Event-triggered Consensus Protocol Research Articles

Optimal Consensus Control for Continuous-Time Linear Multiagent Systems: A Dynamic Event-Triggered Approach.

This article investigates the optimal consensus problem for general linear multiagent systems (MASs) via a dynamic event-triggered approach. First, a modified interaction-related cost function is proposed. Second, a dynamic event-triggered approach is developed by constructing a new distributed dynamic triggering function and a new distributed event-triggered consensus protocol. Consequently, the modified interaction-related cost function can be minimized by applying the distributed control laws, which overcomes the difficulty in the optimal consensus problem that seeking the interaction-related cost function needs all agents' information. Then, some sufficient conditions are obtained to guarantee optimality. It is shown that the developed optimal consensus gain matrices are only related to the designed triggering parameters and the desirable modified interaction-related cost function, relaxing the constraint that the controller design requires the knowledge of system dynamics, initial states, and network scale. Meanwhile, the tradeoff between optimal consensus performance and event-triggered behavior is also considered. Finally, a simulation example is provided to verify the validity of the designed distributed event-triggered optimal controller.

Enhancing DC microgrids cluster performance with distributed event-triggered consensus protocols

Microgrid (MG) clusters offer solutions to the challenges faced by individual MGs in extreme conditions but require precise coordination to manage generation-load imbalances effectively. This paper presents a hierarchical control strategy that combines time-based and event-based consensus protocols (ETC) in the overarching control layer. Traditional time-based protocols require constant sampling, leading to unnecessary communication and computational burdens. To address this, we introduce a mixed time-state dependent distributed event-triggered consensus protocol (MDETC), which reduces communication needs while maintaining MG performance. A set-time consensus algorithm is used at the secondary control level to synchronize currents and voltages quickly. Additionally, the integration of Particle Swarm Optimization (PSO) in primary control ensures efficient current distribution and voltage regulation among neighboring MGs. The study also explores automatic reconfiguration within the cluster to support Plug-N-Play functionality, ensuring seamless MG operation. The effectiveness of this control approach is demonstrated through MATLAB simulations of a four-DC MG cluster, showing improved efficiency in reducing triggering instances and achieving faster current and voltage stabilization under various conditions.

Distributed Dynamic Event-Triggered Consensus Protocol for General Linear Multiagent Systems Without Accurate System Information.

This study focuses on distributed event-triggered consensus control under the scenario where only inaccurate agent model information is available. By designing a novel triggering error, a distributed dynamic event-triggered consensus (DETC) protocol is proposed for multiagent systems (MASs) with general linear dynamics over digraphs, without accurate a priori information of agent models. To improve the efficiency of the dynamic triggering law, a mixed triggering threshold is designed with a resilient function integrated to further enlarge interevent intervals. Within the proposed DETC protocol, the computational cost is significantly reduced especially for MASs with nonsparse and high-dimensional agent system matrices. In addition, for each individual agent, the states of neighboring agents used for triggering detections or controller updates are required in an on-demand (instead of continuous) way, which preserves communication resources and facilitates practical implementation. The feasibility of the designed DETC protocol is corroborated by rigorous theoretical analysis on consensus convergence and Zeno behavior exclusion. Finally, simulations are shown to demonstrate the effectiveness of the studied theory.

Designing adaptive continuous event-triggered consensus protocol for nonlinear multi-agent systems with a nonautonomous leader

This article investigates the leader-follower consensus (LFC) issue for a class of Lipschitz-type nonlinear multi-agent systems (NMASs) that include one leader and multiple followers. To enable the leader to denote a flexible noncooperative reference trajectory, it is considered that the leader's control input (LCI) exists and cannot be obtained by other followers. A novel robust distributed adaptive continuous event-triggered control protocol is developed. Through rigorous analysis, it is shown that under this control protocol, the NMASs can reach LFC and the Zeno behavior is not exhibited. Compared to existing research works, the main merits of this control protocol are as follows: 1) It is chattering-free while can completely eliminate the adverse effects brought by the LCI; 2) The communication traffic between agents is lower; 3) It can be executed in a fully distributed way (i.e., no global information is required for the design process of this control protocol). Finally, the effectiveness of the developed control protocol is validated through an example.

A Proportional–Integral Observer-Based Dynamic Event-Triggered Consensus Protocol for Nonlinear Positive Multi-Agent Systems

This paper investigates the state estimation and event-triggered control for positive nonlinear multi-agent systems. Firstly, a proportional–integral observer is established to estimate the states of the considered nonlinear positive multi-agent systems based on the matrix decomposition method. Then, a dynamic event-triggered mechanism is constructed, and a control protocol is proposed based on the proportional–integral observer and event-triggered mechanism. By combining linear programming with linear co-positive Lyapunov functions, the considered multi-agent systems are guaranteed to be positive and achieve consensus. Moreover, by introducing three new variables and a finite vector, the final convergence point can be changed based on the given vector. Finally, two illustrative examples demonstrate the validity of the proposed theoretical results.

Model-independent event-based consensus of multiple Euler-Lagrange systems with input disturbances

This paper investigates leaderless consensus (LLC) and leader-follower consensus (LFC) issues of multiple Euler-Lagrange systems (MELSs) with uncertain system parameters and input disturbances. Firstly, by utilizing event-based control strategy, event-based consensus protocols are proposed to achieve LLC and LFC, respectively. Then, to confirm that no Euler-Lagrange (EL) system will exhibit Zeno behavior under the above event-based consensus protocols, we show that the low bound of event-triggering interval is strictly positive for any time instants. Distinct with the existing related works, the proposed event-triggered consensus protocols only rely on local sampled state, and are irrelevant to the system parameters. Finally, some simulation examples are presented to illustrate the feasibility of the proposed event-based consensus algorithms.

Event-triggered prescribed-time consensus for nonholonomic multi-agent systems with external disturbances

This paper considers the prescribed-time event-triggered consensus for a class of nonholonomic multi-agent systems (MASs) with external disturbances. Firstly, the nonholonomic chained MASs are divided into two subsystems, and a switching control scheme is introduced. Secondly, a distributed prescribed-time continuous protocol is proposed to ensure that all agents reach average consensus within a prescribed finite-time. Moreover, to reduce the communication costs, an event-triggered consensus protocol is further established and some related theorems are given. In addition, the Zeno behaviour can be excluded by choosing parameters appropriately. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed protocols.

Adaptive output feedback event-triggered consensus control for networked reaction-diffusion PDE systems

This paper explores the adaptive output feedback event-triggered consensus control of a network of parabolic systems modelled by partial differential equations (PDEs). An infinite-dimensional state observer is established to estimate the state based on the relative output information. On the basis of the adaptive state observer, two novel distributed event-triggered controllers are proposed to address the leaderless consensus and leader-follower consensus problem. Based on the Lyapunov method and PDE theory, it is shown that the asymptotic consensus control can be achieved. Compared to the related works, a distinctive feature of the designed event-triggered consensus protocols is fully distributed which does not demand any global information of the graph. In addition, the absence of Zeno behaviour is demonstrated. Lastly, the obtained results are demonstrated using two simulations.

Event-triggered consensus control method with communication faults for multi-UAV

This paper investigates the event-triggered consensus for a group of unmanned aerial vehicles (UAVs) with communication faults under the assumption that the position sensors of some individuals are damaged. The objective is to make the UAV group reach consensus in urgent tasks such as obstacle avoidance or evasion. Using the Lyapunov stability theory, sufficient conditions to achieve system consensus are given based on different velocity and position interaction topologies. Considering the limited capabilities of sensors and processors, an event-triggered consensus protocol is adopted to reduce the sampling frequency. Finally, simulation results illustrate the effectiveness of our approach.

Sampled-Data Consensus Protocols for a Class of Second-Order Switched Nonlinear Multiagent Systems.

In this study, the sampled-data consensus problem is investigated for a class of heterogeneous multiagent systems (MASs) in which each agent is described by a second-order switched nonlinear system. Owing to the heterogeneity and the occurrence of dynamic switching in the MASs, the sampled-data consensus protocol design problem is challenging. In this study, two periodic sampled-data consensus protocols and an event-triggered consensus protocol are developed. Here, we first propose a new periodic sampled-data consensus protocol that involves the local objective trajectory interaction among agents. The protocol is then improved by applying the finite-time control and sliding-mode control techniques. Notably, the improved protocol can be implemented without the transmission of constructed auxiliary dynamical variables, which is a major feature of the present study. It is shown that complete consensus of the underlying MASs can be achieved by the two proposed protocols with only sampled-data measurements. To further reduce the communication load, we introduce an event-triggered mechanism to obtain a new protocol. Finally, the effectiveness of the given schemes is demonstrated by considering a numerical example.

Dynamic Periodic Event-Triggered Consensus Protocols for Linear Multiagent Systems With Network Delay

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.

Event-triggered consensus control for singular multi-agent systems based on observers

This paper is devoted to the problem of event-triggered consensus for a class of general linear singular multi-agent systems with undirected topology. Considering that the system states are not measurable, state observers are designed first, and then a new observer-based event-triggered sampling mechanism is proposed, which naturally avoids Zeno behavior. Furthermore, a distributed event-triggered consensus protocol is designed. By employing the Lyapunov-Krasovskii functional method and model transformation approach, sufficient conditions are obtained such that the consensus of the singular multi-agent systems can be achieved, while the explicit dynamic expression of the consensus function is also given. Finally, a numerical example is included to illustrate the effectiveness of the proposed results.

Event-Triggered Bipartite Consensus for Fuzzy Multiagent Systems Under Markovian Switching Signed Topology

In this article, we study the problems of bipartite and cooperative consensus with a strictly dissipative performance for fuzzy multiagent systems (MASs) in a unified framework. First, we prove that bipartite consensus over a structurally balanced signed graph is equivalent to cooperative consensus over the corresponding unsigned graph by leveraging the gauge transformation for a class of nonlinear MASs. Then, a polynomial fuzzy model is constructed to describe the nonlinear MAS formed by one leader and followers. For mitigating communication and computational load, a mode-dependent event-triggered transmission strategy is proposed. By establishing the switching topologies through Markovian process, a new sampled-data event-triggered consensus protocol is designed. With a mode-dependent Lyapunov–Krasovskii function, a novel relaxed dissipative criterion is obtained. The criterion guarantees that all agents can achieve both event-triggered cooperative consensus and event-triggered bipartite consensus with the same magnitude but opposite signs for MASs over structurally balanced signed directed graphs and Markovian switching topologies. Moreover, the event-triggered parameters and consensus control gains can be numerically solved via the sum-of-squares method. Simulation results are given to show the effectiveness of the proposed design method.

On Topology Optimization for Event-Triggered Consensus With Triggered Events Reducing and Convergence Rate Improving

This brief considers the network topology optimization problem for event-triggered consensus of multi-agent systems (MASs) to reduce the triggered events and improve the convergence rate. For a MAS with an undirected graph as its communication network, edge swapping operations are applied to optimize its network topology, which keep the number of links incident to each agent unchanged. Based on the theory of graph spectra, a necessary condition is provided to determine an effective edge swapping operation which leads to less event triggered times and faster convergence rate. An iterative algorithm is developed to optimize the network topology for MASs under the first-order event-triggered consensus protocol. Finally, some numerical simulations are given to illustrate the effectiveness of the approach.

Adaptive event-triggered consensus of multi-agent systems with general linear dynamics

This paper is concerned with adaptive event-triggered consensus of general linear multi-agent systems (MASs). Leaderless consensus and leader-following consensus are both considered. In order to avoid dependence on global information about system topology and reduce communication frequency, distributed adaptive event-triggered consensus protocols are designed. Through model transformation, the consensus problems of MASs are transformed into the stability problems of the corresponding error systems. By using algebraic graph theory and Lyapunov stability theory, some sufficient criteria for MASs to achieve consensus are obtained. Meanwhile, it is proved that the proposed event-trigger conditions can exclude Zeno behaviour effectively. One simulation example is provided to validate the effectiveness of obtained theoretical results.

Distributed event-triggered consensus protocols for discrete-time multiagent systems

Abstract This paper focuses on leader-following and leaderless consensus problems of discrete-time multiagent systems. A distributed observer-based consensus protocol is proposed to investigate the consensus problem for multiagent systems of general discrete-time linear dynamics. By means of the observer, the distributed control law of each agent is designed using local information to guarantee consensus, and the corresponding sufficient conditions are obtained by exploiting graph and control theory approach. A modified distributed event-triggered consensus protocol is designed to reduce communication congestion. Detailed analysis of the leaderless and the leader-following consensus is presented for both observer-based and full-information protocols. Finally, two simulation examples are provided to demonstrate the effectiveness and capabilities of the established theories.

An event-triggered consensus protocol for quantized second-order multi-agent systems with network delay and process noise

This paper focuses on the quantized consensus problem of discrete-time second-order multi-agent systems which suffer from bounded process noise. In such systems, neighboring agents exchange information through a digital network that has only a finite bit rate and is subject to bounded network delay. Network delay may exacerbate the effects of quantization error and degrade the control performance by reducing the information to be extracted from receiving time instants of exchange packets. To handle network delay and save communication bit rates, an event-triggered distributed control protocol based on a dynamic encoding–decoding policy is proposed. Under the proposed event-triggered protocol, the asymptotic consensus of the concerned noise-free multi-agent systems can be achieved at a lower bit rate than that of periodic sampling control. This bit rate superiority results from the fact that our protocol makes use of the extra information being extracted from the event-triggering time instants. Moreover, it is shown that no higher bit rate is required to guarantee the desired consensus in the existence of bounded process noise. Simulations are done to demonstrate the effectiveness of our consensus protocol. As shown by our numerical examples, the occupied bit rate to ensure the desired consensus can be saved by up to 50% compared with periodic sampling strategies.

Output Consensus for Heterogeneous Linear Multiagent Systems With a Predictive Event-Triggered Mechanism.

In this paper, an output consensus problem for a heterogeneous linear multiagent system with a predictive event-triggered mechanism on directed graphs is investigated. An event-triggered consensus protocol is proposed by introducing an internal reference model for each agent to handle the heterogeneity existing in the system. With the proposed mechanism, each agent predicts its internal reference model's input by employing the estimate of the internal reference model's state differences between itself and its neighbor agents. As it considers the internal reference model's inputs of agents, the system requires far fewer event-triggered times to achieve consensus, leading to a significant reduction in communication cost among agents. A necessary and sufficient condition of the output consensus for the heterogeneous linear multiagent system is put forth. Furthermore, Zeno behavior can be ruled out for each agent. Some numerical examples are given to demonstrate the effectiveness of the proposed control mechanism.

Event-triggered consensus control of second-order nonlinear multi-agent systems under denial-of-service attacks

This paper investigates the event-triggered consensus problem of second-order nonlinear multi-agent systems subject to denial-of-service (DoS) attacks, which make the communication network unable to provide normal services. Considering a general class of DoS attack with limited duration, a novel distributed event-triggered consensus protocol accompanied with first-order hold is adopted to guarantee the globally bounded consensus convergence under directed network topology. Based on the linear matrix inequality approach and Lyapunov stability method, consensus converging properties are analysed and sufficient criteria are obtained. Furthermore, Zeno-free triggering of our proposed protocol is demonstrated. Finally, a numerical simulation is given to show the effectiveness of our theoretical results.

Event-triggered Consensus Control of Nonlinear Multi-agent Systems based on First-order Hold

In this paper, consensus problem is studied for the first-order nonlinear multi-agent systems under directed topology, and a novel event-triggered consensus protocol is proposed. Different from the existing results with general zero-order hold, the first-order hold is adopted to construct the event-triggered control signal so as to reduce the triggering rate. By using Lyapunov stability method and matrix theory, a sufficient consensus condition is derived for the agents to reach the asymptotic consensus, and Zeno-behavior can be avoided. Finally, a numerical example is presented to demonstrate the effectiveness of our proposed protocol.