In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent...In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.展开更多
This paper studies the output synchronization problem for a class of networked non-linear multi-agent systems with switching topology and time-varying delays. To synchronize the outputs,a leader is introduced whose co...This paper studies the output synchronization problem for a class of networked non-linear multi-agent systems with switching topology and time-varying delays. To synchronize the outputs,a leader is introduced whose connectivity to the followers varies with time, and a novel data-driven consensus protocol based on model free adaptive control is proposed, where the reference input of each follower is designed to be the time-varying average of the neighboring agents＇ outputs. Both the case when the leader is with a prescribed reference input and the case otherwise are considered.The proposed protocol allows for time-varying delays, switching topology, and does not use the agent structure or the dynamics information implicitly or explicitly. Sufficient conditions are derived to guarantee the closed-loop stability, and conditions for consensus convergence are obtained, where only a joint spanning tree is required. Numerical simulations and practical experiments are conducted to demonstrate the effectiveness of the proposed protocol.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61174094)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11202148)
文摘In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61333003 and 61773144
文摘This paper studies the output synchronization problem for a class of networked non-linear multi-agent systems with switching topology and time-varying delays. To synchronize the outputs,a leader is introduced whose connectivity to the followers varies with time, and a novel data-driven consensus protocol based on model free adaptive control is proposed, where the reference input of each follower is designed to be the time-varying average of the neighboring agents＇ outputs. Both the case when the leader is with a prescribed reference input and the case otherwise are considered.The proposed protocol allows for time-varying delays, switching topology, and does not use the agent structure or the dynamics information implicitly or explicitly. Sufficient conditions are derived to guarantee the closed-loop stability, and conditions for consensus convergence are obtained, where only a joint spanning tree is required. Numerical simulations and practical experiments are conducted to demonstrate the effectiveness of the proposed protocol.
