Finite-time Leader-following Consensus Research Articles

A novel finite-time leader-follower consensus control for a disturbed mechanical nonlinear system in presence of actuator saturation

This paper presents a novel leader-follower consensus control for a particular class of nonlinear multi-agent mechanical systems in the presence of control input constraints and external disturbances which includes robot system dynamics with a wide range of potential applications in industry. In this case, one of the agents is selected as the leader to direct the other agents in such a way that the whole system can reach consensus within certain prescribed performance transient bounds. Due to the presence of disturbances in most practical systems, the effect of limited disturbance in the consensus control method has been investigated, and actuator saturation is included in the design process. A terminal sliding mode control method has been adapted to ensure the stability of the overall system and fast finite-time leader-follower consensus control. The simulation results of the multi-agent nonlinear robot system in MATLAB environment, in different scenarios with simultaneous consideration of actuator saturation and external disturbance, will show the efficiency of the proposed control method.

Dynamic event-triggered adaptive finite-time consensus control for multi-agent systems with time-varying actuator faults.

In this study, the adaptive finite-time leader-following consensus control for multi-agent systems (MASs) subjected to unknown time-varying actuator faults is reported based on dynamic event-triggering mechanism (DETM). Neural networks (NNs) are used to approximate unknown nonlinear functions. Command filter and compensating signal mechanism are introduced to alleviate the computational burden. Unlike the existing methods, by combining adaptive backstepping method with DETM, a novel finite time control strategy is presented, which can compensate the actuator efficiency successfully, reduce the update frequency of the controller and save resources. At the same time, under the proposed strategy, it is guaranteed that all followers can track the trajectory of the leader in the sense that consensus errors converge to a neighborhood of the origin in finite time, and all signals in the closed-loop system are bounded. Finally, the availability of the designed strategy is validated by two simulation results.

Finite-time fault-tolerant consensus for leader-following multi-agent systems with semi-Markov switching topologies

This paper investigates the finite-time leader-following consensus problem for multi-agent systems with switching topologies. First of all, consider the characteristic of failures, a failure distribution model which is more in line with the actual situation is established, and a semi-Markov chain is used to describe the topology switching of the multi-agent system, in which the transfer rate is time-varying. Secondly, based on the past state information, a topology-dependent consensus protocol is established, then the fault-tolerant consensus problem of leader-following multi-agent is transformed into the issue of system stability, according to the mode-dependent Lyapunov function and the finite time stochastic theorem, the sufficient conditions for the stability of the closed-loop system and the constraints of average residence time are obtained. In addition, an initial-state based H ∞ performance index is proposed to reduce the influence of zero initial conditions on the system. Finally, a numerical example is provided to show the effectiveness of the proposed method.

Fully distributed adaptive finite-time consensus over uncertain network topology

ABSTRACT Communication network could suffer uncertainties originating from link faults and network attacks. This situation, in multi-agent systems, can be featured by unknown weights of network topology. To impair the influence of the uncertain topology, typical compensation should be taken into account in distributed protocols to the workability of multi-agent systems. This paper, in the context of uncertain topology, addresses finite-time leader-following consensus for second-order uncertain nonlinear multi-agent systems. In addition to uncertainties in topology, the systems also allow unknown control coefficients, which together with the unknown weights renders the realisation of finite-time leader-following consensus nontrivial. Specifically, a fully distributed protocol based on distributed finite-time observer is designed via integrating the adaptive compensation scheme. Notably, in the designed protocol, dynamic high gains are introduced for the compensations of the network uncertainties and agents uncertainties. It turns out that the designed fully distributed protocol guarantees the global finite-time leader-following consensus. Simulation examples are provided to illustrate the validity of the proposed approach.

Finite-time leader-follower consensus of a discrete-time system via sliding mode control

Finite-time leader-follower consensus of a discrete-time system via sliding mode control

Finite-Time Leader-Following Consensus of Multiagent Systems With Actuator Faults and Input Saturation

This article studies the fault-tolerant leader-following consensus problem for multiagent systems with input saturation. The main contribution is to present a modified low-and-high gain feedback approach to deal with multiple actuator faults, including partial loss of effectiveness, outage, and stuck simultaneously. First, without consideration of saturation, a distributed fault-tolerant control scheme is put forward by the adaptive technique, and a practical finite-time stability result is established. Second, by employing the fault-tolerant theory and introducing a novel form of parametric algebraic Riccati equation, a modified low-and-high gain feedback approach is developed for the saturated control strategy. It is proven that the practical finite-time stability can be achieved, and both the steady-state consensus error and the settling time can be well estimated. Finally, numerical simulations are provided to validate the effectiveness of the theoretical results.

Agent-Based Finite-Time Leader-Following Consensus for Earth-Observation Tasks on Multiple Airships

In this technical note, we investigate the agent-based finite-time leader-following consensus for Earth-observation systems with multiple stratosphere airships, in which the high-order nonlinear dynamic and external disturbances are considered for multi-agent systems. Based on the distributed observer, which is used to acquire the state of the leader airship for the following airships, the dynamic cascade control is designed to realize the finite-time leader-following consensus for Earth-observation systems. It is mathematically proven that the convergence is finite for the stratosphere airship earth-observation system. Simulation results are given to illustrate the effectiveness of the proposed scheme.

Event-Triggered Finite-Time Sliding Mode Control for Leader-Following Second-Order Nonlinear Multi-Agent Systems

Finite-time leader-following consensus problem of second-order multi-agent system (MAS) with nonlinear dynamics under directed communication topology is investigated in this paper. Based on the event triggered mechanism, a novel finite-time integral sliding mode control strategy is proposed to guarantee that the consensus stability of MAS can be reached within the upper limit of the time, which can be predicted according to the initial state of MAS. The event-triggered condition on the basis of the defined novel measurement error effectively reduces the energy dissipation of the system and the update frequency of the controller, and the deduced lower bound expression of the event-triggered time interval avoids the occurrence of zeno behavior. Numerical simulation results illustrate the effectiveness and feasibility of the proposed algorithm.

Prescribed finite-time consensus with severe unknown nonlinearities and mismatched disturbances

This paper considers the problem of prescribed finite-time leader-following consensus for a class of second-order multi-agent systems (MAS). Compared to the existing methods, the dynamics of the followers in the proposed method is rather general, containing some severe unknown nonlinearities and mismatched disturbances. First, a time-varying distributed observer is proposed to estimate the leader information in prescribed finite time. The leader is driven by a control input that is unknown to all the followers. Then, a new composite controller with a time-varying disturbance observer is presented. By gracefully combining the barrier Lyapunov functions and logic-based switching rules, we show that the unknown nonlinearities and mismatched disturbances can be well handled. Thus, the prescribed finite-time consensus problem can be solved. Finally, by the properties of Lyapunov functions and time-varying gains, we present a new method to show that the control signals are bounded. A simulation example is provided to verify the effectiveness of the proposed method.

Leader–follower consensus control for a nonlinear multi-agent robot system with input saturation and external disturbance

This paper addresses the leader–follower consensus control problem for a nonlinear multi-agent robot system with control input constraint and external disturbances. Robot system is one of the most important practical systems in the industry. Due to the presence of disturbances in most practical systems, this paper considers the issue of finite-time leader–follower consensus control of the nonlinear multi-agent robot system along with actuator saturation and bounded disturbance. The modified terminal sliding mode control method is suggested for the system which is able to guarantee the stability of the overall system and fast finite-time leader–follower consensus control. For two different scenarios, the simulation of multi-agent robot system has been performed. The results show the effectiveness of the proposed control method.

Event-Triggered Finite-Time Consensus of Second-Order Leader-Follower Multiagent Systems With Uncertain Disturbances.

In this article, for second-order multiagent systems with uncertain disturbances, the finite-time leader-follower consensus problem has been investigated. First, by considering that the leader's states are only available to part of the followers, a distributed estimator is constructed to estimate the state tracking errors between the leader and each follower. Then, an estimator-based control scheme is proposed under the event-triggered strategy to achieve finite-time leader-follower consensus. Besides, the event-triggered intervals are with a positive lower bound such that the Zeno behavior can be avoided. Note that the system is discontinuous under the event-triggered mechanism; thus, a nonsmooth analysis is performed. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

Finite-time leader-following output consensus for multi-agent systems via extended state observer

In this paper, the finite-time leader-following output consensus problem is investigated for a multi-agent system subjected to directed topology and disturbance. Firstly, a distributed finite-time extended state observer (DFTESO) is designed to provide estimate for unmeasured consensus errors and disturbances. The sufficient condition is provided in terms of linear matrix inequality (LMI) to ensure that the error dynamics of the DFTESO is convergent in finite time. Then, based on the designed observer, the leader-following consensus protocol based on dynamic gain method is proposed under the directed topology. Finally, an example on the multi-spacecraft system is provided to illustrate the effectiveness of the proposed methodology.

Finite-time output feedback leader-following consensus for high-order time-varying nonlinear multi-agent systems

This paper addresses the finite-time leader-following output-feedback consensus problem for a class of high-order nonlinear multi-agent systems. The agents dynamics are supposed to be in lower-triangular form and satisfy Lipschitz conditions with time-varying gains. Based on the dynamic output approach and dynamic gain control method, a new distributed output feedback consensus protocol is proposed with two online tuned gains such that the finite-time leader-following consensus is achieved. Different from some exiting observer-based output feedback approaches that the observers embedded in agents have to share full observation information with their neighbors, the proposed protocol only requires the output information of neighboring agents to be transmitted, and thus the network communication burden is reduced. In addition, compared to the traditional backstepping method that commonly used for finite time control of nonlinear system, the proposed controller can avoid the repeated derivation problem in backstepping control and thereby is simple and convenient for use. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

Finite-time consensus algorithms of leader-follower higher-order multi-agent systems with uncertain nonlinearities

In this paper, the finite-time consensus problem of leader-follower higher-order multi-agent systems with uncertain nonlinearities is studied, where the uncertainties are assumed to satisfy Hölder conditions. To solve this problem, distributed adding a power integrator method, feedback domination technique and integral sliding-mode control are combined together. Firstly, by using distributed adding a power integrator method, a distributed recursive control scheme is proposed. In the recursive control design, based on feedback domination method, the Hölder conditions of the unknown nonlinearities are introduced into the virtual controllers design. Secondly, on the basis of the designed recursive controllers, integral sliding-mode surfaces are designed and then the corresponding distributed sliding-mode controllers are proposed. The designed sliding-mode controllers guarantee that the finite-time leader-follower consensus problem is solved without using a distributed observer. The stability analysis of the closed-loop systems is presented based on finite-time stability theory. Moreover, simulations show the effectiveness of the proposed consensus algorithms.

Finite time consensus of nonlinear multi-agent systems in the presence of communication time delays

In this paper, the finite-time leader-follower consensus of nonlinear Lagrangian multi-agent systems in the presence of communication time delays and dynamic parameter uncertainties is considered. In this regard, three different cases are studied. In the first case, all follower agents are considered informed, i.e., they receive the leader signals. The second case reads a situation where some followers are informed and the others are uninformed, and there is a directed spanning tree topology. In the third case, a new adaptive algorithm in the presence of dynamic parameter uncertainties is proposed. In all these cases, the finite-time consensus of the position and velocity signals is shown. All proofs are derived using the Lyapunov technique without the need to LMIs formulation, a common framework for the stability analysis of delay systems, which is often hard to get feasibility conditions of their solution. At last, in the line of verification of the theoretical results, simulation results on a group of ten identical planar 2-DOF manipulators as the agents of the system are presented.

Finite-time consensus of Markov jumping multi-agent systems with time-varying actuator faults and input saturation

This paper gives attention to the issue of finite-time leader-following consensus of nonlinear discrete-time multi-agent systems with Markov jump parameters. A robust fault-tolerant control protocol that takes the effect of time-varying actuator faults and actuator saturation into account is considered for the addressed system. The main purpose of the paper is to design a fault-tolerant controller such that the leader-following consensus of the addressed system is achieved over a prescribed finite-time interval. By using the Lyapunov functional approach, Abel’s lemma and some properties of Kronecker product, a sufficient condition for the existence of fault-tolerant state feedback controller for the addressed system is presented and an explicit parameterization of such a controller is obtained. Eventually, a numerical example along with its simulation results is exploited to reflect the applicability of the proposed design method, wherein the robust performance of controller is exhibited despite the presence of actuator saturation and time-varying actuator faults.

Aggregated Energy Storage for Power System Frequency Control: A Finite-Time Consensus Approach

In future power systems, widespread small-scale energy storage systems (ESSs) can be aggregated to provide ancillary services. In this context, a new load frequency control scheme which incorporates the energy storage aggregator (ESA) and its associated disturbance observer is proposed. The disturbance observer is designed to supplement the secondary frequency control for the ESA, therefore the system frequency response and recovery can be improved. Within the ESA, a finite-time leader–follower consensus algorithm is proposed to control the small-scale ESSs via sparse communication networks. This algorithm ensures that the ESA tracks the frequency control signals, while the state-of-charge among each ESS is balanced in finite-time. The external characteristics of the ESA will resemble to that of one large-scale ESS. Numerical examples demonstrate the convergence of the ESA under different communication graphs. The effectiveness of the entire scheme for power system frequency control is validated under a variety of scenarios that include contingency and normal operation.

Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances

ABSTRACTIn this paper, finite-time consensus tracking is investigated via time-varying feedback for uncertain nonlinear multi-agent systems (NMASs). The presence of inherent uncertainties and disturbances in the NMASs highlights the main novelty : (1) The inherent uncertainties imply that more serious unknowns and time-variations are allowed in the nonlineartities and the control coefficients of the NMASs. (2) The inherent disturbances mean that the upper bound of the disturbances is unknown. To compensate the inherent uncertainties and disturbances, time-varying protocols are proposed by integrating time-varying technique and sliding mode method. Based on the proposed protocols, the finite-time leader-following consensus and finite-time containment are achieved under directed graph. Finally, the validation of the proposed protocols is verified by two examples.

Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics

ABSTRACTThis paper is concerned with finite-time and fixed-time consensus of multi-agent systems in a leader-following framework. Different from conventional leader-following tracking approaches where inherent dynamics satisfying the Lipschitz continuous condition is required, a more generalised case is investigated: discontinuous inherent dynamics. By nonsmooth techniques, a nonlinear protocol is first proposed to achieve the finite-time leader-following consensus. Then, based on fixed-time stability strategies, the fixed-time leader-following consensus problem is solved. An upper bound of settling time is obtained by using a new protocol, and such a bound is independent of initial states, thereby providing additional options for designers in practical scenarios where initial conditions are unavailable. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Leader-following consensus for a class of high-order nonlinear multi-agent systems

The finite-time leader-following consensus problem is addressed for a class of high-order multi-agent systems with uncertain nonlinear dynamics. Each follower node is modeled by lower-triangular system. By using recursive method, we develop the finite-time consensus control design scheme. Based on finite-time Lyapunov stability theorem and matrix theory, we prove that the finite-time consensus of high-order uncertain nonlinear multi-agent systems is guaranteed by non-lipschitz continuous control laws. Simulation results are given to illustrate the effectiveness of the theoretical results.