Leader In Finite Time Research Articles

Event-Triggered Adaptive Finite-Time Containment Control for Fractional-Order Nonlinear Multiagent Systems.

This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders' trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.

Finite-time robust formation control of multiple aerial robotic vehicles with uncertainties and time-varying complex perturbations

Formation control of aerial robotic vehicles (ARVs) has a wide range of applications in the battlefield reconnaissance, medical rescue and load transportation, etc. System parameter variations and complex disturbances are inevitable in the formation control of ARVs, and the effects of them on the formation stability control of ARVs are unnegligible. This paper addresses the robust formation control problem of finite-time leader–follower for multiple ARVs suffering from parameter uncertainties and time-varying perturbations. To ensure the states (e.g. position and velocity) of all followers to converge to leader in finite time, a novel finite-time high-order sliding mode consensus control (HOSMCC) scheme is designed. To better cope with the parameter uncertainties and time-varying disturbances, improve formation control accuracy and achieve the robust formation control of finite-time leader–follower in multiple ARV systems, a new finite time high-order sliding mode formation control (HOSMFC) scheme on the basis of finite-time HOSMCC is proposed. The finite-time stability of multi-ARV formation control system is guaranteed, and the desired formation pattern of multi-ARV systems is achieved using Lyapunov stability theorem. Performance comparisons with proportional differential formation controller (PDFC) and sliding mode formation controller (SMFC) are studied on a four-ARV formation control system. The results validate the designed formation control scheme.

Robust adaptive finite-time containment control for nonlinear multi-agent systems with unknown input saturations

In this article, the distributed adaptive finite-time containment control problem is investigated for nonlinear multi-agent systems with unknown input saturations. Since the leaders are only available to partial subsystems, a distributed estimator is designed to estimate the local reference signals. The saturated function is converted to the combination of a linear part and a nonlinear part, thus overcomes the difficulties caused by unknown saturated bounds. By utilising the command filtered and backstepping control techniques, a two-step method is adopted to construct the controller, under which the effect of unknown input saturations can be compensated well. It is proved that the closed-loop system is practical finite-time stable, and the output of each follower can converge to the dynamic convex hull spanned by the leaders in finite time. Finally, a group of four one-link manipulator systems is used to support the feasibility of the developed control scheme.

Finite-time tolerant containment control for IT2 T–S fuzzy network multi-agent systems with actuator faults, packet dropouts and DoS attacks

This article studies finite-time tolerant containment control issue for uncertain nonlinear networked multi-agent systems (MASs) with actuator faults, denial-of-service (DoS) attacks and packet dropouts, under the framework of interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy method. Firstly, based on establishing the actuator fault models and introducing Bernoulli random distribution to represent the packet dropouts phenomenon, the IT2 T–S fuzzy network MASs under actuator faults and packet dropouts are constructed as switchable systems according to the attack situations on the communication channels. Secondly, the slack matrix with more information of lower and upper membership functions is introduced in the stability analysis to reduce conservatism. And on basis of Lyapunov stability theory and average dwell-time method, finite-time tolerant containment control protocol is proposed, which makes the follower’ states converge to the convex hull controlled by the leaders in finite time. Finally, the effectiveness of the control protocol designed in this article is verified by numerical simulation.

Distributed containment control for multiple ocean bottom flying nodes with velocity error constraint and input saturation

This paper uses the directed communication topology to investigate the finite-time error constraint containment control for multiple Ocean Bottom Flying Node (OBFN) systems with thruster faults. The OBFN is a benthic Autonomous Underwater Vehicle (AUV), which has been used to explore submarine resources. The model uncertainties, velocity error constraint, external disturbances, and thruster faults of OBFNs motivate the design of containment controller. Moreover, some followers could obtain the states of leader OBFNs. We designed the command filter and the input signal is a hyperbolic tangent function. The virtual velocity error command is generated to follow the velocity error. Then the novel velocity error constraint distributed control algorithm is developed. Furthermore, for the problem of input saturation, by designing a stable anti-saturation compensator, an improved containment algorithm is proposed. It is proved that both the proposed approaches can converge the containment errors towards zero through Lyapunov theory in finite time, which means the followers can reach the convex hull formed by leaders in finite time. Finally, simulation results demonstrate the effectiveness of the two strategies.

Finite-Time Containment Control for Nonlinear Multi-Agent Systems Based on High Order Sliding Mode

Several finite-time containment control issues under stationary and dynamic leadership are the main emphasis of this thesis, which is concerned with a typical class of second-order nonlinear multi-agent systems susceptible to outside intervention. According to a given network topology, the second-order super-twisting sliding mode control is a technique for distributed control that has been developed. In this paper, we mainly consider the situation that the leader moves at a uniform speed. With the proposed method, the followers update status in real time via communication with each other such that all of them are able to eventually converge to the convex hulls consisting of stationary leaders and dynamic leaders in finite time. It leads to make the followers remain stationary or keep moving within the designed region. Eventually, according to the matrix theory and finite-time stability theorem, the paper proves the stability of the finite-time on the proposed control protocol and validates its effectiveness and correctness through simulation.

Finite time time‐varying formation tracking for second‐order multiagent systems with prescribed transient performance

AbstractThis paper studies the finite time output formation tracking for a class of second‐order multiagent systems subject to prescribed transient performance. The considered leader–follower time‐varying formation tracking is realized under a directed communication topology. First, a performance function is introduced into a time‐varying barrier Lyapunov function (TV‐BLF) for the purpose of shaping the transient behavior. Then, based on the TV‐BLF and adding a power integrator technology, a distributed formation control law is constructed such that all followers can form a predefined formation pattern while tracking the leader in finite time with satisfied transient performance. Moreover, a robust term is designed in the proposed controller to improve the disturbance rejection capability of the formation system. Finally, a simulation example is carried out to verify the effectiveness and superiority of the presented formation control protocol.

Finite-Time Consensus of Nonlinear Multiagent Systems With Nonidentical Input Delays via Event-Triggered Observer

In this article, the finite-time consensus problem is investigated for a group of heterogeneous nonlinear multiagent systems with input delays. Different from the existing results, input delays are assumed to be nonidentical and time-varying. To overcome the difficulty of nonidentical input delays, a novel compensation mechanism is introduced. Moreover, in order to save communication resources, a distributed finite-time self-triggered observer is constructed. By employing the observer and the dynamic surface control strategy, the finite-time adaptive neural control protocol is proposed. It is proved that not only the followers’ outputs can be synchronized with the leader in finite time, but also continuous communication among followers is avoided. Finally, two simulation examples are provided to illustrate the validity of the proposed control strategy.

Distributed Adaptive Finite-Time Bipartite Containment Control of Linear Multi-Agent Systems

Predefined the problem of finite-time bipartite containment control for heterogeneous linear multi-agent systems under directed topokogy. By designing a distributed bipartite compensator, the problem of bipartite containment can be considered as the problem of cooperative output regulation. Adaptive protocols are put forward by allocating a time-varying coupling weight to each follower. We thereby raise the distributed dynamic state feedback protocols combined with adaptive control, by which followers are driven to move to convex hull spanned by leaders in finite time. Furthermore, by employing the method of Lyapunov function, some plentitude criteria are inferred to pledge adaptive finite-time bipartite containment of heterogeneous agents. The final simulation examples proof the feasibility of the desired theoretical results.

Finite-time robust containment control for autonomous surface vehicle with input saturation constraint

In this paper, a finite-time containment robust control scheme is proposed for autonomous surface vehicle with input saturation constraint. Firstly, to achieve finite-time containment control, a saturated distributed equivalent control algorithm is proposed based on the position and velocity measurements of neighbors and a part of leaders; In light of the tools from algebraic graph theory and homogeneous theory, it is theoretically proven that all the follower will converge to the convex hull formed by the virtual leaders in finite-time; Then, in order to suppress the influence of external disturbance, a nonlinear integral sliding mode surface based on equivalent control law is designed. Combined with finite-time Lyapunov stability theory, a finite-time cooperative control law is proposed, which makes the system tend to sliding surface in finite-time from any initial state; Finally, simulation results are presented to verify the effectiveness of the proposed control scheme.

Finite-time observer based tracking control of uncertain heterogeneous underwater vehicles using adaptive sliding mode approach

In this study, a finite-time consensus tracking problem is investigated for a group of autonomous underwater vehicles (AUVs) with heterogeneous uncertain dynamics. We firstly propose a two-layer distributed control strategy, which consists of an upper-layer distributed observer and a lower-layer controller, without using any global information. Based on Hölder’s inequality and the theory of finite-time stability, a distributed finite-time observer is developed for each follower to estimate the position information of a leader (i.e., an exosystem). Based on the sliding mode control method, a consensus tracking control scheme is designed for each AUV, by which all follower AUVs can track the leader in finite time. Secondly, when the parameters in the AUV dynamics are uncertain, a parameter-adaptive sliding mode control algorithm is introduced to improve the control performance. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control algorithms.

Observer-Based Fuzzy Adaptive Finite-Time Containment Control of Nonlinear Multiagent Systems With Input Delay.

This article is concerned with the finite-time containment control problem for nonlinear multiagent systems, in which the states are not available for control design and the control input contains time delay. Fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear functions and a novel distributed fuzzy state observer is proposed to obtain the unmeasured states. Under the framework of cooperative control and finite-time Lyapunov function theory, an observer-based adaptive fuzzy finite-time output-feedback containment control scheme is developed via the adaptive backstepping control design algorithm and integral compensator technique. The proposed adaptive fuzzy containment control method can ensure that the closed-loop system is stable and all followers can converge to the convex hull built by the leaders in finite time. A simulation example is provided to confirm the effectiveness of the proposed control method.

Cooperative Tracking Control of Heterogeneous Mixed-Order Multiagent Systems With Higher-Order Nonlinear Dynamics

This article investigates a class of finite-time cooperative tracking problems of heterogeneous mixed-order multiagent systems (MASs) with higher-order dynamics. Different from the previous works of heterogeneous MASs, the agents in this study are considered to have different first-, second-, or even higher-order nonlinear dynamics. It means that, according to different tasks and situations, the following agents can have nonidentical orders or different numbers of states to be synchronized, which is more general for the practical cooperative applications. The leader is a higher-order nonautonomous system and contains full state information to be synchronized for all agents with mixed-order dynamics. Accordingly, the spanning tree is defined based on the specific state rather than on the agent to guarantee that each following agent can receive adequate state information. Distributed control protocols are designed for all agents to achieve the ultimate state synchronization to the leader in finite time. The Lyapunov approach is used for the stability analysis and a practical example of mixed-order mechanical MASs verifies the effectiveness and performance of the proposed distributed control protocols.

Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input

This paper studies the finite-time time-varying formation-containment tracking problems for second-order multi-agent systems with directed topology, where the multi-agent system consists of one virtual leader with fully unknown input, several real leaders and followers. In contrast with traditional formation and containment cases studied in most of the existing literature, apart from accomplishing the expected time-varying formation, the real leaders are required to track the trajectory generated by the virtual leader, and the followers need to get into the convex envelope spanned by the real leaders in finite time. The method for solving the finite-time formation-containment tracking problems is divided into the following steps. First, distributed finite-time observers are designed for each real leader and follower, in order to obtain the estimated states of their neighbor agents. Then, formation-containment tracking protocols are presented by using the neighboring information for both real leaders and followers. Furthermore, based on Lyapunov theory, it is proved that the given formation-containment tracking can be realized in finite time by the multi-agent system under the designed protocols. Finally, a case study on multi-robot transport operation is given to verify the effectiveness of the theoretical results.

Distributed finite‐time fault‐tolerant error constraint containment algorithm for multiple ocean bottom flying nodes with tan‐type barrier Lyapunov function

SummaryThe ocean bottom flying node (OBFN) is a special autonomous underwater vehicle (AUV) for seabed resource exploration. In this article, unmodeled uncertainties, thruster faults, and ocean disturbances are considered. The trajectory errors are constrained. Based on the directed topology, the distributed finite‐time fault‐tolerant error constraint containment control problem for multiple OBFN systems is solved, while only a part of follower OBFNs can measure the state of leaders. By using the backstepping method and a tan‐type barrier lyapunov function (BLF), a novel form of virtual controller is constructed. Neural network is employed to approximate and compensate the general disturbances. And the upper bound of the estimation error is dealt with by proposing an adaptive law. Besides, the trajectory errors can be constrained to a small neighborhood of zero in finite time. In other words, follower OBFNs can reach the convex hull consisted of leaders in finite time. The effectiveness of the designed algorithm is shown by presenting numerical experiment.

Composite sliding‐mode consensus algorithms for higher‐order multi‐agent systems subject to disturbances

Consensus problems for both leaderless and leader-follower disturbed higher-order multi-agent systems are investigated in this study. Based on the combination of integral sliding-mode control and disturbance observer techniques, composite sliding-mode consensus protocols are proposed for leaderless and leader-follower disturbed multi-agent systems, respectively. First, for the leaderless case, composite sliding-mode consensus protocols are designed to make the agents achieve asymptotic consensus. Second, for the leader-follower case, finite-time composite sliding-mode consensus protocols are presented to make the followers achieve consensus with the leader in finite time. Then based on the consensus algorithms proposed in this study, a consensus control strategy is given to realise the velocity and altitude finite-time consensus for a class of leader-follower multi-hypersonic vehicle systems. Finally, the numerical simulations are conducted to validate the efficiency of the proposed consensus algorithms.

Finite-Time Time-Varying Formation Tracking for High-Order Multiagent Systems With Mismatched Disturbances

This paper studies the finite-time time-varying formation tracking problems for high-order multiagent systems (MASs) under the influences of both mismatched disturbances and the leader’s unknown input. The outputs of the followers can not only realize the prespecified finite-time formation but also track the desired trajectory generated by the leader in finite time. First, a disturbance observer is designed for every follower to estimate the disturbances in finite time. Then, based on the homogeneous finite-time control, the integral sliding mode control, and the super-twisting algorithm, a distributed formation tracking protocol is presented utilizing the neighboring interaction. The proposed protocol is continuous, so the large chattering of the control inputs can be avoided effectively. Furthermore, it is proved that the desired formation tracking can be realized in finite time by MASs in the presence of mismatched disturbances and the leader’s unknown input. Finally, a simulation example is designed to verify the theoretical results.

Chattering-free full-order recursive sliding mode control for finite-time attitude synchronization of rigid spacecraft

This paper investigates a quaternion-based finite-time cooperative attitude synchronization and tracking of multiple rigid spacecraft with a virtual leader subject to bounded external disturbances. Firstly, the communication network between followers is assumed to be an undirected graph and every follower can get a direct access to the virtual leader, by using two neighborhood attitude error signals, a novel chattering-free recursive full-order sliding mode control algorithm is proposed such that all follower spacecraft synchronize to the virtual leader in finite time. In the proposed algorithm, the sliding mode surface is constructed by two layers of sliding mode surfaces, which are called as the outer and the inner sliding mode surfaces. To achieve finite-time performance of sliding mode dynamics, the outer sliding mode surface is designed as a terminal sliding mode manifold, and the inner one is designed as a fast nonsingular terminal sliding mode manifold, respectively. Then, to reduce the heavy communication burden, a distributed recursive full-order sliding mode control law is designed by introducing a distributed finite-time sliding mode estimator such that only a subset of the group members has access to the virtual leader. Finally, a numerical example is illustrated to demonstrate the validity of the proposed results.

A Robust Finite-Time Output Feedback Control Scheme for Marine Surface Vehicles Formation

In view of the marine surface vehicles are subject to unknown time-varying external disturbance and its velocities are not available for feedback, a robust finite-time output feedback control scheme is presented for multiple marine surface vehicles to achieve precise formation control in this paper. Without neglecting the first time derivative of disturbance, a novel finite-time extended state observer (FTESO) is proposed to precisely estimate the external disturbance and velocity information in finite time. Based on the outputs of FTESO, the distributed formation controller is designed to guarantee that a group of marine surface vehicles can track the time-varying virtual leader in finite time with precise tracking performance. The errors of the proposed FTESO and formation controller can be guaranteed to converge to zero in finite time by using the homogeneous method and the Lyapunov theory. Numerical simulations are presented to illustrate the effectiveness of the proposed finite-time output feedback formation control scheme.

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

ABSTRACTAimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.