Finite-time Consensus Problem Research Articles

Event-triggered finite-time consensus control under uncertain disturbances with fully continuous communication and chattering free

This paper focuses on event-triggered finite-time consensus problem of second-order multi-agent system, which is subjected to external bounded disturbance. First, a novel finite-time consensus control algorithm based on the event-triggering control scheme is proposed. The proposed algorithm contains a saturation function that is disturbance rejection and aims at eliminating the chattering problem caused by the discontinuity of the control algorithm in some existing work. Further, the utilization of saturation function reduces damages to the actuators and decreases energy consumptions in practical applications. Second, an event-triggering function is developed to generate the control event sequences, which is fully continuous communication free and avoids continuous update of the controller by contrast with real-time control method and continuous communication event-triggered control scheme. Third, finite-time bounded consensus can be reached with the scale of the convergence region adjusted by appropriate parameter selecting. A rigorous proof based on Lyapunov stability analysis is given to verify that the event-triggered control algorithm, under the derived conditions, solves the second-order finite-time consensus with chattering free and being robust to external disturbances as well as excluding the Zeno behavior. Finally, two simulation examples are performed to validate the effectiveness of the results.

Bipartite finite-time output consensus of heterogeneous multi-agent systems by finite-time event-triggered observer

This paper investigates the bipartite finite-time output consensus problem of heterogeneous linear multi-agent systems (HL-MASs) described by a directed signed graph. First, by combining the event-triggered mechanism and finite-time control, we propose a bipartite finite-time event-triggered observer (bipartite FT-ET observer) to estimate the leader’s state. Triggering condition is presented by introducing a dynamic variable. Compared with conventional observer to solve the output consensus problem, exact estimation of the leader’s state can be achieved by only intermitted communication among agents. Moreover, Zeno behavior can be avoided by choosing parameters appropriately. Then, we construct a finite-time controller based on bipartite FT-ET observer, such that the bipartite output consensus can be achieved in a finite time. Finally, an example is provided to illustrate the effectiveness of the results.

Finite-Time Consensus of Second-Order Switched Nonlinear Multi-Agent Systems.

In this brief, the practical finite-time consensus (FTC) problem is investigated for the second-order heterogeneous switched nonlinear multi-agent systems (MASs), where the subsystems and the switching signal for each agent are different. Mainly due to that agents' dynamics are switched and the unknown nonlinearities in the systems are more general, the practical FTC problem of the MASs is rather difficult to be solved by existing methods. As such, a new protocol design framework for the FTC problem is developed. Then, a novel adaptive protocol is proposed for the switched nonlinear MASs based on the developed design framework and the neural network method. The sufficient conditions for the practical FTC of nonlinear MASs under arbitrary switching are given. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control scheme.

Global finite-time event-triggered consensus for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs

In this paper, we mainly investigate the global finite-time event-triggered consensus problem for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs under directed network topology. Under an appropriate assumption, a novel finite-time event-triggered consensus protocol is proposed to reduce the communication burden from the controller to the actuator. Based on the backstepping method, a synthetic trigger function is derived, and it is proven theoretically that the Zeno behavior is avoided for each agent under this trigger condition. Moreover, to avoid the chattering phenomenon caused by unknown input disturbances, the hysteretic quantizers are incorporated to quantize the input signals. It is shown that the proposed finite-time event-triggered consensus protocol enables the local neighbor position error, and the velocity error between any two agents converges toward a small range of the origin in a finite time. Finally, the proposed method is validated through a numerical example.

A Game-theoretical Approach for a Finite-time Consensus of Second-order Multi-agent System

The second-order consensus problem depends on not only the topology condition but also the coupling strength of the relative positions and velocities between neighboring agents. This paper seeks to solve the finite-time consensus problem of second-order multi-agent systems by games with special structures. Potential game and weakly acyclic game were applied for modeling the second-order consensus problem with different topologies. Furthermore, this paper introduces the event-triggered asynchronous cellular learning automata algorithm for optimizing the decision making process of the agents, which facilitates a convergence with the Nash equilibrium. Finally, numerical examples illustrate the effectiveness of the models.

Finite-time Asymmetric Bipartite Consensus for Signed Networks of Dynamic Agents

This paper addresses the finite-time asymmetric bipartite consensus problem for multi-agent systems (MAS) associated with signed graphs. Different from bipartite consensus in the previous literatures, asymmetric bipartite consensus means that the states of all agents will converge to two values with different signs and modulus. Two distinct nonlinear consensus control protocols are constructed for the considered system to achieve the finite-time asymmetric bipartite consensus and the fixed-time asymmetric bipartite consensus, respectively. Under the first proposed protocol, it is shown that within a finite time, the considered system can realize asymmetric bipartite consensus. To strengthen the obtained result, the second protocol is proposed, which guarantees that all agents could achieve the asymmetric bipartite consensus in fixed time, that is, the finite-time consensus can be reached before a settling time which is irrelevant with the initial states of the agents. Finally, numerical simulations are given to verify effectiveness of the proposed consensus control protocols.

Event-triggered Finite-time Consensus with Fully Continuous Communication Free for Second-order Multi-agent Systems

This study deals with finite-time consensus problems of second-order multi-agent systems with intrinsic nonlinear dynamics and external bounded disturbances. First, instead of the time-triggered control algorithm, the event-triggered control algorithm is developed by using integral sliding mode control strategy. Then, a triggering function is explicitly constructed to generate event sequences, and the triggering function is fully continuous communication free. Rigorous proof is given by using Lyapunov stability theory and finite-time stability theory. Several conditions are derived to guarantee the finite-time consensus and exclude Zeno behavior. Finally, a simulation of single-link robotic arms is given to verify the effectiveness of the results.

Finite-time consensus of high-order heterogeneous multi-agent systems with mismatched disturbances and nonlinear dynamics

In this study, we investigate the finite-time consensus problem for a general class of high-order nonlinear heterogeneous multi-agent systems, for which not only the unknown nonlinear dynamics, mismatched disturbances but also the system orders are not required to be identical. We propose two families of consensus algorithms, and the output consensus can be achieved with them in a finite time even with nonlinear dynamics and mismatched disturbances. The Lipschitz-like condition generally required in the literature is removed in this paper. The integral sliding-mode control technique is used to construct the first family of consensus algorithms, which may cause chattering problem for the existence of high-frequency switching terms. To overcome the chattering phenomenon, a new variable-gain finite-time observer is developed to construct the second family of continuous algorithms based on a different assumption. It is shown that some existing consensus protocols can be broadened in several directions through the framework of this study; moreover, the output feedback finite-time consensus can also be solved.

Finite-Time Connectivity-Preserving Consensus for Second-Order Nonlinear Multiagent Systems

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.

Finite-Time and Fixed-Time Consensus of Multiagent Networks with Pinning Control and Noise Perturbation

In this paper we investigate the finite-time and fixed-time consensus problems of multiagent networks with pinning control and noise perturbation. In order to reach the finite-time and fixed-time c...

Event-Triggered Finite-Time Integral Sliding Mode Controller for Consensus-Based Formation of Multirobot Systems With Disturbances

This paper deals with the distributed fast and finite-time consensus problem of multiagent systems with bounded disturbances in a leader-follower-based frame work. A novel integral sliding mode-based robust finite-time event-triggered control strategy has been proposed. A fast reaching law is also utilized to improve the speed of convergence. The triggering condition is derived based on the defined novel measurement error, suited for systems with model uncertainties/disturbances. The expression for the lower bound for the interexecution time has been derived to ensure that the zeno behavior is avoided. The proposed nonlinear consensus protocol is such that the desired relative state deviation between the agents can be achieved with a directed graph topology. The theoretical results are validated through real-time experimentations done using Pioneer P3-DX as well as FireBird VI robots.

Finite-Time Bipartite Consensus for Multi-Agent Systems on Directed Signed Networks

This paper addresses the finite-time bipartite consensus problem for multi-agent systems (MASs) on a directed signed network. Some properties for signed digraphs are first investigated and two nonlinear control protocols are then designed for first- and second-order MASs, respectively, where agents may be influenced by bounded disturbances. Particularly, for MASs with second-order dynamics, a new estimation technique is developed to estimate the settling time. Simulation results are finally presented to verify the effectiveness of the proposed control protocols.

Finite-Time Consensus and Tracking Control of A Class of Nonlinear Multiagent Systems

In this technical note, we consider the finite-time consensus and tracking problems for a class of nonlinear multiagent systems with directed topology. By using the homogeneous function, we firstly give a finite-time consensus protocol for high-order linear multiagent systems. Then, we present the finite-time consensus and tracking protocols for strict feedback nonlinear multiagent systems. When state information is not available, the finite-time convergent observer is used to estimate each agent’ states, and we give the finite-time consensus and tracking protocols based on the finite-time observers.

Event-triggered sliding mode based consensus tracking in second order heterogeneous nonlinear multi-agent systems

This work targets the problem of leader following consensus in heterogeneous multi-agent systems described by second order nonlinear dynamics. The controller proposed in the study is an event-based sliding mode controller. Synthesis of the controller has been partitioned into two parts– a finite time consensus problem and an event-based control mechanism. In the first part, the leader following heterogeneous multi-agents of second order having inherent nonlinear dynamics have been addressed and a novel sliding mode reaching law based on inverse sine hyperbolic function has been designed to drive the agents towards consensus. In the second part, an event-based implementation of the control law has been incorporated to minimize computational load on the computational device equipped with the agents and reduce energy expenditure. The triggering rule proposed in this work is dynamic and taking samples respecting this rule ascertains that the desired closed-loop performance of the system is not compromised while exhibiting robustness and high efficacy. The advantage of using such a scheme, i.e., an event-based sliding mode controller is rooted in the robustness capabilities of sliding mode controller and reducing computational expenses via event-based mechanisms. Numerical simulations and mathematical foundations confirm the effectuality of the controller proposed in this study.

Finite-time consensus of input delayed multi-agent systems via non-fragile controller subject to switching topology

Abstract This paper focuses on the problem of finite-time consensus of linear multi-agent systems with input time-varying delay by employing a non-fragile control scheme, where the network topology of the communication process among agents is subject to a switching directed graph. The main intention of this paper is to propose a non-fragile controller design protocol that guarantees the finite-time stability of the resulting closed-loop system even in the presence of time-varying delay in the input channel. Sufficient conditions for the solvability of such a problem are obtained by using the Lyapunov–Krasovskii stability theory, the algebraic graph theory and some integral inequalities. Based on the obtained conditions, an explicit expression of the desired non-fragile control gain matrix is then presented. Finally, an illustrative example is given to exhibit the applicability and effectiveness of the proposed finite-time consensus control design method.

Finite-time leaderless consensus of uncertain multi-agent systems against time-varying actuator faults

Abstract This paper addresses the finite-time leaderless consensus problem for a class of continuous-time multi-agent systems subject to linear fractional transformation uncertain parameters using an observer-based fault-tolerant controller. Here, it is considered that the network of the system is described by an undirected graph subject to fixed topology and the aforementioned controller is impacted by time-varying actuator faults. Then, the desired consensus protocols are proposed in such a way that the effects of possible uncertainties and actuator faults are compensated efficiently within a prescribed finite-time period. More precisely, the leaderless consensus analysis is carried out in the framework of Lyapunov-Krasovskii functional and the required conditions for the existence of proposed fault-tolerant controller are derived in terms of linear matrix inequalities. Moreover, the proposed consensus design parameters can be computed by solving a set of linear matrix inequality constraints. Finally, two examples including a formation flying satellites model are provided to show the efficiency and usefulness of the proposed control scheme.

Consensus in first order nonlinear heterogeneous multi-agent systems with event-based sliding mode control

ABSTRACT This article is aimed at solving leader-following consensus problem with an event-based sliding mode controller. The proposed control technique is partitioned into two parts – a finite time consensus problem and an event-based control mechanism. Leader-following heterogeneous multi-agents of first order having inherent nonlinear dynamics have been analysed to demonstrate efficacy and robustness of the proposed controller. In the first part, states of the follower agents have been attempted to be kept in consistence with those of the virtual leader using sliding mode control. In the second part, an event-based implementation of the control law has been incorporated to minimise the computational load on, and energy expenditure of the computational device equipped with the agents, while ensuring that the desired closed-loop performance of the system is not compromised. The advantage of using such a scheme, i.e. an event-based sliding mode controller, lies in the robustness capabilities of sliding mode controller and reduced computational expense of event-based mechanism. Numerical simulations and mathematical foundations ascertain the effectuality of the controller proposed herein.

Finite-time median-related group consensus over directed networks

ABSTRACTIn this paper, we investigate a novel finite-time median-related group consensus problem, where the finial consensus value can be identified as a desired function of the median of initial states instead of the much studied average value. The underlying communication topology is modelled by a weighted dynamical directed network. A distributed control protocol is firstly introduced to ensure that the agents can reach a median-related consensus in finite time in a collaboration network, meaning that all edge-weights of the communication network are non-negative. We then generalise the results to cooperation–competition networks, where the communication network is divided into predetermined collaboration subnetworks allowing possibly negative weights. Effective group control protocols are designed to guarantee the median-related group consensus in finite time. Finally, numerical simulations are presented to illustrate the availability of our theoretical results.

Adaptive finite-time consensus of a class of disturbed multi-agent systems

In this paper, the finite-time exponential consensus problem is addressed for a class of multi-agent systems against some disturbed factors, which include system uncertainties, communication perturbations, and actuator faults. All disturbed factors are supposed to be influenced by internal and external effects of systems. The internal effects are described in terms of dependency on the system states, while the external actions are restricted by constant bounds. To obtain the information of the rate of dependency on the states and constant bounds, an adaptive mechanism is designed to estimate the rate and bounds. Based on these estimates, a distributed adaptive sliding mode controller is constructed to eliminate the effects of those disturbed factors. Then exponential consensus of the closed-loop adaptive multi-agent system is achieved within a finite time based on Lyapunov stability theory. The efficiency of the developed adaptive consensus control strategy is verified by a coupled system with four F-18 aircrafts of decoupled longitudinal model.

Finite-time consensus for nonlinear multi-agent systems with time-varying delay: An auxiliary system approach

This paper investigates the finite-time consensus problem of uncertain nonlinear multi-agent systems with asymmetric time-varying delays and directed communication topology. An auxiliary system is firstly designed to deal with the continuous or discontinuous time-varying communication delays. Based on the finite-time input-to-output framework, a novel consensus scheme relying on local delayed information exchange is proposed. Moreover, by utilizing an auxiliary integrated regressor matrix and vector method, the system uncertainties can be accurately estimated. Then the consensus of multi-agent systems can be achieved within finite time by selecting the control gains simply. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed control algorithms.