In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabili...In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.展开更多
The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles （multi-UUVs） formation in the case of leader-following is adapted. As the communica...The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles （multi-UUVs） formation in the case of leader-following is adapted. As the communication between the UUVs is difficult and it is easy to be interfered under the water, time delay is assumed to be time-varying during the members communicate with each other. Meanwhile, the state feedback linearization method is used to transfer the nonlinear and coupling model of UUV into double-integrator dynamic. With this simplified double-integrator math model, the UUV formation coordinate control is regarded as consensus problem with time-varying communication delays. In addition, the position and velocity topologies are adapted to reduce the data volume in each data packet which is sent between members in formation. With two independent topologies designed, two cases of communication delay which are same and different are considered and the sufficient conditions are proposed and analyzed. The stability of the multi-UUVs formation is proven by using Lyapunov-Razumilkhin theorem. Finally, the simulation results are presented to confirm and illustrate the theoretical results.展开更多
基金Supported by the National Natural Science Foundation of China (61863022)the Natural Science Foundation of Gansu Province(20JR10RA329)Scientific Research and Innovation Fund Project of Gansu University of Chinese Medicine in 2019 (2019KCYB-10)。
文摘In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.
基金Projects(51309067,51679057,51609048)supported by the National Natural Science Foundation of ChinaProject(JC2016007)supported by the Outstanding Youth Science Foundation of Heilongjiang Province,ChinaProject(HEUCFX041401)supported by the Fundamental Research Funds for the Central Universities,China
文摘The new method which uses the consensus algorithm to solve the coordinate control problems of multiple unmanned underwater vehicles （multi-UUVs） formation in the case of leader-following is adapted. As the communication between the UUVs is difficult and it is easy to be interfered under the water, time delay is assumed to be time-varying during the members communicate with each other. Meanwhile, the state feedback linearization method is used to transfer the nonlinear and coupling model of UUV into double-integrator dynamic. With this simplified double-integrator math model, the UUV formation coordinate control is regarded as consensus problem with time-varying communication delays. In addition, the position and velocity topologies are adapted to reduce the data volume in each data packet which is sent between members in formation. With two independent topologies designed, two cases of communication delay which are same and different are considered and the sufficient conditions are proposed and analyzed. The stability of the multi-UUVs formation is proven by using Lyapunov-Razumilkhin theorem. Finally, the simulation results are presented to confirm and illustrate the theoretical results.
