Impulsive synchronization of networked nonlinear dynamical systems

In this letter, leader-following consensus of a nonlinear MASs satisfying Lipschitz conditions with partial actuator saturation constraints is investigated First of all, an impulse control protocol which only requires local information of agents and their neighbors is proposed. Then, using Lyapunov stability theory, impulse control theory, and algebraic graph theory, sufficient conditions for the consensus of multi-agent systems are provided. Ultimately, numerical simulations are employed to show that the research findings are accurate.

Second-order consensus of multi-agent systems with nonlinear dynamics via impulsive control

In this paper, we consider the distributed synchronization problem of nonlinear dynamic networked systems with heterogeneous disturbances. For the rejection of disturbances, we propose dynamic controllers which do not rely on the disturbance information. By graph theory and Lyapunov methods, a sufficient condition for the synchronization of nonlinear networked systems is established and it relies on the knowledge of the smallest nonzero eigenvalues of graph Laplacians. In order to implement the proposed disturbance rejection protocols in a fully distributed fashion, adaptive control laws are proposed for the adjustment of coupling strengths of each subsystem. We show that connected network topologies are sufficient for synchronizing the networked systems with the proposed adaptive control laws. A simulation example is given to illustrate the disturbance rejection performance.

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

Second-order consensus in directed networks of identical nonlinear dynamics via impulsive control

This paper presents how to apply a newly developed general theory for the global transversality and tangency of flows in n-dimensional nonlinear dynamical systems to a 2-D nonlinear dynamical system (i.e. a periodically forced, damped Duffing oscillator). The global tangency and transversality of the periodic and chaotic motions to the separatrix for such a nonlinear system are discussed to help us understand the complexity of chaos in nonlinear dynamical systems. This paper presents the concept that the global transversality and tangency to the separatrix are independent of the Melnikov function (or the energy increment). Chaos in nonlinear dynamical systems makes the exact energy increment quantity to be chaotic no matter if the nonlinear dynamical systems have separatrices or not. The simple zero of the Melnikov function cannot be used to simply determine the existence of chaos in nonlinear dynamical systems. Through this paper, the expectation is that, from now on, one can use the alternative aspect to look into the complexity of chaos in nonlinear dynamical systems. Therefore, in this paper, the analytical conditions for global transversality and tangency of 2-D nonlinear dynamical systems are presented. The first integral quantity increment (i.e. the energy increment) for a certain time interval is achieved for periodic flows and chaos in the 2-D nonlinear dynamical systems. Under the perturbation assumptions and convergent conditions, the Melnikov function is recovered from the first integral quantity increment. A periodically forced, damped Duffing oscillator with a separatrix is investigated as a sampled problem. The corresponding analytical conditions for the global transversality and tangency to the separatrix are obtained and verified by numerical simulations. The switching planes and the corresponding local and global mappings are defined on the separatrix. The mapping structures are developed for local and global periodic flows passing through the separatrix. The mapping structures of global chaos in the damped Duffing oscillator are also discussed. Bifurcation scenarios of the damped Duffing oscillator are presented through the traditional Poincaré mapping section and the switching planes. The first integral quantity increment (i.e. L-function) is presented to observe the periodicity of flows. In addition, the global tangency of periodic flows in such an oscillator is measured by the G-function and G(1)-function, and is verified by numerical simulations. The first integral quantity increment of periodic flows is zero for their complete periodic cycles. Numerical simulations of chaos in such a Duffing oscillator are carried out through the Poincaré mapping sections. The conservative energy distribution, G-function and L-function along the displacement of Poincaré mapping points are presented to observe the complexity of chaos. The first integral quantity increment (i.e. L-function) of chaotic flows at the Poincaré mapping points is nonzero and chaotic. The switching planes of chaos are presented on the separatrix for a better understanding of the global transversality to the separatrix. The switching point distribution on the separatrix is presented and the switching G-function on the separatrix is given to show the global transversality of chaos on the separatrix. The analytical conditions are obtained from the new theory rather than the Melnikov method. The new conditions for the global transversality and tangency are more accurate and independent of the small parameters.

This article investigates the leader-following consensus of nonlinear time-delay multiagent system under impulsive control with simultaneous consideration of packet loss and parameter mismatch. Specifically, the inherent parameter mismatch between the leader's dynamics and followers' dynamics is explicitly addressed. To mitigate communication frequency, two novel impulsive control protocols are developed: 1) a pure impulsive scheme for theoretical analysis and 2) a limited impulsive strategy for practical implementation. Furthermore, an auxiliary function is introduced to characterize packet loss phenomena during information transmission, ensuring alignment with real-world communication constraints. By integrating impulsive control theory with reverse average dwell-time analysis, sufficient consensus criteria are rigorously derived for multiagent system with time delays and heterogeneous parameters. Finally some numerical simulations validate the effectiveness of the proposed control framework, demonstrating its capability to achieve consensus under practical communication imperfections.

This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.

Modeling of Microblogging Social Networks: Dynamical System vs. Random Dynamical System

Multi-formation control of nonlinear leader-following multi-agent systems

This paper focuses on addressing consensus and flocking issues in second-order nonlinear multi-agent systems (MASs) under the false data injection attacks. Novel adaptive control protocols are proposed to effectively mitigate the impact of these attacks by updating adaptive parameters. Based on algebraic graph theory, matrix theory and the Lyapunov approach, various sufficient conditions are established, which show the fixed-time consensus and finite-time flocking can be achieved for the MASs. Moreover, some upper bounds for the settling time are derived in terms of the parameters of the model. Finally, three simulation examples are presented to validate the efficacy of our proposed theoretical results.

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

This paper investigates the problem of fixed-time event-triggered consensus control for a class of multi-agent systems with disturbed and non-linear dynamics. A fixed-time consensus protocol based on an event-triggered strategy is proposed, which can ensure a fixed-time event-triggered consensus, reduce energy consumption, and decrease the frequency of controller updates. The control protocol can also be applied to the case when the systems are free of disturbances; it solves the problem of high convergence time of the systems and reduces energy consumption of the systems. Sufficient conditions are proposed for the multi-agent systems with disturbed and non-linear dynamics to achieve the fixed-time event-triggered consensus by using algebraic graph theory, inequalities, fixed-time stability theory, and Lyapunov stability theory. Finally, simulation results show that the proposed control protocol has the advantages of both event-triggered and fixed-time convergence; compared to previous work, the convergence time of the new control protocol is greatly reduced (about 1.5 s) and the update times are also greatly reduced (less than 50 times), which is consistent with the theoretical results.

Tins paper is concerned with a class of nonlinear networked control systems with network-induced delay shorter than one sample period. Based on the assumptions that the actuator node is time-driven and the controller node is event-driven, a Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear networked systems with delay. By means of Lyapunov functions, a method for designing a fuzzy state feedback controller to satisfy the prescribed H/sub /spl infin// performance index is proposed. The results are presented in terms of linear matrix inequalities (LMIs) which can be solved by LMI toolbox in Matlab 6.5. Finally, a numerical example is given to validate the proposed method.