Output bipartite consensus of heterogeneous linear multi-agent systems under switching topologies

In this work, stochastic consensus of linear multi-agent systems with multiplicative measurement noises is investigated under undirected graphs. Based on the algebraic graph theory and the matrix theory, the consensus problem is converted into the stochastic stability problem of stochastic differential equations (SDEs) driven by multiplicative noises. Then by stochastic stability theorem for SDEs, the stochastic consensus conditions are given for the multi-agent systems. For the general linear multi-agent systems, the sufficient conditions for the mean square and the almost sure consensus are obtained based on the solution to an algebraic Riccati equation, where the consentability condition on the algebraic connectivity and the channel uncertainties is revealed. For the case of second-order integrator dynamics, by choosing some appropriate Lyapunov functions, the sufficient conditions for the mean square and the almost sure consensus, and the necessary conditions for the mean square consensus are derived. Moreover, it is shown that for any bounded noise intensities, the mean square and the almost sure consensus can be achieved by carefully choosing the control gain.

This technical note introduces a novel design approach to address the leader-following consensus problem in linear multi-agent systems (MASs) through distributed impulsive control. First, robust stability criteria are established for a class of linear impulsive systems with parametric input matrix. These criteria are then applied to the design of the distributed impulsive controller. The proposed design approach decouples the design of the impulsive control gains from the detailed graph properties, making it applicable to a class of communication networks. Furthermore, the state feedback results are extended to the output feedback case by constructing a distributed impulsive observer-based controller. In both scenarios, it is demonstrated that the novel impulsive controller/observer developed at the individual agent level can also be utilized to achieve leader-following consensus for a class of linear MASs, provided that the relationship between the dynamics of the individual agents and the graph properties satisfies a certain condition. Finally, the efficiency and the scalability of the theoretical results are verified through two illustrative examples.

In this paper, the leader-following consensus problem of higher order multi-agent systems is considered. The dynamics of each agent is given in general form of linear system and the communication topology among the agents is assumed to be undirected and switching. To track the active leader, a distributed observer-based consensus protocol is proposed to each following agent, which is based on the relative outputs of neighboring agents. A sufficient consensus condition is established by used parameter-dependent lyapunov function method under switching communication topologies. Two gain matrices used in the proposed protocol can be constructed by solving the Riccati equation and Sylvester equation respectively. Finally, a simulation example is given to illustrate our obtained result.

In this brief, a novel distributed leader-following consensus controller for linear multi-agent systems (MASs) with one leader and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> followers is designed for optimal leader-following consensus control. A user-friendly global objective function is well designed in a quadratic form. The proper choice of the weighting matrices and necessary and sufficient conditions for optimizing the objective function are given. The proposed controller can guarantee the optimization of the objective function and the achievement of the leader-following consensus of the MASs. To deal with the coupling in the controllers, we propose a dynamic average consensus-based algorithm to estimate the controller distributedly, and the estimate errors converge to zero in finite time. A simulation example is provided to demonstrate the results.

This article investigates the double dynamic event-triggered consensus of linear multiagent systems with periodic sampled-data via a novel decentralized output feedback stabilization approach. A novel dynamic event-triggered strategy based on periodic sampled-data is proposed for the sensor-to-controller channel and controller-to-actuator channel, respectively. This strategy can further reduce the number of triggers without affecting the system’s performance. We use a state linear transformation based on a directed spanning tree of the communication topology to equivalently transform the consensus problem into the decentralized output feedback stabilization problem of the corresponding edge-state system and propose a decentralized pole assignment approach to design the gain matrix for the consensus protocol. Then, by employing the Lyapunov function combined with the lossless S-procedure, we derive consensus criteria containing matrix inequalities. Finally, numerical examples are provided to verify the effectiveness of the proposed approach.

In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.In this paper, the consensus problem is studied for a class of multi-agent systems with sampled data and packet losses, where random and deterministic packet losses are considered, respectively. For random packet losses, a Bernoulli-distributed white sequence is used to describe packet dropouts among agents in a stochastic way. For deterministic packet losses, a switched system with stable and unstable subsystems is employed to model packet dropouts in a deterministic way. The purpose of this paper is to derive consensus criteria, such that linear multi-agent systems with sampled-data and packet losses can reach consensus. By means of the Lyapunov function approach and the decomposition method, the design problem of a distributed controller is solved in terms of convex optimization. The interplay among the allowable bound of the sampling interval, the probability of random packet losses, and the rate of deterministic packet losses are explicitly derived to characterize consensus conditions. The obtained criteria are closely related to the maximum eigenvalue of the Laplacian matrix versus the second minimum eigenvalue of the Laplacian matrix, which reveals the intrinsic effect of communication topologies on consensus performance. Finally, simulations are given to show the effectiveness of the proposed results.

This paper investigates the problem of leader-following consensus of a linear multi-agent system on a switching network. The input of each agent is subject to saturation. Low gain feedback based distributed consensus protocols are developed. It is established that, under the assumptions that each agent is asymptotically null controllable with bounded controls and that the network is connected or jointly connected, semi-global leader-following consensus of the multi-agent system can be achieved. Numerical examples are presented to illustrate this result.

This paper proposes a robust distributed event-triggered approach for consensus in linear multi-agent systems (MAS) with uncertain network topologies. To achieve consensus, each agent transmits its information only when a certain event-triggering condition is fulfilled. The connection weights in the network are uncertain and hence the information received by each agent is unreliable. In such an uncertain topology, the objective is to co-design robust consensus parameters (namely, the state transmission threshold and local control gains) that collectively ensure an exponential rate for consensus convergence. An objective function incorporating the transmission load and control effort is minimized to compute the design parameters. Numerical simulations quantify the effectiveness of the proposed event-triggered consensus approach in a second-order MAS.

This note further studies the previously proposed consensus protocol for linear multi-agent systems with communication noises in [15], [16]. Each agent is allowed to have its own time-varying gain to attenuate the effect of communication noises. Therefore, the common assumption in most references that all agents have the same noise-attenuation gain is not necessary. It has been proved that if all noise-attenuation gains are infinitesimal of the same order, then the mean square leader-following consensus can be reached. Furthermore, the convergence rate of the multi-agent system has been investigated. If the noise-attenuation gains belong to a class of functions which are bounded above and below by $t^{-\beta}$ $(\beta\in(0,1))$ asymptotically, then the states of all follower agents are convergent in mean square to the leader's state with the rate characterized by a function bounded above by $t^{-\beta}$ asymptotically.

This paper studies bipartite consensus problem for general linear multi-agent systems, where both collaboration and competition between agents coexist. We establish an equivalence between output feedback bipartite consensus problems and the conventional output feedback consensus problems, which enables a direct application of existing output feedback consensus algorithms to solve bipartite consensus problems. Moreover, we propose a systematic approach to design output feedback bipartite consensus controller.

Robust consensus for linear multi-agent systems with mixed uncertainties

In this paper, bipartite consensus is discussed for multi-agent systems (MASs) under jointly connected switching topologies. An adaptive bipartite consensus protocol is proposed for MASs under jointly connected topologies. Under the proposed protocol, bipartite consensus can be realized with some fully conditions. Finally, a simulation example is shown to verify the theoretical results.KeywordsBipartite consensusMulti-agent systems (MASs)Adaptive controlJointly connected switching topologies

Bipartite event-triggered impulsive output consensus for switching multi-agent systems with dynamic leader

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper investigates the consensus problem of linear multi-agent systems subject to external disturbances via distributed event-triggered adaptive control. First, a distributed event-triggered adaptive output feedback control strategy is proposed for each agent. It is shown that under this control strategy, the consensus problem can be solved for any connected undirected communication graph in a fully distributed manner without using any global information. Then a distributed self-triggered adaptive output feedback control strategy is designed with which continuous monitoring of the measurement error is no longer needed. It is further shown that for the proposed event-triggered and self-triggered control strategies, no agent will exhibit Zeno behavior. Finally, the effectiveness of the proposed two control strategies is illustrated on a group of two-mass-spring systems.