Finite-time Consensus Research Articles

Consensus-Based Merging and Spacing Method for Aircraft Self-Separation at Intersections

Within the context of delegating separation related tasks from an air traffic controller to the flight deck, this paper analyzes the merging and spacing problem for autonomous aircraft operations at busy airway intersections. A consensus-based control protocol is developed to achieve an ordered and safe traffic flow at a given intersection waypoint. Two primary implementation steps are covered in the protocol. In the first step, consensus on the target merging flow is achieved, where the merging stream is modeled as a straight line with the minimum total converging distance. In the second step, multiple aircraft with double-integrator dynamics and time-varying communication topologies are guided to merge into the target flow while maintaining appropriate interaircraft spacing. A state control law is designed, and the Lyapunov analysis method is leveraged to derive sufficient conditions on the communication topology and the control parameter for merging agents to reach consensus in finite time. Performance of the proposed method is evaluated through experimental simulations under different hypothetical scenarios in the two-dimensional plane.

Nonsingular adaptive finite-time consensus control for uncertain nonlinear multi-agent systems with input quantization

This paperinvestigates the distributed consensus control for nonlinear multi-agent systems with input quantization in a directed communication topology. A nonsingular adaptive finite-time control (NAFTC) scheme is proposed by combining the filtered backstepping method with neural network control. Both chattering and singularity problems of the control signals are avoided thanks to its [Formula: see text] continuity, so that the contradiction between discontinuous- and [Formula: see text] continuous finite-time control with input quantization does not exist in our scheme. At the same time, a novel inequality for the input-output relationship of hysteresis quantizer is derived, which can simply handle the input quantization without requiring additional stability analysis. What is more, some common assumptions, such as Lipschitz assumption and Holder-continuity assumption, are not required in our scheme. Finally, stability analysis and numerical simulation are provided.

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.

Robust Finite-Time Consensus of Coupled Markovian Logical Dynamic Networks

Robust Finite-Time Consensus of Coupled Markovian Logical Dynamic Networks

Finite-Time Consensus Adaptive Neural Network Control for Nonlinear Multiagent Systems Under PDE Models.

In this article, a novel adaptive control method based on neural networks is proposed for a class of multiagent systems (MASs) with nonlinear functions and external disturbances. First, the approximation properties of neural networks are used to approximate the MAS partial differential equation (PDE) model with nonlinear terms containing two variables, time t, and spatial variable x. Second, an adaptive controller is constructed to actuate the parabolic MAS to reach consensus under external disturbances. Based on this, the finite-time theorem and special inequalities are applied to prove the stability of the closed-loop system. Thus, MAS that have nonlinear functions and external disturbances are enabled with finite-time consensus. Finally, the effectiveness of the proposed control method is demonstrated by numerical simulations.

Finite-time consensus control for MASs under hidden Markov model mechanism

Finite-time consensus control for MASs under hidden Markov model mechanism

A Finite-Time Consensus Continuous-Time Algorithm for Distributed Pseudoconvex Optimization with Local Constraints

A Finite-Time Consensus Continuous-Time Algorithm for Distributed Pseudoconvex Optimization with Local Constraints

Distributed time-varying optimization control protocol for multi-agent systems via finite-time consensus approach

This paper addresses a distributed time-varying optimization problem with inequality constraints based on multi-agent systems over switching communication graphs. To reduce the influence of time-varying inequality constraints, an exact penalty method and smoothing technique are employed. Then, a Hessian-based distributed control protocol is presented to seek the time-varying optimal solution of the distributed time-varying optimization problem by virtue of only local information and interaction. It is shown that all agents not only achieve finite-time consensus but also track the time-varying global optimal target eventually. Compared with the existing distributed optimization protocols, the proposed control protocol is suitable for more general distributed time-varying optimization problems and enjoys high-efficiency convergence. Finally, numerical examples and experiment on moving target tracking of Unmanned Aircraft Vehicle (UAV) are performed to illustrate the effectiveness of the proposed control protocol.

Adaptive Finite-Time Consensus for Stochastic Multiagent Systems With Uncertain Actuator Faults

This paper aims to develop fully distributed adaptive protocols and establish the finite-time consensus criteria for nonlinear stochastic multi-agent systems that are subjected to serious multiple uncertainties not only in the agents' states and inherent nonlinearities but also in their actuators. Firstly, we propose a new continuous fully distributed consensus protocol for leaderless stochastic multi-agent systems by leveraging the adaptive technology, enabling the agents to achieve the finite-time consensus in probability efficiently. Secondly, we develop an adaptive protocol for leader-following multi-agent systems, and remarkably our protocol contains only one dynamic gain, which is adequate to resist serious multiple uncertainties and to ensure the realization of finite-time consensus in probability. Finally, we provide numerical simulations to verify the effectiveness of our protocols.

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.

Event-Based Finite-Time Neural Control for Human-in-the-Loop UAV Attitude Systems.

This article focuses on the event-based finite-time neural attitude consensus control problem for the six-rotor unmanned aerial vehicle (UAV) systems with unknown disturbances. It is assumed that the six-rotor UAV systems are controlled by a human operator sending command signals to the leader. A disturbance observer and radial basis function neural networks (RBF NNs) are applied to address the problems regarding external disturbances and uncertain nonlinear dynamics, respectively. In addition, the proposed finite-time command filtered (FTCF) backstepping method effectively manages the issue of "explosion of complexity," where filtering errors are eliminated by the error compensation mechanism. In addition, an event-triggered mechanism is considered to alleviate the communication burden between the controller and the actuator in practice. It is shown that all signals of the six-rotor UAV systems are bounded and the consensus errors converge to a small neighborhood of the origin in finite time. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.

A Distributed Robust System-Wide State Estimation Method for Power Systems Based on Maximum Correntropy

The distribution of measurement noise applied in practical power system state estimation (PSSE) can deviate from the assumed Gaussian model and the performance of an estimator becomes bad if the Gaussian model is still used. This paper proposes a new distributed robust PSSE method for multi-area power systems. The non-Gaussian model is utilized to fit the measurement noise distribution to reach high model accuracy. The proposed distributed method is derived based on the maximum correntropy criterion to further reduce the impact of non-Gaussian measurement noise and outliers. The influence function combined with the finite-time average consensus algorithm is used to implement the proposed distributed robust method in a fully distributed manner. Simulations conducted on the IEEE 30-bus, 118-bus and 300-bus systems and the Polish 2383-bus system demonstrate the robustness and effectiveness of the proposed distributed method. Each local area can get the system-wide robust state estimation solution by only using local information and small amounts of data from neighboring areas. Our proposed distributed robust method has at least twelve percent improvement in reducing the mean squared error under Gaussian-Uniform noise. It is verified the communication network applied for the proposed method is fairly flexible while the existing distributed approaches use a fixed communication network when the power systems are partitioned. The simulation results also verify the robustness of the proposed method to bad data and communication failure.

A Continuous Algorithm for Finite-Time Consensus of Disturbed Fractional-Order Multiagent Systems Over Digraphs

This work studies the finite-time distributed consensus problem of fractional-order multiagent systems (FOMASs) with disturbances over directed graphs (digraphs). By utilizing the finite-time Lyapunov stability theorem and distributed estimator technique, a continuous estimator-based finite-time fully distributed algorithm with a fractional power is proposed. Under the designed algorithm, all agents’ states globally converge to a common value within a finite time in a fully distributed manner. The upper bound of the finite time is given explicitly. Finally, a numerical example is provided to validate the results.

Finite-time and Fixed-time Bipartite Consensus Tracking for Second-order Multi-agent Systems via an Integral Sliding-mode Approach

Finite-time and Fixed-time Bipartite Consensus Tracking for Second-order Multi-agent Systems via an Integral Sliding-mode Approach

Two-Phase Performance Adjustment Approach for Distributed Neuroadaptive Consensus Control of Strict-Feedback Multiagent Systems.

This article addresses the practical prescribed-time leaderless consensus problem for multiple networked strict-feedback systems under directed topology. Different from most existing protocols for finite-time consensus that rely on the signum function or fractional power state feedback (thus, the finite convergence time is contingent upon the initial positions of the agents or other design parameters), the proposed distributed neuroadaptive consensus solution is based on a two-phase performance adjustment approach, which exhibits several salient features: 1) the consensus error is ensured to converge to a preassigned arbitrarily small residual set within prescribed time; 2) the tunable transient behavior and desired steady-state control performance of the consensus error is maintained under any unknown initial conditions; and 3) the control scheme involves only one parameter estimation, significantly reducing the design complexity and online computation. Furthermore, we extend the result to practical prescribed-time leader-following consensus control under directed communication topology. Numerical simulation verifies the benefits and efficiency of the proposed method.

Distributed Adaptive-Neural Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems Subject to Saturated Inputs.

In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.

A Discrete-Time Event-Driven Near-Optimal Second-Order SMC for Multirobotic System Formation Prone to Network Uncertainties.

In this article, we propose a novel stochastic event-driven near-optimal sliding-mode controller design for addressing the consensus of a multiagent system in a network. The system is prone to external disturbances and network uncertainties, such as losses and delays of data packets. The randomness of network uncertainties introduces stochasticity in the system. The design starts with the formulation of control-affine dynamics based on a single integrator robot model, formation error, and sliding surface dynamics. An event-triggering condition is then derived for an update of control input for each agent. These input updates guarantee desired consensus in finite time with reaching time of each agent's sliding surface having an upper bound. The admissibility of event-driven near-optimal control updates is also ensured for each agent. The near-optimal control design for each agent has achieved through neural-network-based actor-critic architecture. The implementation of Pioneer P3-DX mobile robots illustrates threefold efficacy of the proposed design: 1) advantages of event-driven approach and higher order sliding mode controller; 2) robustness to network uncertainties; and 3) near-optimality in system performance.

The Cucker–Smale Model With Nonlinear Velocity Couplings and Power-Law Attractive Potentials

When the communication weight has a short range, the distance between agents could tend to infinity for some initial conditions, which leads to the non-existence of well studied flocking behavior in the Cucher-Smale model with (or without) nonlinear velocity couplings. To control the distance, it is natural to consider this model with pairwise attractive potentials. Therefore, this note investigates the Cucker — Smale model with nonlinear velocity couplings and attractive potentials. When the attractive potential is any power-law function, it is proved that this model not only exhibits flocking but also achieves consensus regardless of initial conditions. More importantly, by constructing two delicate Lyapunov functions, the precise convergence rates (including polynomial convergence, exponential convergence, finite time consensus and consensus independent of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> ) are derived for different kinds of nonlinear velocity couplings and power-law potentials.

Almost-Sure Finite-Time Stochastic Min-Max Consensus

In this brief, a novel stochastic minimum-maximum finite-time consensus protocol is proposed. The stochastic consensus protocol is then applied to a system of agents with continuous high-order dynamics. Based on this protocol, new continuous auxiliary variables are defined, which use only samples of the neighbors’ outputs. If those variables are regulated to zero in finite time, it is proven that finite-time output consensus is achieved. This regulation problem is then solved using a standard finite-time control law. Simulations are provided that illustrate the efficiency of this distributed finite-time control scheme.

Distributed Consensus Seeking With Different Convergence Performance Requirements: A Unified Control Framework.

In this article, we investigate distributed consensus seeking with multiple convergence performance requirements for single-integrator multiagent systems under undirected graphs. A unified distributed control framework is proposed to ensure consensus or practical consensus as well as performance time requirements, which contains most existing complex protocol schemes as special cases. In the proposed framework, three functions with specific properties in the controller play different roles and can be freely designed to achieve desired convergence performances, which guarantee a high-level scalability for multiple control requirements in addition to convergence time. For highlighting the compatibility and flexibility of the proposed method, four typical scenarios are discussed to reach exponential, finite-time, fixed-time, and appointed-time consensus seeking, respectively. Finally, numerical simulations are carried out to verify the effectiveness of the theoretical analysis.