Finite-time Consensus Problem Research Articles

Finite-Time Partial Component Consensus for Nonlinear Leader-Following Multi-Agent Systems

The problem of finite-time partial component consensus (FTPCC) for first-order nonlinear multi-agent systems (MASs) is investigated in this paper for the first time. By incorporating the permutation matrix approach, we derive a novel error system for identical components, which facilitates stability analysis. Leveraging partial variable stability theory and related foundational knowledge, we devise two adaptable protocols. These protocols are tailored to achieve FTPCC in nonlinear MASs, one for systems without disturbances and another for those with bounded disturbances. To validate our findings, numerical examples are provided, demonstrating the effectiveness of the proposed results.

Bipartite finite-time consensus of multi-agent systems with intermittent communication via event-triggered impulsive control

This paper concentrates on the bipartite finite-time consensus (BFTC) problem of nonlinear multi-agent systems (MASs) under intermittent communication via event-triggered impulsive control. First, a finite-time consensus (FTC) protocol with an event-triggered mechanism is developed for the MASs with nonlinear dynamics to save limited resources. Then, an impulsive control scheme is introduced to the designed algorithm to further improve the control performance. Based on the structurally balanced graph theory, both antagonistic and cooperative interactions are discussed in this article. Regarding whether the MASs have encountered intermittent communication, sufficient conditions are provided for achieving consensus of the MASs by using the Lyapunov theory and inductive methods. Moreover, the Zeno behavior is excluded. Finally, numerical simulations are given to validate the effectiveness of the algorithm. The result shows that the designed event-triggered BFTC control protocol with an impulsive strategy has a faster convergence rate than that without an impulsive strategy.

Privacy-preserving finite-time average consensus and its application to power allocation of battery energy storage systems

In this paper, the privacy-preserving problem of finite-time discrete-time average consensus is studied by adding random numbers. The privacy leakage conditions are given for systems with curious but not malicious nodes and eavesdroppers, respectively. By introducing the random numbers and node decomposition mechanism, the privacy information of the nodes cannot be estimated by the adversaries. The proposed algorithm is applied to the power allocation problem of distributed battery energy storage systems. Based on the previous proposed multi-rate sampling method, the privacy-preserving finite-time discrete-time average consensus is utilized to estimate the accurate average value within finite steps. The accurate power allocation based on the same relative SoC variation rate can be achieved with the privacy preservation of the transmission information. Finally, based on a networked battery energy storage system, simulation studies are presented to verify the effectiveness of the proposed method.

Finite-Time Consensus of Second-Order Multi-Agent Systems via Event-Triggered Impulsive Control

In this study, the finite-time consensus problem of second-order multi-agent systems via event-triggered impulsive control is investigated. We leverage a novel approach that combines impulsive control, event-triggered communication, and finite-time stability theory. This successful combination achieves finite-time consensus while minimizing communication. In addition, the event-triggered condition determines both the impulsive instants and the update times for the finite-time control. Furthermore, it is shown that the Zeno-behavior and chattering phenomenon can be eliminated under our work. Numerical examples and simulations are provided to validate the effectiveness of the proposed control strategy.

Finite-Time Bipartite Consensus for Second-Order Nonlinear Multi-Agent Systems Under Random Switching Topologies

In this paper, the finite-time bipartite consensus problem for second-order nonlinear multi-agent systems (MASs) under random switching topologies is studied. Considering the transformation of the existence of communication and the transformation of the cooperation-competition relationship between the follower and the leader, a topological switching based on structural balance is proposed. Through the finite-time control protocol, sufficient conditions are obtained for all agents to achieve the practical finite-time bipartite consensus. Among them, the nonlinear function is approximated using the radial basis function neural network (RBFNN) fitting. Finally, the feasibility of the control protocol is proved by a example.

Distributed finite‐time control with event triggered mechanism for multi‐agent systems under fixed and switching topologies

AbstractThis paper addresses the problem of distributed finite‐time (FT) event‐triggered consensus of multi‐agent systems (MASs) under fixed and switching topologies. To conserve the limited communication resources, a new distributed event‐triggered control protocol is proposed, in which the agents exchange information via discontinuous communication among the follower agents. Then, to solve the FT consensus problem, norm‐normalized sign functions are employed, and sufficient Lyapunov conditions are provided. On this basis, the MASs proves capable of reaching consensus within finite time under fixed and switching topologies. Finally, the effectiveness of the developed algorithm is verified via numerical simulation.

Output-feedback anti-disturbance consensus for multi-agent systems with application to secondary voltage regulation for microgrids

This paper investigates a distributed finite-time consensus problem for second-order multi-agent systems (MASs) with disturbances and unmeasurable states. Output-feedback anti-disturbance consensus protocols are designed by finite-time observer (FTO) methods and the nonsingular integral terminal sliding-mode control (NITSMC). Some FTOs are first introduced for the agents to estimate the disturbances and unmeasurable states together. Then, the nonsingular integral terminal sliding-mode surfaces are proposed, based on which consensus protocols are proposed. Moreover, the consensus methods are also applied to microgrids (MGs). Based on MG systems, output voltages achieve consensus through secondary regulation. Simulations verify the effectiveness.

Finite-time general function consensus for multi-agent systems over signed digraphs

This paper solves the finite-time consensus problem for discrete time multi-agent systems (MASs) where agents update their values via linear iteration and the interactions between them are described by signed digraphs. A sufficient condition is presented that the agents can reach consensus on any given linear function of multiple initial signals in finite time, i.e., there exists an eventually positive Laplacian-based matrix associated with the underlying graph. We prove that the linear iterative framework “ratio consensus” developed for unsigned graphs in the literature can be extended to the computation for signed graphs with appropriate modifications. Our method weakens the limitation of the iterative framework on the “marginal Schur stability” of the weight matrix without increasing the computational complexity. Reaching average consensus on unsigned graphs as in the literature is regarded as a special case of our algorithm. Two illustrative examples are presented to demonstrate the correctness of the proposed results.

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.

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.

Design Finite-time Consensus Protocol for High-order Linear Multi-agent Systems: A Gain Scheduled Approach⋆

This paper revisits the finite-time consensus problem for high-order linear multi-agent networks by using smooth state-feedback. By following a gain scheduled approach, this paper first presents finite-time consensus protocol with a state-independent parameter, which takes the time-varying solution of parametric Lyapunov equation to design control gain. Note that the state-independent parameter is selected based on the connectivity of topology, which is a piece of global information. To get rid of this dependence, a node-based adaptive parameter is further proposed to achieve fully distributed consensus. Through finite-time stability theory, both the prepared parameters, including state-independent and adaptive parameters, for control protocol make the agents achieve finite-time consensus. Particularly, a specific convergence time is given by following the concept of finite-time escaping function. Finally, we provide a practical simulation on finite-time formation problem of six satellites, demonstrating the validity of theoretical results.

Adaptive fuzzy singularity-free finite-time optimal control for nonlinear pure-feedback multiagent systems

In this paper, we investigate the adaptive fuzzy singularity-free finite-time optimal consensus problem for nonlinear pure-feedback multiagent systems (MASs). For purpose of achieving the optimized control, the fuzzy approximation-based reinforcement learning is employed under critic-actor architecture. By virtue of Butterworth low-pass filter, a distributed adaptive finite-time optimal consensus method is developed for nonlinear pure-feedback MASs, which solves algebraic loop problem produced in the construction of the optimal controller. Most importantly, to be free of singularity, we design a new dynamic filtering optimized backstepping method to avoid the differentiations of virtual optimal controllers, and the errors between first-order filter signals and virtual optimal controllers can be counteracted by designing the smooth robust compensators for the first time. It is shown that, with the developed adaptive finite-time optimal consensus control, both the optimal consensus tracking performance and finite-time convergence for the closed-loop systems are ensured. Three simulation examples are presented to verify the effectiveness of the proposed approach.

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.

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.

Fast finite-time consensus protocol of multi-agent systems with nonholonomic constraints

In this paper, a fast finite-time consensus protocol for multi-agent systems with nonholonomic constraints is studied. First, the chained form nonholonomic systems are transformed into two subsystems, which are the first-order subsystem and the reduced-order subsystem. Based on graph theory content and fast finite-time control theory, the fast finite-time consensus problems of the two subsystems are taken into consideration separately. Second, a switching control strategy is proposed to ensure that all states of multiple nonholonomic systems converge instantly to the same state in finite time. Finally, a numerical example is given to verify the effectiveness of the proposed control algorithm.

Adaptive Fault-Tolerant Fast Finite-Time Consensus Protocols for Multiple Mechanical Systems With Output Constraints

In this article, we discuss fast finite-time consensus (FFTC) problems for uncertain nonlinear multiple mechanical systems with actuator faults and time-varying asymmetric output constraints. In order to guarantee the constraints are satisfied, an appropriate nonlinear mapping (NM) is employed to transform the original system with output constrains into an corresponding unconstrained one. Combining neural networks technology, graph theory, fast finite-time control theory, and backstepping technology, the actuator faults are considered to propose a distributed adaptive finite-time consensus (FTC) protocol, which can guarantee the position errors as well as the velocity errors reaching a region in finite time. Finally, an illustrative example is presented to support the obtained theoretical results.

Fault-tolerant finite-time dynamical consensus of double-integrator multi-agent systems with partial agents subject to synchronous self-sensing function failure

This paper investigates fault-tolerant finite-time dynamical consensus problems of double-integrator multi-agent systems (MASs) with partial agents subject to synchronous self-sensing function failure (SSFF). A strategy of recovering the connectivity of network topology among normal agents based on multi-hop communication and a fault-tolerant finite-time dynamical consensus protocol with time-varying gains are proposed to resist synchronous SSFF. It is proved that double-integrator MASs with partial agents subject to synchronous SSFF using the proposed strategy of network topology connectivity recovery and fault-tolerant finite-time dynamical consensus protocol with the proper time-varying gains can achieve finite-time dynamical consensus. Numerical simulations are given to illustrate the effectiveness of the theoretical results.

Distributed Finite-Time Consensus Algorithm for Multiagent Systems via Aperiodically Intermittent Protocol

This brief focuses on the dynamic finite-time consensus (FTC) problem of linear multiagent systems (MASs) via distributed intermittent control under directed topology. Firstly, a new neighbor-based intermittent control algorithm is formulated for the MASs, which guarantees all agents can achieve consensus in finite time. Secondly, most of existing works about FTC algorithm is based on the continuous communication. However, in practice, we need to consider the consensus problem under discontinuous communication. Aimed at filling the research gap, the intermittent control FTC algorithm is proposed and results in less communication energy among agents. In addition, it is proved that increasing coupling weight among agents will be an effective method to improve the convergence rate of the considered MASs. Finally, simulation is performed to validate the effectiveness of the proposed scheme.

Passivity-Based Finite-Time Lag Consensus for Nonlinear Multi-Agent Systems

The finite-time lag consensus problem of nonlinear multi-agent system (MAS) is investigated by applying finite-time passivity (FTP) in this brief. Two sufficient conditions are obtained for insuring FTP of the MAS by choosing the proper state feedback control strategy and adaptive state feedback control strategy. In view of FTP, the finite-time lag consensus criteria for the MAS are developed. Finally, a simulation example which demonstrates the availability of the derived results is proposed.

Fully Distributed Adaptive Finite-Time Consensus for Uncertain Nonlinear Multiagent Systems.

In this article, the adaptive finite-time consensus problem is discussed for uncertain nonlinear multiagent systems. In contrast with the correlative literature, the systems permit multiple uncertainties (not only in control coefficients but also in inherent nonlinearities), and typically the consensus protocol is pursued in a fully distributed fashion (independent from any global information of network topology). This essentially challenges the realization of the finite-time consensus. To overcome the challenge, a new continuous fully distributed protocol is proposed by combining adaptive techniques such that the finite-time consensus of the systems under investigation is achieved. Remarkably, a dynamic high gain, rather than multiple ones in the related literature, is adequate to resist two kinds of uncertainties and to guarantee the fully distributed fashion of the consensus protocol. Moreover, the adaptive finite-time consensus protocol is specified on the scenario of leader-following multiagent systems. Simulation results of three interaction topologies are acquired to illustrate the validity and the wider applicability of the proposed protocol.