Second-order Nonlinear Multi-agent Systems Research Articles

Leader-following consensus of heterogeneous nonlinear multi-agent systems within arbitrary pre-specified time

Abstract The leader-following consensus problem of second-order heterogeneous nonlinear multi-agent systems (MASs) is studied in this paper. Based on the free-will arbitrary time (FWAT) theory, a piecewise distributed controller is developed to solve this problem within an arbitrary pre-specified convergence time. It should be noted that the pre-specified convergence time is independent of any system parameters and initial conditions. Furthermore, compared with the existing FWAT methods, consensus can still be maintained after the convergence time under the protocol designed in this work. Finally, numerical examples are given to illustrate the validity of the proposed method.

Pinning Group Consensus of Multi-agent Systems Under DoS Attacks

In this paper, group consensus is investigated for a class of nonlinear multi-agent systems suffered from the DoS attacks. Firstly, a first-order nonlinear multi-agent system is constructed, which is divided into M subsystems and each subsystem has an unique leader. Then a protocol is proposed and a Lyapunov function candidate is chosen. By means of the stability theory, a sufficient criterion, which involves the duration of DoS attacks, coupling strength and control gain, is obtained for achieving group consensus in first-order system. That is, the nodes in each subsystem can track the leader of that group. Furthermore, the result is extended to nonlinear second-order multi-agent systems and the controller is also improved to obtain sufficient conditions for group consensus. Additionally, the lower bounds of the coupling strength and average interval of DoS attacks can be determined from the obtained sufficient conditions. Finally, several numerical simulations are presented to explain the effectiveness of the proposed controllers and the derived theoretical results.

Fast finite-time formation control with obstacle avoidance of second-order multi-agent systems with input saturation

This paper proposes a leader-follower formation control protocol using fast finite-time (FFT) theory, based on second-order nonlinear multi-agent systems (MASs) with input saturation constraints. The artificial potential field method is addressed to implement the formation control with obstacle avoidance of the MASs. An adaptive FFT strategy is constructed that all the agents follow required formation performance. Neural networks are considered to approximate uncertain functions, which improved convergence and ensuring safety of distributed formation control. Finally, the validity of the theoretical approach is demonstrated by FFT stability theory validated by simulation examples.

Distributed Fixed-Time Optimization for Second-Order Nonlinear Multiagent Systems: State and Output Feedback Designs

Distributed Fixed-Time Optimization for Second-Order Nonlinear Multiagent Systems: State and Output Feedback Designs

Fixed-time cooperative output regulation for second-order nonlinear multiagent systems with an unknown exosystem

This paper investigates the fixed-time cooperative output regulation (FTCOR) problem with unknown exosystem of second-order nonlinear multiagent systems. To solve this problem, it is necessary to ensure that each agent can obtain the reference trajectory originating from an unknown exosystem and reconstruct the solution of the regulator equation containing the exogenous signal and unknown parameter vectors within a fixed time, and the unknown exosystem makes it difficult to solve these two problems with existing tools. By using auxiliary filtering variables, we propose a fixed-time adaptive distributed observer (FTADO) and design a fixed-time distributed internal model (FTDIM) based on this FTADO. These two new tools ensure the solvability of the two problems just mentioned. Then, based on these two tools, we transform the problem into a fixed-time stabilization problem of a so-called augmented system. Through the backstepping technique, we propose a distributed controller that solves this fixed-time stabilization problem while relaxing the assumptions of similar references.

Parameter variational based adaptive bipartite formation control of second-order multi-agent systems with antagonistic interactions

This article mainly concentrates on researching the leader-following bipartite formation of second-order nonlinear multi-agent systems (MASs) with antagonistic interactions and time-varying delay. A novel distributed feedback control and impulsive control strategy is proposed for realizing the bipartite formation. By establishing an error system, the bipartite formation issue of the MASs is transformed into the stability issue of the error systems. Sufficient conditions for achieving the bipartite formation of second-order nonlinear MASs are obtained by jointly employing the extended parameters variation formula, the comparison principle and the definition of average impulsive interval. In addition, in order to obtain the optimal control gains and control effects, an adaptive control strategy is taken into account by designing the adaptive updating laws. Ultimately, the effectiveness of the theoretical results is demonstrated by two numerical simulations.

Practical fixed-time event-triggered output feedback containment control for second-order nonlinear multi-agent systems with switching topologies

This paper studies the fixed-time containment of the second-order nonlinear multi-agent system (MAS) accompanied by switching topologies and event-triggered communication. The agent is subjected to unknown nonlinear dynamics. A fixed-time RBF observer was constructed based on information obtained from neural networks and event-triggered communication. By combining the controller with the identification information from the observer, it is demonstrated that the system can achieve practical fixed-time output feedback containment and exclude Zeno behavior during the control process. The effectiveness of the proposed event-triggered control method for fixed-time output feedback containment control of the second-order nonlinear MAS is verified by simulation examples.

Impulsive consensus algorithms for vector second-order Lipschitz nonlinear multi-agent systems using only velocity regulation

The existing impulsive consensus algorithms for second-order Lipschitz nonlinear multi-agent systems require to apply the impulsive control to both position and velocity vectors at the same time. Such a requirement cannot be met in most of the real-world applications. To overcome the limitations of these impulsive algorithms, two kinds of new second-order impulsive consensus algorithms using only velocity regulation are proposed. Through developing a weighted discontinuous Lyapunov function-based approach that is able to leverage the spectral property of Laplacian matrix, impulse-dwell-time-dependent sufficient conditions for solving second-order impulsive consensus are derived in the form of linear matrix inequalities. Further, it is shown that if the impulsively controlled velocity subsystems are globally exponentially stable, the impulsive static consensus algorithm is able to ensure that all agents tend to an agreed position. Based on the consensus conditions, two convex optimization problems are formulated, by which the impulsive gain matrices for ensuring a prescribed exponential convergence rate can be designed. Finally, the effectiveness of the proposed distributed impulsive consensus algorithms is certified through numerical simulations.

Event-Triggered Fixed-Time Consensus of Second-Order Nonlinear Multi-Agent Systems with Delay and Switching Topologies

Event-Triggered Fixed-Time Consensus of Second-Order Nonlinear Multi-Agent Systems with Delay and Switching Topologies

Event-triggered control strategy based on absolute velocity and relative position measurements for second-order nonlinear multi-agent systems under DoS attacks

Consensus control in multi-agent systems (MASs) has wide-ranging applications in various domains. As the scope of applications continues to expand, ensuring the secure control of these systems to counter a diverse range of network attacks becomes highly necessary. Among these threats, Denial of Service (DoS) attacks have emerged as a major network security threat, capable of rendering targeted agents or networks unable to provide normal services. This paper presents an effective control protocol aiming to achieve leader-following consensus in a second-order MAS with event-triggered control mechanism and nonlinear dynamics under DoS attacks. The protocol utilizes absolute velocity and relative position measurements. The maximum attack frequency and duration of the DoS attacks have been obtained. Furthermore, the possibility of Zeno behavior is eliminated. Theoretical analysis demonstrates that, even under DoS attacks, consensus can be maintained among the leaders and followers within the MASs. In conclusion, the effectiveness of the proposed distributed security control protocol is validated through a case study involving a multi-vehicle cooperative system with unmanned cars.

Neural Network-Based Fixed-Time Tracking and Containment Control of Second-Order Heterogeneous Nonlinear Multiagent Systems.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

Event-triggered impulsive control for second-order nonlinear multi-agent systems under DoS attacks

<abstract><p>We investigated impulsive consensus in second-order nonlinear multi-agent systems (MASs) under Denial-of-Service (DoS) attacks. We consided scenarios where the communication network is subjected to DoS attacks, disrupting communication links and causing changes in the communication topology. An event-triggered impulsive control(ETIC) approach is proposed to flexibly address these issues. Additionally, an upper bound on the DoS attack period is introduced. Finally, a numerical example is given to verify the validity of the major results.</p></abstract>

Prescribed-Time Network-Based Deployment of Nonlinear Multiagent Systems: A Discrete-Space PDE Method.

This article attempts to design the prescribed-time time-varying deployment schemes for first-order and second-order nonlinear multiagent systems (MASs). We assume that all agents can obtain the information of their current and final relative positions with their neighbors, and the final absolute velocities (as well as their current and final relative velocities, the final absolute accelerations for the second-order MASs) through a communication network, whereas two boundary agents are able to obtain their current and final absolute positions (as well as their current and final absolute velocities for the second-order MASs). The neighbor relationship of all agents is described by a spatial variable and two static-feedback controllers are introduced, which can be expressed as a second-order space difference of the spatial variable. Then, the deployment of MASs can be transformed into the stabilization of discrete-space partial differential equation (PDE) systems. Three virtual agents are introduced to constitute the Dirchlet and Neumann boundary conditions. Several algebraic inequality criteria are derived to guarantee that the prescribed-time time-varying deployment can be achieved within a prescribed time under the Dirchlet and mixed boundary conditions. Unlike the published results, our results are derived based on the discrete-space PDE systems instead of continuous-space PDE systems, which is consistent with the discrete spatial distribution of agents. Finally, two numerical examples are given to illustrate the effectiveness of our results.

PD and PI Control for the Lag Consensus of Nonlinear Multiagent Systems With and Without External Disturbances.

In this article, we investigate the lag consensus and lag H∞ consensus problems for second-order nonlinear multiagent systems (MASs) by utilizing the proportional-derivative (PD) and proportional-integral (PI) control methods. On the one hand, a criterion is developed for ensuring the lag consensus of the MAS by choosing an appropriate PD control protocol. Moreover, a PI controller is also provided to guarantee that the MAS can achieve lag consensus. On the other hand, several lag H∞ consensus criteria are also given for the case in which external disturbances appear in the MAS; these criteria are developed by exploiting the PD and PI control strategies. Finally, the devised control schemes and the developed criteria are verified by employing two numerical examples.

Distributed Nash Equilibrium Seeking for Constrained Multi-Cluster Games of Second-Order Nonlinear Multi-Agent Systems

Distributed Nash Equilibrium Seeking for Constrained Multi-Cluster Games of Second-Order Nonlinear Multi-Agent Systems

Predefined-Time Consensus for Second-Order Nonlinear Multi-Agent Systems via Sliding Mode Technique

Predefined-Time Consensus for Second-Order Nonlinear Multi-Agent Systems via Sliding Mode Technique

Practical finite-time and fixed-time containment for second-order nonlinear multi-agent systems with IDAs and Markov switching topology

In this article, the finite-time containment problem and the fixed-time containment problem accompanied by injection and deception attacks (IDAs) and Markov switching topology for second-order nonlinear multi-agent systems (MASs) are investigated, respectively. By introducing a radial basis function neural network (RBFNN), the approximation property of radial basis neural networks is used to solve the unmeasurable difficulties of nonlinear functions and injection attacks. Finite-time and fixed-time distributed control protocols are proposed for switching topologies and attack-induced state deception and control injection, and finite-time and fixed-time containment as well as obtaining their corresponding sufficient conditions are achieved, respectively. Correspondingly, two examples are shown to demonstrate the feasibility of the control 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.

Fully distributed containment control of second-order nonlinear multi-agent systems using disturbance observer with directed graph

Fully distributed containment control of second-order nonlinear multi-agent systems using disturbance observer with directed graph

Fixed-time output consensus for nonlinear heterogeneous multi-agent systems with disturbances

The fixed-time output consensus is considered in this article for heterogeneous nonlinear first-order and second-order multi-agent systems with disturbances. Firstly, we design a distributed observer by the fixed-time consensus theory, realizing distributed control of the system under directed graph. Secondly, designing a fixed-time controller for the first-order nonlinear system with disturbances by using constant exponential and time-varying exponential coefficient methods. For the second-order nonlinear system with both matched and mismatched disturbances, designing a fixed-time tracking controller by using the backstepping method and robust sliding mode control. The designed controller effectively suppresses the mismatched disturbance of system and makes the multi-agent system achieve output consensus in a fixed time. Finally, we demonstrate the effectiveness of the protocol through numerical examples.