Distributed finite-time tracking of second-order multi-agent systems based on dynamic event triggering

This paper investigates the finite-time leader-following consensus problem of second-order nonlinear multi-agent systems with switching topology. The unknown nonlinearity of each agent can be formulated as the production of a known constant function vector and an unknown parameter vector. Under this circumstance, the finite-time consensus problem of the system under the switching topologies can be transferred into an finite-time adaptive tracking control problem of switched systems. This paper derives the finite-time adaptive tracking conditions on the nonlinear switched systems with unknown parameters in terms of the finite-time Lyapunov stability theory and the average dwell time technique. A novel finite-time adaptive distributed consensus control protocl is proposed to make the tracking error converge to a small neighborhood of the origin in finite time. Finally, the numerical simulations illustrate the effectiveness of the method.

Event-triggered finite-time formation control is considered for second-order leader-following multi-agent systems with nonlinear term time delay in this study. Collision avoidance radius is designed for a class of second-order nonlinear multiagent systems to avoid collisions between agents. Collision avoidance control is realised by detecting the flight radius. Control cost is economised, and communication volume is reduced by controlling key nodes and designing an event-triggered control strategy. The system can realise formation control in finite time by designing an FTC function. Some sufficient conditions for the formation of the second-order multi-agent system in finite time are obtained by using Lyapunov stability theory and analysis. The integral sliding mode control algorithm and finite-time stability theory are used to enhance the robustness of the system, and the upper bound of finite time is given. At the same time, the ability of the designed event-triggered function to avoid Zeno behaviour is proven. Finally, the feasibility of the results is verified through a numerical simulation.

In this paper, the finite-time consensus problem for second-order nonlinear multiagent systems under communication constraints is investigated, where each agent has a limited sensing range. A distributed discontinuous control protocol is proposed to make a team of agents reach consensus in finite time when disturbances exist in multiagent systems. Then, for multiagent systems without disturbances, a new piece-wise continuous protocol is presented to make the agents achieve consensus in finite time. Furthermore, it is shown that initial interaction patterns are preserved under these control protocols. Finally, some numerical examples are provided to illustrate the theoretical results.

This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.

This paper investigates the distributed finite-time consensus problem of second-order multi-agent systems (MAS) with one leader or multiple leaders in the presence of bounded disturbances. Based on the continuous homogeneous finite-time consensus protocol for the nominal MAS, the discontinuous and continuous super-twisting protocols upon integral sliding mode (ISM) algorithm are respectively developed to achieve finite-time tracking consensus of MAS with one leader and finite-time containment consensus of MAS with multiple leaders in spite of the disturbances. Simulation results illustrates the effectiveness of the proposed protocols.

Sliding-mode consensus algorithms for disturbed second-order multi-agent systems

In this paper, the finite-time output consensus problem is considered for a class of second-order multiagent systems (MASs), where the mismatched disturbance exists in the dynamics of each agent, and the communication topology is directed. First of all, a basic backstepping control protocol is proposed to solve the finite-time consensus problem without mismatched disturbance. Then, a finite-time disturbance observer is designed to estimate the mismatched disturbance, based on which, two adaptive finite-time consensus protocols are proposed to solve the finite-time output consensus and tracking consensus problems without using any global information with respect to the communication topology. Finally, two simulation examples are illustrated to verify the theoretical results.

Finite-time consensus of second-order leader-following multi-agent systems without velocity measurements

This paper studies the finite-time consensus problem for both leader-follower and leaderless second-order multi-agent systems. To solve the problem, a nonsmooth embedded control scheme is used, which is made up of two parts. In part one, for each case, based on nonsmooth control theory, a distributed virtual signal generator is designed. For the leaderless case, the outputs of the designed generator reach finite-time consensus and for the leader-follower case, virtual position and velocity signals of the designed generator track the leader's position and velocity in finite time. In part two, for each case, through embedding the generator into the feedback loop and taking its outputs (i.e., outputs for the leaderless case and virtual position and velocity signals for the leader-follower case) as the reference outputs for the agents (i.e., all the agents for the leaderless case and the followers for the leader-follower case), some tracking controllers are designed for the agents to track their reference outputs in finite time. Based on this scheme, some consensus algorithms are proposed. Under the proposed consensus algorithms, leaderless and leader-follower multi-agent systems achieve finite-time consensus. Numerical simulations verify the validity of the proposed consensus algorithms.

Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics

The study considers the problem of finite-time event-triggered H-infinity consensus for second-order multi-agent systems (MASs) with intrinsic nonlinear dynamics and external bounded disturbances. Based on the designed triggering function, a distributed event-triggered control strategy is presented on the basis of the designed triggering function to ensure consensus in the system, which effectively reduces the data transmission. Then, sufficient conditions for the finite-time consensus with H-infinity performance level of the resulting event-triggered MAS are derived by utilizing the Lyapunov function and finite-time stability theory. Furthermore, Zeno behavior is proven to be excluded under the proposed event-triggered scheme. Finally, the validity of the proposed results is verified by numerical simulation.

This paper considers the problem of finite-time synchronization for a class of second-order nonlinear multi-agent systems with a leader-follower architecture. By using the finite-time control technique and homogenous systems theory, a finite-time state feedback controller is first proposed. Then to address the lack of velocity measurement, a finite-time convergent observer is constructed to estimate the unknown velocity information in a finite time. Finally, an observer-based finite-time output feedback controller is developed. Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leader's states. In addition, for some special second-order multi-agent systems, a bounded finite-time output feedback controller can also be designed.

This article discusses how second-order nonlinear multi-agent systems achieve bipartite consensus in finite-time using intermittent event-triggered control strategies. Due to the problem arising from antagonistic links between neighboring nodes of second-order multi-agents, the finite-time bipartite consensus analysis is investigated, which is more challenging than that with only cooperative communication links. Accounting for limitations of communication bandwidths, an intermittent framework is proposed first. By utilizing algebraic graph theories and gauge transformations, sufficient conditions are given to achieve finite-time consensus in signed second-order multi-agent systems. Second, a hybrid control mechanism combining intermittent control with event-triggered control is developed. Therefore, some finite-time synchronization conditions of second-order multi-agents on signed graphs are further studied. The proposed protocol reduces the updating frequency of the controller, which saves communication resources a lot. Finally, the Zeno behavior is excluded and some numerical examples are performed to show the effectiveness of the theoretical analysis.

ABSTRACTThis article investigates the containment control problem for a class of second-order multi-agent systems with inherent nonlinear dynamics, under the common assumption that each agent can only obtain the relative information of its neighbours intermittently. A kind of distributed protocol based only on the relative local intermittent measurements of neighbouring agents is designed for containment control under fixed directed topology. In the absence of delays, based on the Lyapunov function technology and the intermittent control method, some sufficient conditions are presented to guarantee the intermittent containment control of second-order nonlinear multi-agent systems. In the presence of delays, some containment conditions are also obtained for a second-order multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Moreover, the similar results are obtained for second-order nonlinear multi-agent systems under switching directed topology. Finally, simulation examples are given to illustrate the correctness and effectiveness of the theoretical analysis.

Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics