Consensus Of Second-order Multi-agent Systems Research Articles

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.

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.

Novel Reference Trajectory-Based Finite-Time Consensus Protocols for Multiagent Systems With Non-Identical Nonlinear Dynamics

This paper investigates the finite-time consensus for second-order multiagent systems under directed networks, where each agent is described by a non-identical nonlinear system. By using the reference trajectory-based method, two novel protocols are developed for the leader-follower and leaderless cases, respectively. It is noted that the dynamical evolutions of each agent's state and the reference trajectory are coupled, and the information of reference trajectories is not allowed to transmit in the communication channels. By the developed protocols, the relative state errors among agents can converge to the origin (instead of a neighborhood of the origin) within a finite time, though there are unknown parameters in agents' dynamics. The nonlinear terms in agents' dynamics are not required to be bounded by known constants or functions, which invalidates many consensus schemes based on the sliding mode control. Using the graph theory, Lyapunov functional method and finite-time stability theory, sufficient conditions are established for the finite-time consensus of considered multiagent systems. Finally, simulation examples are given to validate the effectivity of the proposed protocols.

Resilient Bipartite Consensus of Second-Order Multiagent Systems With Event-Triggered Communication

This article investigates the resilient bipartite consensus problem for continuous-time second-order multiagent systems in the presence of totally bounded malicious nodes under signed digraphs. An event-based resilient impulsive algorithm is employed, which cannot only mitigate the malicious nodes’ influence on the convergence of normal ones but also reduce the communication loads of agents. A necessary and sufficient condition related to the network topology is established for solving resilient bipartite consensus by using system transformation. A numerical simulation illustrates the effectiveness of the result.

Distributed Predefined-Time Optimization for Second-Order Systems under Detail-Balanced Graphs

This paper studies the problem of distributed predefined-time optimization for leaderless consensus of second-order multi-agent systems under a class of weighted digraphs. The proposed framework has two main steps. In the first step, the agents communicate to perform a consensus-based distributed predefined-time optimization and to generate a constant optimal output reference for each agent. In the second step, each agent tracks its corresponding optimal output reference, using a sliding-mode controller to reach the global optimum in a predefined time, even under matched disturbances. The proposed algorithm relies explicitly on user-defined constant parameters. Numerical simulations are performed to validate the efficacy of the algorithm.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

The problem of fixed-time group consensus for second-order multi-agent systems with disturbances is investigated. For cooperative-competitive network, two different control protocols, fixed-time group consensus and fixed-time event-triggered group consensus, are designed. It is demonstrated that there is no Zeno behavior under the designed event-triggered control. Meanwhile, it is proved that for an arbitrary initial state of the system, group consensus within the settling time could be obtained under the proposed control protocols by using matrix analysis and graph theory. Finally, a series of numerical examples are propounded to illustrate the performance of the proposed control protocol.