi‐definite Lyapunov–Krasovskii functions are introduced. Using algebraic graph theory and these Lyapunov–Krasovskii functions, sufficient conditions are derived by contradiction under which all agents asymptotically reach consensus. Finally, the effectiveness of the obtained theoretical results is demonstrated through numerical simulations.     

Time‐varying output formation control for linear multi‐agent systems with switching topologies

Time‐varying output formation control problems for linear multi‐agent systems with switching topologies are studied, where two types of switching topologies are considered: (1) the topology is undirected and jointly connected, and 2) each topology is directed and has a spanning tree. An output formation protocol under switching topologies is constructed using the outputs of neighboring agents via dynamic output feedback. Two algorithms are proposed to design the dynamic protocols under both jointly connected topologies and switching directed topologies. Time‐varying output formation feasibility conditions are given to describe the compatible relationship among the desired time‐varying output formation, the dynamics of each agent, and the switching topologies. The stability of the closed‐loop multi‐agent systems under the proposed two algorithms is investigated based on the common Lyapunov functional theory and the piecewise Lyapunov functional theory, respectively. In the case where the topologies are jointly connected, time‐varying output formation can be achieved for multi‐agent systems using the designed protocol if the given time‐varying output formation satisfies the feasible constraint. For the case where the switching topologies are directed and have a spanning tree, the time‐varying output formation can be realized if the output formation feasibility constraint is satisfied and the dwell time is larger than a positive threshold. Moreover, approaches to determine the output formation references are provided to describe the macroscopic movement of the time‐varying output formation. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Uniform synchronization in multi‐agent systems with switching topologies

This paper deals with uniform synchronization analysis of multi‐agent systems with switching topologies. The agents are assumed to have general, yet identical, linear dynamics. The underlying communication topology may switch arbitrarily within a finite set of admissible topologies. We establish conditions under which the network is uniformly synchronized meaning that synchronization is valid under all possible switching scenarios. The primary conditions established are in terms of a pair of Lyapunov strict inequalities. Following those conditions, small gain and passivity types of conditions are proposed under which uniform synchronization is guaranteed. The proposed results are also extended to the case of observer‐based protocols. Copyright © 2015 John Wiley & Sons, Ltd.     

Guaranteed cost consensus for multi‐agent systems with switching topologies

Firstly, guaranteed cost consensus for multi‐agent systems is introduced based on state errors among neighboring agents and control inputs of all agents, where a tradeoff between the consensus regulation performance and the control effort is considered. Then, a sufficient condition for guaranteed cost consensus is given by the state‐space decomposition approach and the Lyapunov method, where an upper bound of the cost function is determined and an approach is proposed to determine the control gain. It is worth mentioning that the criterions for guaranteed cost consensus are only dependent on the maximum eigenvalue of the Laplacian matrices of switching topologies. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus in multi‐agent systems with communication constraints

The problem of second‐order consensus is investigated in this paper for a class of multi‐agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second‐order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second‐order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

Controllability of switching networks of multi‐agent systems

This paper addresses the controllability of a switching network of multi‐agent systems with a leader obeying nearest‐neighbor communication rules. The leader is a particular agent acting as an external input to control other member agents. Some computationally efficient sufficient conditions for such multi‐agent systems to be controllable are derived. The results show that a multi‐agent system can be controllable even if each of its subsystem is not controllable, by appropriately selecting one of the agents as the leader and suitably designing the neighbor‐interaction rules via a switching topology. The fixed topology case is analyzed and new controllability conditions and formula of inputs for the desired formation of the network are presented. The controllability of a switching network of multi‐agent systems in the presence of communication delay is also investigated. Examples with numerical simulations are given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Consensus in second‐order Markovian jump multi‐agent systems via impulsive control using sampled information with heterogenous delays

This paper investigates the consensus problem of second‐order Markovian jump multi‐agent systems with delays. Both network‐induced random delay and node‐induced state delay are considered, where the network‐induced random delay, subjected to a Markov chain, exists in the switching signal and the node‐induced state delay, related to switching topologies, is heterogeneous between any two linked agents. In order to reduce communication and control energy, an impulsive protocol is proposed, where each agent only can get delayed relative positions to neighbors and the velocity of itself at impulsive instants. By performing three steps of model transformation and introducing a mapping for two independent Markov chains, the consensus problem of the original continuous‐time system is equivalent to the stability problem of a discrete‐time expand error system with two Markovian jumping parameters and a necessary and sufficient criterion is derived. A numerical example is given to illustrate the effectiveness of the theoretical result.@@@@This work is supported by the National Natural Science Foundation of China under Grants 61374171, 61572210, and 51537003, the Fundamental Research Funds for the Central Universities (2015TS030), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245).     

Consensus of heterogeneous first‐ and second‐order multi‐agent systems with directed communication topologies

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.     

Consensus seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Semi‐global cooperative output regulation of a class of nonlinear uncertain multi‐agent systems under switching networks

In this paper, we consider the semi‐global cooperative output regulation problem for a class of nonlinear uncertain multi‐agent systems under switching networks. At first, we study the nonadaptive case when the exosystem has no parametric uncertainties and construct a common Lyapunov function to achieve the output regulation for general switching connected networks. Next, we study the case when the exosystem contains some parametric uncertainties. To solve the problem, we establish a stability result for a class of time‐varying system, which is then used in the design of distributed adaptive internal model‐based control. Then we construct multiple Lyapunov functions for the switching signal with its average dwell time lower bounded by a given constant. Throughout the paper, we treat the closed‐loop multi‐agent system from the viewpoint of singular perturbation. In fact, the singular perturbation‐based method provides an effective tool to handle the multi‐agent system under switching networks. Finally, we give numerical simulations based on Duffing systems and flexible manipulator systems to illustrate the effectiveness of our method. Copyright © 2017 John Wiley & Sons, Ltd.     

Consensus of nonlinear multiagent systems with mode-dependent delay via stochastic sampled data under Markovian switching topologies

In this article, we investigate the mean-square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time-varying delay switch randomly which are regulated by a time-homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean-square consensus. For the undirected topology case, a low-dimensional LMI-based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.     

Consensus for multi‐agent systems under double integrator dynamics with time‐varying communication delays

In this paper, the consensus control problems for multi‐agent systems under double integrator dynamics with time‐varying communication delays are investigated. We assume that the interaction graphs among agents are directed. Two kinds of protocols are considered. One is an absolute damping protocol, and the other is a relative damping protocol. For the first protocol, Lyapunov–Razumikhin functional techniques are used. We derive sufficient conditions that guarantee that all agents asymptotically reach consensus under fixed topology and switching topology, respectively. Moreover, the allowable upper bound for communication delays is given. For the second protocol, Lyapunov–Krasovskii functional techniques are used. Linear matrix inequality (LMI)‐form sufficient conditions are obtained to guarantee the consensus problems to be solved under fixed topology and switching topology, respectively. The allowable upper bound for communication delays is given as well. The feasibilities of the demanded LMIs are also discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Consensus for formation control of multi‐agent systems

This study considers the formation problem for multi‐agent systems, which are described by the second‐order dynamics on nonlinear manifolds SE(2) and SE(3). In particular, the model of each agent contains information about its attitude. Using a consensus strategy, a control law is developed to guarantee that any desired formation can be achieved asymptotically under the conditions of complete or tree‐shaped communication topologies. Numerical simulations are presented to verify the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Containment control of stochastic multiagent systems with semi‐Markovian switching topologies

The containment control of stochastic multiagent systems with semi‐Markov switching topologies is investigated in this paper. The general case that the distribution function of the sojourn time is dependent on both the current system mode and the target mode is considered. Taking state multiplicative noise into account and using stochastic techniques, sufficient conditions to achieve the containment control in the asymptotic mean square sense are obtained in a form of linear matrix inequalities and the controller design condition is given. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results.     

High‐precision formation control of nonlinear multi‐agent systems with switching topologies: A learning approach

Arbitrary high precision is considered one of the most desirable control objectives in the relative formation for many networked industrial applications, such as flying spacecrafts and mobile robots. The main purpose of this paper is to present design guidelines of applying the iterative schemes to develop distributed formation algorithms in order to achieve this control objective. If certain conditions are met, then the control input signals can be learned by the developed algorithms to accomplish the desired formations with arbitrary high precision. The systems under consideration are a class of multi‐agent systems under directed networks with switching topologies. The agents have discrete‐time affine nonlinear dynamics, but their state functions do not need to be identical. It is shown that the learning processes resulting from the relative output formation of multi‐agent systems can converge exponentially fast with the increase of the iteration number. In particular, this work induces a distributed algorithm that can simultaneously achieve the desired relative output formation between agents and regulate the movement of multi‐agent formations as desired along the time axis. The illustrative numerical simulations are finally performed to demonstrate the effectiveness and performance of the proposed distributed formation algorithms. Copyright © 2014 John Wiley & Sons, Ltd.     

Consensus of multi‐agent systems with fixed inner connections

This paper characterizes a unified consensus region for multi‐agent systems, where there exist fixed physical connections with information exchange. The notions of synchronization region in complex networks and consensus region in multi‐agent systems can be explained under this unified framework. The effect of the coupling terms on the consensus regions in different situations is analyzed specifically. Furthermore, necessary and sufficient conditions for consensus of agents under both distributed state feedback and observer‐based output feedback control are established. On the basis of a parameter‐dependent Lyapunov function, a 2‐step controller design procedure is proposed, which can reduce the conservativeness to some extent in comparison with the conventional direct Lyapunov method. In addition, for the case with disturbance, the robustness of the system is investigated. Finally, some numerical examples are presented to illustrate the theoretical results.