Consensus Of Second-order Multi-agent Systems Research Articles

Finite-time consensus of second-order multi-agent connectivity preserving based on adaptive sliding mode control

This study addresses the problem of robust finite-time connectivity preserving consensus for second-order multi-agent systems (MASs) with a limited communication range. Considering that the communication ability of agents in practical applications is limited, this study introduces an innovative approach to the consensus protocol, which involves the incorporation of a potential function aimed at ensuring sustained communication connection within a MAS. In addition, a finite-time fault-tolerant consensus protocol for a second-order MAS with actuator additive faults and external disturbances is designed by combining sliding mode control (SMC) and adaptive control. Following the homogeneous theorem and the finite-time consensus theory, this study concludes that, under specific conditions, a MAS can achieve finite-time consensus. Moreover, an advanced control protocol named a super-twisting sliding mode control protocol is introduced to mitigate the undesirable chattering phenomenon in the SMC. Finally, the effectiveness and superiority of the proposed method are verified by numerical examples.

Novel distributed event/self-triggered sliding-mode control: Application to practical fixed-time consensus of second-order multi-agent systems

This paper presents a novel terminal sliding-mode control (SMC) protocol to accomplish the practical fixed-time (PFXT) consensus of second-order multi-agent systems (MASs) through event-triggered scheme (ETS). The main challenge is the digitization of SMC which prevents the controlled system from reaching an ideal sliding phase and the singularity problem in terminal sliding-mode controllers. Firstly, a novel method of PFXT stability is proposed, which guarantees the non-singularity for the controller. Secondly, based on the proposed PFXT control method, a practical non-singular terminal SMC strategy is designed to accomplish the PFXT consensus of MASs through ETS. Besides, a strictly positive minimal triggering interval of each follower is given to exclude the Zeno phenomenon. Different with conventional terminal SMC, maintaining the sliding trajectory constrained on the sliding manifold is not a premise to guarantee the system stability. Then, to eliminate the requirement of continuous monitoring for ETS, the SMC strategy is generalized to the self-triggered approach. At last, a numerical example is presented to validate the developed methods.

Differentially Private Consensus for Second-Order Multiagent Systems With Quantized Communication.

This article considers the differentially private consensus problem of discrete-time second-order multiagent systems with partially measurable states and limited communication channel capacity, where only the integer-value information of agents can be transmitted. To reduce the potential risk of state information disclosure in digital communication, a differentially private consensus algorithm via dynamic encoding-decoding is proposed for the second-order multiagent system to make agents achieve mean-square consensus by transmitting quantized integer values with privacy protection. To deal with the uncertainty of the quantizer saturation, the statistical analysis is given for the boundedness of the input of quantizers. It is shown that the expectation of the minimum memory capacity of quantizers is 2 bits. Finally, some simulation results are given to visualize our conclusions.

Fixed-time leader–follower consensus for second-order multi-agent systems: Variable exponent sliding mode control approach

This paper investigates the fixed-time leader–follower consensus (LFC) problem of second-order multi-agent systems (MASs) with bounded disturbance under directed interaction topology. First, a sliding mode manifold (SMM) with consensus errors–dependent variable exponential coefficient is given. Then, two sliding mode control (SMC) protocols are proposed. The proposed control protocols can eliminate the singularity, while guaranteeing the fixed-time reachability of the consensus errors to the sliding mode surface (SMS) and the fixed-time convergence of the consensus errors toward the origin along the SMS. Finally, the validity of the obtained methodology is confirmed by two simulation examples.

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.

Adaptive practical predefined-time leader-follower consensus for second-order multiagent systems with uncertain disturbances

This article investigates the predefined-time consensus tracking problem for second-order multiagent systems (MASs) with uncertain disturbances. First, a distributed estimator is proposed to estimate the leader's states within predefined time. Then, a novel sliding mode surface is constructed and an adaptive sliding mode observer is established to estimate the uncertain disturbances within predefined time. Subsequently, by employing the predefined-time sliding surface and the adaptive technique, a novel adaptive sliding mode consensus protocol is proposed to overcome the singularity problem and achieve practical predefined-time convergence of the tracking errors to the neighborhood of origin. The Lyapunov approach is employed to prove the practical predefined-time stability of second-order MAS and the settling time is only determined by a single parameter, which facilitates the control protocol design according to the convergence time requirement. Simulation results illustrate the effectiveness of the proposed control scheme.

Event-triggered global consensus of second-order multi-agent systems with asymmetric input saturation

This paper addresses the event-triggered global consensus issue of second-order multi-agent systems (MASs) with asymmetric input saturation, where the zero saturation bounds are allowed. First, for the leaderless situation, we propose an event-triggered mechanism and give the criterion for realizing global consensus. Different from the traditional event-triggered strategy in an effort to exclude the Zeno behavior, a preset minimum triggering interval is introduced. That is, the control input will not be updated within this interval after the latest trigger time, and the event-triggered condition is activated after this interval. Moreover, the above results are extended to the leader–follower case. Finally, some numerical examples illustrate the effectiveness of the developed schemes.

Asynchronous impulsive control for interval consensus of second-order multi-agent systems

This paper investigates the interval consensus problem of second-order multi-agent systems over a directed graph, where each agent is allowed to propose an interval constraint on the achievable consensus value. In order to reduce the communication among agents, a distributed impulsive controller is given. The impulsive control is implemented only at impulsive instants. Moreover, each agent has its own impulsive instants independently and the impulsive intervals are aperiodic. Sufficient conditions are established to guarantee the achievement of interval consensus for the considered systems. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained result.

Protocol selection for second-order consensus against disturbance

Noticing that both the absolute and the relative velocity protocols can solve the second-order consensus of multi-agent systems, this paper aims to investigate which of the above two protocols has better anti-disturbance capability, in which the anti-disturbance capability is measured by the L2 gains from disturbance to consensus errors. More specifically, by the orthogonal transformation technique, the analytic expression of the L2 gain of a second-order multi-agent system with the absolute velocity protocol is firstly derived, followed by the counterpart with the relative velocity protocol. It is shown that both the L2 gains for the absolute and the relative velocity protocols are determined only by the minimum non-zero eigenvalues of Laplacian matrices and the tunable gains of position-like and velocity-like states. Then, we establish the graph conditions to tell which protocol has better anti-disturbance capability. Moreover, we propose a two-step scheme to improve the anti-disturbance capability of second-order multi-agent systems. Finally, numerical tests are given for different types of interaction graphs.

Fully- and Partially- Distributed Adaptive Consensus of Second-Order Multi-Agent Systems Using Only Relative Position Measurements

Fully- and Partially- Distributed Adaptive Consensus of Second-Order Multi-Agent Systems Using Only Relative Position Measurements

Memory-Based Accelerated Consensus for Second-Order Multi-Agent Systems With Delay

Memory-Based Accelerated Consensus for Second-Order Multi-Agent Systems With Delay

Fixed-time Coordinated Tracking Consensus of Second-order Multi-agent Systems via Non-singular Terminal Sliding Mode

Fixed-time Coordinated Tracking Consensus of Second-order Multi-agent Systems via Non-singular Terminal Sliding Mode

Neural network-based adaptive consensus of second-order multi-agent systems with nonlinear uncertainties and unknown time delay

This paper studies the leader-following adaptive optimal neural network consensus (AONNC) of second-order multi-agent systems (SOMASs) with nonlinear uncertainties and unknown time delay. An objective function involving the squared distance error and control effort is introduced which will be minimized by the AONNC method. The controller consists of two main parts. The first linear part is based on state feedback control idea and it is designed in such a way that the linear part of each agent dynamics is stable and the objective function is minimum. The nonlinear part which is designed based on the neural network (NN) will compensate for the nonlinear uncertainties and the external disturbances. By defining the distance error between each follower and the leader and taking time derivative of it, the error dynamics of each agent is obtained. To estimate the NN gains, appropriate adaptive rules are presented. The Lyapunov stability criterion is employed to prove the asymptotic stability of SOMAS. It is proved that the time derivative of the Lyapunov function for the aforementioned AONNC method and the adaptation laws is negative and therefore, the consensus of SOMAS is achieved. To verify the AONNC protocol, a SOMAS consisting of five agents (one leader and four followers) is considered and the obtained results are discussed.

Finite-time dynamic event-triggered consensus of multi-agent systems with mismatched disturbances based on disturbance observer

In this paper, the finite-time dynamic event-triggered consensus of second-order multi-agent systems with mismatched disturbances is studied. First, a nonlinear finite-time disturbance observer is designed to estimate the mismatched and matched disturbance of each follower. Second, the nonlinear dynamic integral sliding surface is developed through the mismatched and matched disturbance estimated by the observer. Then, combined with the dynamic event trigger strategy and the designed integral sliding surface, a new distributed control protocol is proposed, ensuring the finite-time consensus of the system. An analysis of Zeno behavior has found that the event-triggered interval has a positive lower bound. Finally, the effectiveness of the proposed control algorithm is verified by numerical simulation.

Leader-following Consensus of Second-order Multi-agent Systems With Input Delays

Leader-following Consensus of Second-order Multi-agent Systems With Input Delays

Adaptive super-twisting control for leader-following consensus of second-order multi-agent systems based on time-varying gains

In this paper, robust distributed consensus control is designed based on adaptive time-varying gains for a class of nonlinear multi-agent systems (MAS) in the presence of uncertain parameters and external disturbances with unknown upper bounds. Due to various conditions and constraints, different dynamical models for the agents can be considered in practice. On the basis of a continuous homogeneous consensus method which has been proposed for the nominal nonlinear MAS, the discontinuous and continuous adaptive integral sliding mode control strategies are particularly designed and extended to accomplish exact and precise consensus for non-identical MASs influenced by imposed perturbations. However, it is noted that in practical problems, the exact upper bound of perturbations is unknown. Then, the proposed controllers have been improved in an adaptive scheme to overcome this drawback. In addition to the adaptive estimation strategy and time-varying gains, which address considered uncertain parameters in the dynamics of the following agents, the designed distributed super-twisting sliding mode strategy for nonlinear agents adjusts the gain of the control inputs and guarantees that the proposed protocol performs properly without any setbacks of the chattering phenomenon. The illustrative simulations depict the robustness, accuracy, and effectiveness of the designed methods.

Fixed-time consensus of second-order multi-agent systems with nonlinear dynamics

The authors mainly discuss finite-time tracking consensus and fixed-time tracking consensus of multi-agent systems for second-order with inherent nonlinear function and disturbance under a directed interaction graph in this work. By sliding mode control theory, consensus tracking controllers are proposed to ensure that sliding mode can be reached and maintain on it in finite time and fixed time. By using some theoretical knowledge of control, such as graph theory and Lyapunov theory, we make the system to reach consensus in finite time and fixed time by choosing the right parameters. In addition, the calculation leads to the conclusion that settling time of finite-time consensus is associated to initial state, while settling time of fixed-time consensus is interrelated to parameters but not to the initial state. The feasibility of the theory is proved by simulation experiments.

P Components of Cluster-Lag Consensus for Second-Order Multiagent Systems With Adaptive Controller on Cooperative-Competitive Networks.

The consensus tracking problem means that a group of followers tracks the desired trajectory with local communication. In this article, partial components of cluster consensus have been considered. In this scenario, the p components of the followers in different clusters track the leader at different lag times, while p components of each agent in the same cluster reach a consensus, which is called p components of cluster-lag (PCCL) consensus. By using a seminorm ||xi||2,p and a Lyapunov-Krasovskii functional, PCCL consensus for second-order multiagent systems with homogeneous nonlinear systems on cooperative-competitive networks has been considered. For the case that the communication network graph is undirected, a decentralized adaptive controller, which is based on the exchanged neighbors' information from the same cluster, is designed such that all the agents reach PCCL consensus. For the directed graph case, an adaptive protocol based on the intracoupling strength is constructed for each cluster to achieve PCCL consensus. Finally, two simulation examples are illustrated to show the effectiveness of the proposed control protocols.

Weighted Average Consensus of Second-order Multi-agent Systems with Various Intelligence Levels via Sampled-data Control

Weighted Average Consensus of Second-order Multi-agent Systems with Various Intelligence Levels via Sampled-data Control

Prescribed-time distributed observer based practical predefined-time leader-follower output consensus of second-order multiagent system with communication noises

This paper studies predefined-time leader-follower consensus issue for second-order multi-agent system (MAS) with communication noises over digraph. Crosstalk resistant adaptive noise canceller is utilized to filter out communication noise. Next, with the filtered states received from its neighbors, a prescribed-time distributed observer is first proposed, which requires no global information and provides prescribed-time leader's states estimation under noisy communication environment and directed communication graph. Then, an adaptive predefined-time control strategy is presented to counteract the mismatched disturbance caused by estimation error and achieve practical predefined-time leader-follower output consensus of the studied MAS. Lyapunov stability analysis proves that the developed distributed observer achieves prescribed-time convergence and the developed tracking controller achieves predefined-time convergence. Finally, the developed control strategy is applied to consensus tracking of networked single-link robotic manipulators and simulation results show its effectiveness.