Event-Triggered Control for Multi-Agent Systems using Consensus Protocol

An adaptive neural network (NN) event-triggered control scheme is proposed for nonlinear nonstrict-feedback multiagent systems (MASs) against input saturation, unknown disturbance, and sensor faults. Mean-value theorem and Nussbaum-type function are invoked to transform the structure of the input saturation and overcome the difficulty of unknown control directions, respectively. On the basis of the universal approximation property of NNs, a nonlinear disturbance observer is designed to estimate the unknown compounded disturbance composed of external disturbance and the residual term of input saturation. According to the measurement error defined by control signal, an event-triggered mechanism is developed to save network transmission resource and reduce the number of controller update. Then, an adaptive NN compensation control approach is proposed to tackle the problem of sensor faults via the dynamic surface control (DSC) technique. It is proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, simulation results demonstrate the effectiveness of the presented control strategy.

This paper studies the consensus problem for multi-agent systems with quantised information communication via event-triggered control. First, the asynchronous event-triggered control for multi-agent systems is considered based on distributed uniform-quantised protocols. It is shown that practical consensus among agents is guaranteed and occurrence of Zeno behaviour is prevented under the designed event-triggering mechanisms. Second, under the proposed protocols using logarithmic quantised information, both synchronous and asynchronous event-triggered control algorithms are given to solve the practical consensus problem. Meanwhile, Zeno behaviour of the closed-loop systems can be excluded under the proposed event-triggered algorithms. Finally, numerical simulations are given to illustrate the effectiveness of the derived results.

We propose two distributed dynamic triggering laws to solve the consensus problem for multi-agent systems with event-triggered control. Compared with existing triggering laws, the proposed triggering laws involve internal dynamic variables which play an essential role to guarantee that the triggering time sequence does not exhibit Zeno behavior. Some existing triggering laws are special cases of our dynamic triggering laws. Under the condition that the underlying graph is undirected and connected, it is proven that the proposed dynamic triggering laws together with the event-triggered control make the state of each agent converges exponentially to the average of the agents' initial states. Numerical simulations illustrate the effectiveness of the theoretical results and show that the dynamic triggering laws lead to reduction of actuation updates and inter-agent communications.

An output-feedback-based decentralized controller that uses event-triggered communication is developed for the leader-follower consensus problem. An observer is designed to estimate the state of each agent, and the estimated state is communicated to its neighboring agents for interaction. To eliminate continuous inter-agent communication, another estimators that estimate the states of neighboring agents are designed for control feedback and are updated via intermittent communication to reset increasing estimate errors. The communication times are based on an event-triggered strategy and are adapted based on the interplay between the control performance and the amount of reduced communication. The main contribution of the developed triggering approach is that inter-agent communication is not required to determine when a state update is needed. Since the developed control scheme introduces switched dynamics, analysis is conducted to indicate that Zeno behavior does not exist. A convergence analysis is also conducted to show bounded convergence of the developed control methodology.

In this paper the suboptimal event-triggered control problem of multi-agent systems is studied. Firstly the combinational measurement approach is presented. Compared with the existing works, agents are only triggered at their own event time instants in this approach, which reduces the amount of controller updates in practice. Then based on the convergence proof of the system, we have investigated the system average cost and proposed a suboptimal approach to determine the triggering condition. The effectiveness of the proposed strategy is illustrated by numerical examples.

Event-triggered control for multi-agent systems with randomly occurring nonlinear dynamics and time-varying delay

This article addresses the reset observer-based event-triggered consensus control problem of multi-agent systems (MAS) with directed network and disturbances. Reset observer is developed instead of traditional observer, which contains an additional reset element. The reset element contributes to accelerating convergence rate of the estimation errors. An improved dynamic event-triggering mechanism (ETM) is developed, and it is rigorously prove that the developed dynamic ETM leads to larger inter-event times than the current results, and Zeno triggering behavior is ruled out by adding an exponential term in the ETM. Then, a hybrid dynamic model, is established for the MAS. On the basis of the hybrid model, whether the developed reset observer based controller can guarantee consensus property and the explicit form of event conditions are given. It is shown that convergence performance is enforced in contrast with linear observer-based approaches. Finally, the reset observer based design is illustrated by numerical simulation.

Fuzzy Adaptive Event-triggered Control of Multi-agent Systems With Command Filter

Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The controller updates considered here are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation is considered first and then its distributed counterpart, in which agents require knowledge only of their neighbors' states for the controller implementation. The results are then extended to a self-triggered setup, where each agent computes its next update time at the previous one, without having to keep track of the state error that triggers the actuation between two consecutive update instants. The results are illustrated through simulation examples.

Consensus problem with faster convergence rate of consensus problem has been considered in this paper. Adding more edges such as that connecting each agent and its second-nearest neighbor or changing the consensus protocol such as mixing asymptotic terms and terms of finite-time has been proved to be possible ways in increasing the convergence rate of multi-agent system in this paper. Based on analysis of Laplacian matrix, increasing of the convergence rate has been proved using the second-smallest eigenvalue for the first method. Concerning the second method, advantages of asymptotic consensus protocol and finite-time consensus protocol have been mixed together with the help of homogeneity function and theory of Lyapunov. Simulation results using matlab are also presented to illustrate the newly designed consensus protocols in increasing the convergence rate.

Inspired by the encirclement behavior of dolphins to entrap fishes, we investigate the bionic encirclement control by employing the bearing rigidity theory. To begin with, we transform the encirclement problem into target formation with time-varying bearing constraint. Then, to achieve a dynamic circle to entrap the target as well as gradually tighten the encirclement, we propose a distributed control law by combining orthogonal projection operator and the consensus protocol. In addition, we analyze the stability of the coordination tasks by using Lyapunov method and small-gain theorem. Moreover, we figure out that the shrinkage of the formation scale is according to exponential law and also provide the estimates of the tightening rate. Finally, simulation results are given to verify the theoretical analysis.

In this article, the adaptive finite-time consensus problem is discussed for uncertain nonlinear multiagent systems. In contrast with the correlative literature, the systems permit multiple uncertainties (not only in control coefficients but also in inherent nonlinearities), and typically the consensus protocol is pursued in a fully distributed fashion (independent from any global information of network topology). This essentially challenges the realization of the finite-time consensus. To overcome the challenge, a new continuous fully distributed protocol is proposed by combining adaptive techniques such that the finite-time consensus of the systems under investigation is achieved. Remarkably, a dynamic high gain, rather than multiple ones in the related literature, is adequate to resist two kinds of uncertainties and to guarantee the fully distributed fashion of the consensus protocol. Moreover, the adaptive finite-time consensus protocol is specified on the scenario of leader-following multiagent systems. Simulation results of three interaction topologies are acquired to illustrate the validity and the wider applicability of the proposed protocol.

The purpose of this paper is two-fold. First, the smoothness of the distributed consensus control (DCC) protocols of multi-agent systems (MAS) with inherent nonlinear dynamics is investigated. Different from the traditional consensus protocols where variable structure control is considered for robust control, a continuous DCC is presented to achieve consensus tracking without control chattering. Using certain types of exponential functions, it is shown that different smooth DCC schemes can be constructed to achieve asymptotic consensus tracking with smooth control input for MAS with connected directed/undirected and fixed/switched communication topologies. Second, the formation control problem of nonholonomic wheeled mobile robots (WMR) is solved via the continuous DCC. By converting the formation problem into consensus problem using the agents’ kinematics, the formation speed-control problem in planar motion is formulated and solved. The translational and rotational speeds inputs to the WMR are computed using continuous distributed consensus protocols to reduce chattering in the control inputs of mobile robots. The distinctive feature of the proposed consensus and formation algorithms is the high tracking precision with smooth control input to agents’ dynamics. In simulation studies, different numerical examples are illustrated to demonstrate the performance and effectiveness of the proposed DCC.

This article devotes a practical finite‐time sampled‐data output consensus investigation for a class of nonlinear multiagent systems with unavailable velocities and undirected topology via output feedback. Noticing that the focused multiagent system features nonlinearities with non‐Lipschitz restriction, and the outputs of the agents are detectable only at the sampling instants, a reduced‐order observer with the sampled output measurement is established for each follower to evaluate the unavailable velocity, and the distributed finite‐time sampled‐data consensus protocols, which are constructed by the established reduced‐order observer as well as the sampled output measurement of the agents, are developed by combining the techniques of adding a power integral and backstepping. By selecting a suitable Lyapunov function candidate, we can verify that the developed sampled‐data consensus protocols which work under the allowable sampling period and the appropriate design parameters can solve the considered practical finite‐time output consensus problem. Finally, two simulation examples, include a numerical and an engineering simulations, are provided to reveal the effectiveness and availability of the proposed consensus scheme.

This paper addresses the finite-horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus problem for general discrete time-varying multi-agent systems with energy-bounded external disturbances and limited network bandwidth resource. A dynamic event-based learning approach is proposed to produce a dynamic discrete-time event-triggered scheme and a dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol. Based on the local state information, the dynamic distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus protocol is developed to guarantee the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> consensus of the general discrete time-varying multi-agent systems with external disturbances. Besides, a novel criterion is established by employing the Lyapunov theory and considering the special dynamic triggering constraint, and the corresponding recursive learning algorithm is developed. In contrast with the previous works, the proposed dynamic event-based approach results in less network bandwidth utilization, and the novel recursive algorithm brings less conservatism of the designed controller. Finally, the effectiveness of the corresponding algorithm and the advantages of the proposed dynamic event-based approach are testified by a numerical simulation.