A Robust Event-Triggered Consensus Strategy for Linear Multi-Agent Systems with Uncertain Network Topology

Robust consensus for linear multi-agent systems with mixed uncertainties

This article systematically studies consensus of linear multiagent systems (MASs) on directed graphs through adaptive event-triggered control. It presents innovative adaptive event-triggered state-feedback protocols with novel composite event-triggering conditions. Two specific designs in terms of different event-triggering conditions and laws of adaption are first discussed for linear MASs on strongly connected directed graphs, which are then extended to general directed graphs that contain a spanning tree. Moreover, another adaptive event-triggered protocol is proposed for solving leader-follower consensus that tracks a leader of a bounded control input. The protocols inherit the merits of both adaptive control and event-triggered control: the protocols can be implemented in a fully distributed way, since the Laplacian is avoided in design, and each agent only needs to know the relative information between neighbors at discrete instants determined by event-triggering conditions. Compared with the existing related results, the proposed protocols are applicable for linear MASs on general directed graphs, and moreover, the time-dependent term in the event-triggering conditions is allowed to be a class of positive L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> functions. Two numerical examples clearly verify the effectiveness of the proposed protocols.

This paper considers bipartite consensus of linear multi-agent systems over signed directed graphs, where both collaboration and competition coexist. The agent dynamics are distinct and can all have different dimensions. The communication graph can be time-varying and need not to be connected at each time. A distributed control law is proposed which enables the group to split into two disjoint subgroups, and the outputs of all agents within each subgroup achieve consensus, but the two subgroups move oppositely towards each other. Rigorous analysis and a simulation example are provided.

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.

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.

In this article, we investigate the event-triggered consensus problem for general linear multiagent systems with bounded communication network delay. To reduce the communication frequency, we propose some dynamic periodic event-triggering strategies, under which an auxiliary dynamic variable and a weighting parameter are introduced for each agent to build its event-triggering condition. Then, a distributed adaptive consensus protocol, which includes a time-varying coupling weight for each edge, is designed based on the proposed event-triggering strategies. With the well-designed updating laws of dynamic variables, coupling weights and weighting parameters, we can theoretically guarantee the consensus of the concerned multiagent systems. Our event-triggering strategies do not require agents to continuously verify the event-triggering conditions or read their neighbors’ real-time state information. Moreover, Zeno behavior is inherently excluded as the interevent intervals are bounded from below by one period in the periodic event-triggering framework. Two numerical examples are provided to verify the effectiveness of the proposed event-triggered consensus protocols.

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.

This paper investigates group consensus for linear multi-agent systems with nonidentical dynamics. A novel adaptive event-triggered communication scheme is presented by using the stochastic sampling information, the event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered condition, where event-triggered parameters can be adjusted with the system dynamics evolving. The group consensus protocol is designed based on the neighboring agents information at event-triggered instants, then a new stochastic sampled-data dependent error model is constructed, some group consensus criteria in mean-square can be derived and the feedback matrices can also be obtained. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

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.

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.

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.

Robust distributed adaptive consensus for discrete-time multiagent systems with uncertain topologies

This paper addresses the event-triggered consensus tracking for general linear multi-agent systems with nonlinear uncertainty dynamics under directed communication topology. The proposed event-triggered consensus strategy relaxes the assumptions in existing works that the control gain and local inputs must be continuous. With the consensus tracking condition being satisfied, the cooperative control law with bounded parameter is developed based on the intermittent samples. It shows that if the sampling condition, in terms of LMIs, is satisfied, the resulting closed-loop general linear multi-agent uncertain systems will achieve the consensus. Simulation results are provided to verify the proposed approach.

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.