Leader In Finite Time Research Articles

Time-varying formation finite-time tracking control for multi-UAV systems under jointly connected topologies

PurposeThe purpose of this paper is to investigate the time-varying finite-time formation tracking control problem for multiple unmanned aerial vehicle systems under switching topologies, where the states of the unmanned aerial vehicles need to form desired time-varying formations while tracking the trajectory of the virtual leader in finite time under jointly connected topologies.Design/methodology/approachA consensus-based formation control protocol is constructed to achieve the desired formation. In this paper, the time-varying formation is specified by a piecewise continuously differentiable vector, while the finite-time convergence is guaranteed by utilizing a non-linear function. Based on the graph theory, the finite-time stability of the close-loop system with the proposed control protocol under jointly connected topologies is proven by applying LaSalle’s invariance principle and the theory of homogeneity with dilation.FindingsThe effectiveness of the proposed protocol is verified by numerical simulations. Consequently, the proposed protocol can successfully achieve the predefined time-varying formation in finite time under jointly connected topologies while tracking the trajectory generated by the leader.Originality/valueThis paper proposes a solution to simultaneously solve the control problems of time-varying formation tracking, finite-time convergence, and switching topologies.

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

Cooperative Control of Mobile Sensor Networks for Environmental Monitoring: An Event-Triggered Finite-Time Control Scheme.

This paper deals with the problem of environmental monitoring by developing an event-triggered finite-time control scheme for mobile sensor networks. The proposed control scheme can be executed by each sensor node independently and consists of two parts: one part is a finite-time consensus algorithm while the other part is an event-triggered rule. The consensus algorithm is employed to enable the positions and velocities of sensor nodes to quickly track the position and velocity of a virtual leader in finite time. The event-triggered rule is used to reduce the updating frequency of controllers in order to save the computational resources of sensor nodes. Some stability conditions are derived for mobile sensor networks with the proposed control scheme under both a fixed communication topology and a switching communication topology. Finally, simulation results illustrate the effectiveness of the proposed control scheme for the problem of environmental monitoring.

Robust finite-time containment control of general linear multi-agent systems under directed communication graphs

In this paper, we study the distributed finite-time containment control problem for general linear multi-agent systems with bounded matched uncertainties under directed communication graphs. In the presence of multiple dynamic leaders, an observer-based distributed controller is proposed such that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Only relative state measurement and relative observer state information are needed in the controller design. As the special case with only one dynamic leader, robust finite-time leader-following control problem is also solved with the proposed control strategy. An application in multiple satellites flying control is used to illustrate the results.

Finite-Time Control for Robust Tracking Consensus in MASs With an Uncertain Leader.

This paper investigates the finite-time control for robust tracking consensus problems of multiagent systems with an uncertain leader for situations where the state of the considered active leader may not be measured and the directed network topology is time-varying. Based on the neighbor-based state-estimation rule and a new Lyapunov stability analysis method, a continuous and nonlinear distributed tracking protocol using only relative position information is designed, under which each agent can follow the leader in finite time if the input (acceleration) of the leader is known, and the tracking errors can converge to a bounded region in finite time if the input of the leader is unknown. In particular, a special continuous distributed tracking protocol with bounded control inputs is introduced to track the active leader in finite time. Numerical simulations are also given to illustrate the effectiveness of the theoretic results.

Finite time tracking control of higher order nonlinear multi agent systems with actuator saturation

Abstract: In this paper a distributed leader follower finite time tracking control of higher order nonlinear multi agent systems (MAS) is presented subject to actuator saturation. A saturated continuous homogeneous consensus control is developed to obtain finite time convergence. For stability of the saturated actuators the geometric homogeneity theory is used and it is proven that all the states of the followers can converge to that of the leader in finite time. Switching control is designed based on super twisting algorithm to nullify the effect of uncertainties and external disturbances. It is also ensures that the sliding surface reaches the equilibrium in finite time. The control law can be effectively used for more general higher order nonlinear agent dynamics. Simulation results verify the effectiveness of the proposed scheme.

Distributed adaptive containment control for second-order multi-agent systems via NTSM

This paper studies the distributed adaptive containment control for second-order multi-agent systems with multiple dynamic leaders and unknown external disturbances. Firstly, the distributed finite-time estimators are given for the followers to estimate the weighted average of the leaders velocities. Then, the nonsingular terminal sliding mode (NTSM) vector is designed, and two continuous distributed adaptive control laws are proposed based on the NTSM, which can not only guarantee the followers converge to an arbitrary small neighborhood of the convex hull formed by the leaders in finite time, but also eliminate the chattering. Simulation results are included to show the effectiveness of proposed method.

Distributed cooperative control design for finite‐time attitude synchronisation of rigid spacecraft

Two finite-time control algorithms are developed for distributed cooperative attitude synchronization of multiple spacecraft with a dynamic virtual leader. Each spacecraft is modeled as a rigid body incorporating with model uncertainty and unknown external disturbance. The virtual leader gives commands to some of the follower spacecraft, and the communication network between followers can be an undirected or a directed graph. By using two neighborhood synchronization error signals, a finite-time control algorithm is designed associated with adaptive mechanism such that all follower spacecraft synchronize to the virtual leader in finite time. Then, a novel estimator-based finite-time distributed cooperative control algorithm is developed by using the followers estimates of the virtual leader, and the convergence of the attitude and angular velocity errors can be guaranteed in finite time. Moreover, both of the control strategies are chattering-free for their continuous design. Simulation examples are illustrated to demonstrate the validity of the two algorithms.

Finite-time containment control without velocity and acceleration measurements

This paper studies the distributed finite-time containment control for a group of mobile agents modeled by double-integrator dynamics under multiple dynamic leaders with bounded unknown acceleration inputs. A class of distributed finite-time containment protocols is proposed without relying velocity and acceleration measurements. This kind of protocols can drive the states of the followers to track the convex hull spanned by those of the leaders in finite time under the constraint that the leaders’ acceleration inputs are unknown but bounded for all the followers. Further, by computing the value of the Lyapunov function at the initial point, the finite settling time can also be theoretically estimated for the second-order finite-time containment control problems. Finally, the effectiveness of the results is illustrated by numerical simulation.

Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration

This paper addresses the distributed finite-time tracking problem for a group of mobile agents modeled by double-integrator dynamics under a leader with bounded unknown acceleration. First, a distributed finite-time tracking protocol is designed based on both the relative position and the relative velocity measurements. This protocol can drive the states of the followers to track the leader in finite time under the constraint that the leader’s acceleration is bounded but unknown to the followers. Then, a novel position-based tracking protocol is designed and analyzed for solving the distributed finite-time tracking problem when both velocity and acceleration measurements are not available for the followers. It is theoretically proved that the followers can move to be with the leader in finite time if the network topology is undirected among the followers but has a directed path from the leader to each follower. In particular, the position-based protocol does not require the relative input information between the agents. Finally, the effectiveness of the algorithms is illustrated by numerical simulations.

Distributed finite-time attitude containment control of multi-rigid-body systems

In this paper, we study the distributed finite-time attitude containment control problem for multi-rigid-body systems with multiple stationary and dynamic leaders under directed graphs. Based upon two sliding mode observation vectors, the input torque is designed to achieve the control goal. In the regulation case, all the followers will converge into the attitude convex hull spanned by the leaders in finite time, while in the dynamic leaders case, not only the attitudes but also the attitude derivatives of the followers will converge into the convex hull of the leaders in finite time. Necessary and sufficient criteria are established for both the two protocols. Finally, all the theoretical results are illustrated by numerical simulations.

Bounded Finite-Time Coordinated Attitude Control via Output Feedback for Spacecraft Formation

AbstractIn this paper, finite-time output feedback coordinated attitude control for spacecraft formation subject to input saturation is investigated. More specifically, a finite-time observer is first designed to remove the requirement of measureable angular velocity. Rigorous proof shows the observer can achieve finite-time stability within given attractive region, which implies that the estimated values can be taken into use instead of the real angular velocity after a certain convergence time. Then, a bounded finite-time control law for the spacecraft formation is designed to render the attitude of each spacecraft to converge to reference attitude provided by the virtual leader in finite time. Finally, numerical simulation results show that the proposed schemes can guarantee the spacecraft formation achieve coordinated attitude consensus and tracking, with high accuracy and fast convergence.

Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.

Distributed finite-time containment control for double-integrator multiagent systems.

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

Distributed tracking for networked Euler-Lagrange systems without velocity measurements

The problem of distributed coordinated tracking control for networked Euler-Lagrange systems without velocity measurements is investigated. Under the condition that only a portion of the followers have access to the leader, sliding mode estimators are developed to estimate the states of the dynamic leader in finite time. To cope with the absence of velocity measurements, the distributed observers which only use position information are designed. Based on the outputs of the estimators and observers, distributed tracking control laws are proposed such that all the followers with parameter uncertainties can track the dynamic leader under a directed graph containing a spanning tree. It is shown that the distributed observer-controller guarantees asymptotical stability of the closed-loop system. Numerical simulations are worked out to illustrate the effectiveness of the control laws.

Finite-time observers for multi-agent systems without velocity measurements and with input saturations

This paper is devoted to the distributed finite-time observers for multi-agent systems, where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a first-order finite-time observer and a high-order finite-time observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers. With mild modifications of our control strategies, the foregoing results are then extended to the distributed finite-time containment control problem, where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders. Numerical simulations are presented to demonstrate the efficiency of our methods.

Iterative Consensus for a Class of Second-order Multi-agent Systems

In this paper, the problem of leader-following consensus for a class of multi-agent systems with double integrator dynamics is investigated based on an iterative learning approach. Consensus errors of individual agents are considered as the anticipation in time, based on which a distributed iterative learning protocol is proposed for the undirected networks with fixed topology to make the followers track the leader in finite time. The dynamic of the leader is assumed to be time-varying and the state information is available to only a portion of the followers. The sufficient condition for solving the consensus problem of the multi-agent system is obtained. A simulation example is provided to demonstrate the effectiveness of the proposed method.

Finite‐time tracking for double‐integrator multi‐agent systems with bounded control input

This study investigates the finite-time tracking for double-integrator multi-agent systems with bounded control input under the conditions of fixed and switching jointly reachable digraphes. In detail, two continuous distributed tracking protocols are designed to track the virtual leader in finite time with the same velocity and converging position. In particular, one introduces a special continuous distributed tracking protocol with bounded control input to track the virtual leader in finite time and reduce the chatter together. An example is also given to validate the proposed approaches.

Finite-Time Distributed Tracking Control for Multi-Agent Systems With a Virtual Leader

This paper aims at further investigating the finite-time distributed tracking control problems for multi-agent systems with a virtual leader under the conditions of fixed and switching topologies, respectively. Two continuous distributed tracking protocols are designed for tracking the virtual leader in finite time. Compared with the traditional distributed tracking protocols, the proposed distributed tracking protocols can reach consensus in finite time. In particular, to eliminate the chattering phenomenon occurred in non-Lipschitz dynamical systems, this paper introduces a saturation function to replace the original sign function in the proposed distributed tracking protocols. The improved protocols can guide all agents to track the virtual leader without chattering phenomenon in finite time for the same position. Numerical simulations are also given to validate the proposed distributed tracking protocols.

Finite‐time consensus tracking for harmonic oscillators using both state feedback control and output feedback control

SUMMARYThis paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.