Finite-time Consensus Research Articles

Finite-time consensus of nonlinear delayed multi-agent system via state-constraint impulsive control under switching topologies

Finite-time consensus of nonlinear delayed multi-agent system via state-constraint impulsive control under switching topologies

Finite-time group-bipartite consensus tracking for second-order nonlinear multi-agent systems

In this paper, the finite-time group-bipartite consensus problem for nonlinear second-order multi-agent systems (MASs) is studied. By designing the control protocol, based on the proof of the system reaching asymptotically group-bipartite consensus, the homogeneous dilation method is used to obtain sufficient conditions for all agents to reach the finite-time group-bipartite consensus. Moreover, nonlinear functions are constrained by the Lipschitz condition. In addition, two examples demonstrate the operability of the control protocol.

Fast Finite-Time Consensus for Multi-agent Systems with Diverse Topologies

Fast Finite-Time Consensus for Multi-agent Systems with Diverse Topologies

Interval consensus of variable quantity multi-agent systems under complex topology

This paper deals with the complicated tracking problem with variable quantity agents. During the tracking process, the quantity of leader agent set and follower agent set are not fixed, this lead to the dimensions of tracking error and Laplacian dynamic are time-varying. Moreover, every agent imposes boundary condition on consensus value. Specifically, two kinds of interval constraints are introduced which driving system value to desired interval. Then, the consensus analysis becomes more difficult. To solve these issues, multiple Lyapunov functions are constructed to deal with the variable quantity multi-agent tracking process. By the way, we also deal with the finite time consensus with variable quantity agents. Finally, two examples are presented to verify the interval consensus and finite time consensus algorithms.

Sliding mode-based finite-time consensus tracking control for multi-agent systems under actuator attacks

Since it is inevitable for multi-agent systems (MASs) to encounter external malicious attack in the complex network environment, this paper studies the finite-time consensus tracking (FTCT) problem of MASs with unknown follower's states via sliding mode control (SMC) in the presence of actuator attacks. First, the states of each follower can be approximated by the designed appropriate observers. Then, the FTCT problem of MASs in two stages (i.e., reaching phase and sliding motion phase) of sliding mode dynamic is discussed by introducing partitioning strategy. Besides, the lower bound for the reaching phase is analyzed to ensure the feasibility of the designed SMC. The optimization problem is then formulated and is efficiently solved by the genetic algorithm (GA). Note that the attacks considered in this paper are false data injection attacks (FDIAs). Finally, simulation results are presented to illustrate the effectiveness and applicability of the proposed control method.

Finite-Time Event-Triggered Output Consensus of Heterogeneous Fractional-Order Multiagent Systems With Intermittent Communication.

The finite-time output consensus (FTOC) issue of heterogeneous fractional-order multiagent systems (HFO-MASs) is investigated in this article. First, a new principle of finite-time convergence for absolutely continuous functions is developed if a fractional derivative inequality is satisfied. Next, in order to remove the assumption that the leader's system matrix is known to all agents in previous studies, a distributed adaptive finite-time observer is designed, which can estimate not only the leader's state but also the leader's system matrix. Then, a novel finite-time event-triggered compensator with intermittent communication is constructed to estimate the leader's state by introducing a dynamic threshold for a novel triggering function. In this case, the high frequency triggering is restrained and the triggering number is significantly reduced. The Zeno behavior does not exist by choosing parameters appropriately. In addition, two finite-time control strategies are constructed based on the above distributed observer and event-triggered compensator, respectively, to achieve output consensus in finite time. The feasibility of the proposed method is ensured by the comprehensive theoretical demonstration of the finite-time consensus stability and the analysis of the Zeno behavior. Finally, the examples are given to demonstrate the conclusion.

Distributed Finite-Time Consensus Tracking Control for Nonlinear Multi-Agent Systems With FDI Attacks and Application to Single-Link Robots

This brief considers the distributed finite-time consensus tracking control problem for nonlinear multi-agent systems with false data injection (FDI) attacks. Firstly, since instability is inevitable when false datas are injected into the researched system, a security control algorithm combining the modified coordinate transformation and the dynamic surface control (DSC) method is developed to eliminate the negative impact of FDI attacks and reduce the burden caused by iterative computations of virtual controls. Besides, there are unknown nonlinearities in the dynamics of each agent, which can not be directly handled by the traditional control design. Thus, the neural-network-based approximation technique is introduced to compensate the unknown nonlinearities. In summary, a novel controller is constructed for each agent, which guarantees the consensus of the outputs of all agents can be achieved and that all the signals of the studied system are bounded within a finite-time period. To prove the correctness of the designed security control algorithm, a simulation example of the multi-agent system composed of multiple single-link robots is presented.

Finite-Time Adaptive Consensus Tracking Control Based on Barrier Function and Cascaded High-Gain Observer

This paper studies the consensus tracking control for a class of uncertain high-order nonlinear multi-agent systems under an undirected leader-following architecture. A novel distributed finite-time adaptive control framework is proposed based on the barrier function. The distributed cascaded high-gain observers are introduced to solve the problem of robust consensus tracking with unmeasured intermediate states in multi-agent systems based on the proposed control framework. The proposed control schemes guarantee the finite-time consensus of multi-agent systems, which is proven by the finite-time Lyapunov stability and singular perturbation theory. In conclusion, numerical simulations verify the proposed control protocols’ effectiveness, and their performance advantages are shown by comparing them with another existing method.

Event-triggered finite-time consensus control of leader–follower multi-agent systems with unknown velocities

We proposed an event-triggered finite-time consensus (FTC) control scheme for second-order leader–follower nonlinear multi-agent systems (MASs) with unknowable velocities and external disturbances. Because of the immeasurable problem of system velocities, a terminal sliding mode observer (TSMO) which forces velocity errors to converge to zero in a finite time is introduced. Then, construct a distributed event-triggered control law by backstepping method, so that each follower can update the control law independently based on its state error threshold. It is demonstrated that the control scheme can achieve FTC stability and simultaneously ensure the global robustness of the system via the Lyapunov stability analysis. Meantime, the control scheme reduces frequent updates of the control law. Furthermore, there exists a positive lower bound for the inter event time sequence so that the Zeno phenomenon is rejected. In conclusion, the validity of the consensus control protocol is verified by the numerical simulations.

Fuzzy finite-time consensus control for uncertain nonlinear multi-agent systems with input delay

A fuzzy finite-time consensus control method for a class of uncertain nonlinear multi-agent systems (MASs) with input delay is developed. The Pade approximation approach and Laplace transform technology are employed to eliminate the effect of input delay. Then, the fuzzy logic systems are applied to deal with the uncertain nonlinear terms. Furthermore, a relative threshold event-triggered control scheme is established to alleviate the communication burden of the control network. Meanwhile, to ensure MASs can synchronize in finite time, an adaptive consensus control method is developed. With the proposed method, even if the MASs suffer from input delay, all followers in the MASs reach finite-time synchronization and track the virtual leader. Finally, the validity of the proposed method is illustrated by the theoretical analysis and simulation examples.

Novel Reference Trajectory-Based Finite-Time Consensus Protocols for Multiagent Systems With Non-Identical Nonlinear Dynamics

This paper investigates the finite-time consensus for second-order multiagent systems under directed networks, where each agent is described by a non-identical nonlinear system. By using the reference trajectory-based method, two novel protocols are developed for the leader-follower and leaderless cases, respectively. It is noted that the dynamical evolutions of each agent's state and the reference trajectory are coupled, and the information of reference trajectories is not allowed to transmit in the communication channels. By the developed protocols, the relative state errors among agents can converge to the origin (instead of a neighborhood of the origin) within a finite time, though there are unknown parameters in agents' dynamics. The nonlinear terms in agents' dynamics are not required to be bounded by known constants or functions, which invalidates many consensus schemes based on the sliding mode control. Using the graph theory, Lyapunov functional method and finite-time stability theory, sufficient conditions are established for the finite-time consensus of considered multiagent systems. Finally, simulation examples are given to validate the effectivity of the proposed protocols.

Fast Finite-Time Event-Triggered Consensus Control for Uncertain Nonlinear Multiagent Systems With Full-State Constraints

The fast finite-time event-triggered consensus control is investigated for a category of uncertain nonlinear multiagent systems (MASs) with full-state constraints. The uncertainty of the system is estimated by the radial basis function neural networks (RBFNNs). Furthermore, to achieve the fast finite-time stability and not violate the full-state constraints, a fast finite-time event-triggered consensus control method is proposed. The proposed control method can achieve the fast finite-time stability of the system, and all the followers can track the output signal of the leader. Meanwhile, the system states do not exceed the boundaries of the full-state constraints, and the communication resources of the system can be saved. Finally, some simulation examples are provided to verify the feasibility of the proposed approach.

Fast Finite-Time Tracking Consensus With Applications on Multiple Servo Motors

This article focuses on the fast finite-time tracking consensus for uncertain nonlinear multiagent systems. By gracefully combining the hierarchical decomposition, adding a barrier power integrator and disturbance compensation techniques, a new adaptive fast finite-time controller is proposed. Compared with the existing works, the proposed method has several distinguishing features: 1) It can achieve fast finite-time convergence with full state constraints; 2) it can deal with some fully unknown nonlinearities and state-dependent disturbance. Moreover, the nonlinearities can be related with the states of all the followers; 3) the input of the leader is not required to be zero, meaning a broad class of references signals can be generated; and 4) the controller is computationally simply and ready to be implemented. No fuzzy logic/neural networks are needed. Applications of the proposed method on multiple servo motors are also studied.

Stability and Robustness Analysis of Finite-Time Consensus Algorithm for Second-Order Multiagent Systems Under Sampled-Data Control

The consensus problem for second-order multiagent systems based on nonsmooth sampled-data control is considered. First, a continuous-time nonsmooth consensus protocol is proposed, which can realize the consensus of systems in a finite time when the external disturbance is absent. Next, based on the sampled data and the zero-order holder, a new discrete-time nonsmooth protocol is proposed. Considering external disturbances, the explicit relationship between the ultimate boundary of errors of any two agents and the sampling period and external disturbance is given with the Lyapunov method and graph theory, which theoretically shows that the nonsmooth control algorithm has a stronger ability to resist external disturbance than the smooth control algorithm. Finally, a simulation example shows the superiority of the nonsmooth consensus algorithm over a smooth consensus algorithm.

Adaptive Fuzzy Output-Feedback Consensus Tracking Control of Nonlinear Multiagent Systems in Prescribed Performance.

This article addresses the finite-time consensus tracking control problem for nonlinear multiagent systems (MASs), in which state variables are unmeasured and nonlinear functions are totally unknown. An observer is designed to estimate state variables and fuzzy-logic systems are employed to approximate nonlinearities. Then, an observer-based adaptive fuzzy consensus tracking controller is developed by using the backstepping technique and constructing a novel barrier Lyapunov function with the consideration of the characteristics of MASs. The proposed control protocol can guarantee that: 1) all signals in the closed-loop system keep bounded and 2) the consensus tracking error converges to a prespecified region of the origin in the prescribed finite time. Compared with the existing observer-based finite/fixed-time control protocols, the settling time and the convergence region in our work can be both preassigned by the designer and not affected by the unknown positive constant, which lies in the Lyapunov derivative inequality. Finally, two comparison simulation examples, including a numerical example and a practical example, check the availability of the designed control scheme.

Dynamic gain scheduling control design for linear multiagent systems subject to input saturation

This paper considers the finite-time bipartite consensus problem governed by linear multiagent systems subject to input saturation under directed interaction topology. Due to the existence of input saturation, the dynamic performance of linear multiagent systems degrades significantly. For the improvement of the dynamic performance of systems, a dynamic gain scheduling control approach is proposed to design a dynamic Laplacian-like feedback controller, which can be obtained from the analytical solution of a parametric Lyapunov equation. Suppose that each agent is asymptotically null controllable with bounded control, and that the corresponding interaction topology of the signed directed graph with a spanning tree is structurally balanced. Then the dynamic Laplacian-like feedback control can ensure that linear multiagent systems will achieve the finite time bipartite consensus. The dynamic gain scheduling control can better improve the bipartite consensus performance of the linear multiagent systems than the static gain scheduling control. Finally, two examples are provided to show the effectiveness of the proposed control design method.

Iteratively distributed instrumental variable-based pseudo-linear information filter for angle-only tracking

This paper presents a distributed filtering problem for three-dimensional angle-only target tracking (AOTT) in sensor (i.e., observer) networks. An instrumental variable-based pseudo-linear information filter (IVIF) is firstly derived on the basis of the designed bias-compensated pseudo-linear information filtering, with the help of summation forms of information quantities and bias compensation in a centralized fusion manner. Then, the distributed IVIF (DIVIF) is put forward by using finite-time average consensus to obtain the arithmetic means of defined information quantities and compensated bias in observer networks, which ensures that the filtering result of every observer is consistent with the centralized one. Finally, the iteratively DIVIF is proposed via gradually approaching the true values of relative distance and the corresponding angles between the target and every observer to get the filtering parameters more and more accurately, in order to achieve higher filtering precision. In addition, the computational complexity of the proposed method is also analyzed. The advantages of filtering precision of the proposed method over the existing pseudo-linear Kalman filter and its variants are demonstrated by an AOTT example in observer networks in terms of iteration steps, different levels of process noises and observer’s accuracy.

Distributed finite-time neural network observer-based consensus tracking control of heterogeneous underwater vehicles

This note scrutinizes the distributed finite-time tracking problem of heterogeneous multi-agent systems with uncertain dynamics and environmental disturbances. To estimate the exogenous disturbances, an adaptive neural network-based disturbance observer is developed in which the approximation error of the neural network is compensated using adaptation laws. Based on finite-time stability theory, a distributed finite-time observer is proposed for each follower in order to estimate the leader's position. Moreover, an adaptive dynamic sliding mode-based controller is also developed for each follower, which ensures finite-time convergence of the tracking error between the leader and the follower. Incorporating adaptive control into the developed composite control structure leads to reducing the chattering, as well as enhancing the robustness and accuracy. Stability analysis and finite-time convergence of the tracking error are performed using the Lyapunov theory and multiple time scale principle, respectively. Finally, simulations and comparisons are performed in order to verify the effectiveness of the developed control algorithm for a group of autonomous underwater vehicles (AUVs).

Asymptotic and Finite-Time Semistability for Nonlinear Discrete-Time Systems With Application to Network Consensus

This article focuses on semistability and finite-time semistability analysis and synthesis of discrete-time dynamical systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this article, we build on the theories of semistability and finite-time semistability for continuous-time dynamical systems to develop a rigorous framework for discrete semistability and discrete finite-time semistability. Specifically, Lyapunov and converse Lyapunov theorems for semistability and finite-time semistability are developed, and the regularity properties of the Lyapunov function establishing finite-time semistability are shown to be related to the settling time function capturing the finite settling time behavior of the dynamical system. These results are then used to develop a general framework for designing semistable and finite-time semistable consensus protocols for discrete dynamical networks for achieving multiagent coordination tasks asymptotically and in finite time. The proposed controller architectures involve the exchange of generalized energy state information between agents guaranteeing that the closed-loop dynamical network is semistable to an equipartitioned equilibrium representing a state of consensus consistent with basic thermodynamic principles.

Prescribed Performance-Based Finite-Time Consensus Technology of Nonlinear Multiagent Systems and Application to FDPs

This brief focuses on an adaptive bipartite consensus issue for nonlinear multi-agent systems (MASs) over signed digraphs from a new way. A new distributed control algorithm, named finite-time prescribed performance control is designed by applying prescribed performance function (PPF) and a novel first-order filter, which not only guarantees that the bipartite consensus errors converge to a prescribed compact set at a finite time, as well as enables the system to achieve the prescribed performance and fast finite time convergence. Furthermore, the neural networks (NNs) are introduced to deal with the continuous unknown nonlinearity and the effect of non-strict feedback structure that exist in the system, and the dynamic surface control (DSC) mechanism applying a novel first-order filter is used to overcome the “explosion of complexity” problem during a controller design process. Simulation experiment of forced damped pendulums (FDPs) is included to show the feasibility of the theoretical works.