The projection of the chaotic attractor observed from the Lorenz system in the X-Z plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype...The projection of the chaotic attractor observed from the Lorenz system in the X-Z plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype model for studying chaotic behaviour since it was coined. In this work we take one step further to investigate some fundamental dynamic behaviours of a novel hybrid Takagi-Sugeno （TS） fuzzy Lorenz-type system, which is essentially derived from the delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains the original Lorenz system of continuous-time TS fuzzy form as a special case. By simply and appropriately tuning the additional parametric perturbations in the two-rule hybrid TS fuzzy Lorenz-type system, complex （two-wing） butterfly attractors observed from this system in the three dimensional （3D） X-Y-Z space are created, which have not yet been reported in the literature, and the forming mechanism of the compound structures have been numerically investigated.展开更多
A control approach where the fuzzy logic methodology is combined with impulsive control is developed for controlling some time-delay chaotic systems in this paper. We first introduce impulses into each subsystem with ...A control approach where the fuzzy logic methodology is combined with impulsive control is developed for controlling some time-delay chaotic systems in this paper. We first introduce impulses into each subsystem with delay of the Takagi-Sugeno （TS） fuzzy IF-THEN rules and then present a unified TS impulsive fuzzy model with delay for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by the Lyapunov Razumikhin method, and a design procedure for estimating bounds on control matrices is also given. Several numerical examples are presented to illustrate the effectiveness of this method.展开更多
An inverse model control based on TS-fuzzy support vector regression( TS-fuzzy SVR) for a quadrotor aircraft is developed. The TS-kernel is the product of linear combination of input and a cluster of output correspond...An inverse model control based on TS-fuzzy support vector regression( TS-fuzzy SVR) for a quadrotor aircraft is developed. The TS-kernel is the product of linear combination of input and a cluster of output corresponding to a cluster of TS-type fuzzy rules. The output of TS-fuzzy SVR is a linear weighted sum of the TSkernels. The dynamical model of the quad-rotor aircraft is derived. A new control scheme combined with TSfuzzy SVR inverse model control and PID control is presented so that the TS-fuzzy SVR inverse model control enhances capabilities of disturbance rejection and the robustness while the PID control enhances fast responsiveness and reliability of the system. Simulation results show the capabilities of the developed control for the attitude system of quad-rotor aircraft.展开更多
In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control...In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.展开更多
Attitude identification method for unmanned helicopter based on fuzzy model at hovering is presented. The dynamical attitude model is considered as basis for attitude control and it is very complex. To reduce the comp...Attitude identification method for unmanned helicopter based on fuzzy model at hovering is presented. The dynamical attitude model is considered as basis for attitude control and it is very complex. To reduce the complexity of model, nonlinear model of unmanned helicopter with unknown parameters are to be determined by fuzzy system first and then derivative based gradient method is used to identify unknown parameters of model. Gradient method is used due to ability that fuzzy system is not necessarily to be linear in parameters, therefore all fuzzy sets for input and output can be adjusted. The validity of the proposed model was verified using experimental data obtained by the commercially available flight simulator X-Plane. The simulation results showed high accuracy of the modeling method and attitude dynamics data matched well with experimental data.展开更多
恒功率负载(constant power loads, CPL)的负阻抗特性是引起前端独立运行能够稳定的变换器带负载时却失去稳定的主要原因,由于电路状态方程的非线性,难以得到状态变量的时域解来判断系统稳定性。基于小信号线性化、以特征根的分布来评...恒功率负载(constant power loads, CPL)的负阻抗特性是引起前端独立运行能够稳定的变换器带负载时却失去稳定的主要原因,由于电路状态方程的非线性,难以得到状态变量的时域解来判断系统稳定性。基于小信号线性化、以特征根的分布来评估系统稳定性的方法,需要在平衡点处线性化并以数值方法求解特征根,且无法描述出大信号扰动时的渐近稳定范围。针对并网型三电平整流器直接带恒功率负载和以LC滤波器连接恒功率负载的2种系统,使用Takagi-Sugeno(TS)模糊推理模型方法建立考虑主电路参数和控制器参数的全阶模型,以线性矩阵不等式(linear matrix inequality,LMI)的半正定规划是否能够求解作为系统稳定判据,从而能够分析系统参数与稳定区间之间的关系。同时构造的Lyapunov备选函数能够绘制出稳定吸引域(stability domain of attraction,DOA),实现大扰动情况下的稳定性分析。仿真和实验验证了该方法的有效性和实用性。展开更多
基金Project partially supported by the Natural Science Foundation of Educational Committee of Anhui Province, China （Grant No 2006kj250B）.
文摘The projection of the chaotic attractor observed from the Lorenz system in the X-Z plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype model for studying chaotic behaviour since it was coined. In this work we take one step further to investigate some fundamental dynamic behaviours of a novel hybrid Takagi-Sugeno （TS） fuzzy Lorenz-type system, which is essentially derived from the delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains the original Lorenz system of continuous-time TS fuzzy form as a special case. By simply and appropriately tuning the additional parametric perturbations in the two-rule hybrid TS fuzzy Lorenz-type system, complex （two-wing） butterfly attractors observed from this system in the three dimensional （3D） X-Y-Z space are created, which have not yet been reported in the literature, and the forming mechanism of the compound structures have been numerically investigated.
基金supported by the Natural Science Foundation of Guandong Province,China (Grant No 8351009001000002)the National Natural Science Foundation of China (Grant Nos 60572073 and 60871025)
文摘A control approach where the fuzzy logic methodology is combined with impulsive control is developed for controlling some time-delay chaotic systems in this paper. We first introduce impulses into each subsystem with delay of the Takagi-Sugeno （TS） fuzzy IF-THEN rules and then present a unified TS impulsive fuzzy model with delay for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by the Lyapunov Razumikhin method, and a design procedure for estimating bounds on control matrices is also given. Several numerical examples are presented to illustrate the effectiveness of this method.
基金Sponsored by the Science and Technology Support Program of Jiangsu Province(Grant No.SBE2014070836)
文摘An inverse model control based on TS-fuzzy support vector regression( TS-fuzzy SVR) for a quadrotor aircraft is developed. The TS-kernel is the product of linear combination of input and a cluster of output corresponding to a cluster of TS-type fuzzy rules. The output of TS-fuzzy SVR is a linear weighted sum of the TSkernels. The dynamical model of the quad-rotor aircraft is derived. A new control scheme combined with TSfuzzy SVR inverse model control and PID control is presented so that the TS-fuzzy SVR inverse model control enhances capabilities of disturbance rejection and the robustness while the PID control enhances fast responsiveness and reliability of the system. Simulation results show the capabilities of the developed control for the attitude system of quad-rotor aircraft.
基金Project supported by the Natural Science Foundation of Yangzhou University of China （Grant No KK0513109）.
文摘In this paper, an approach to the control of continuous-time chaotic systems is proposed using the Takagi-Sugeno （TS） fuzzy model and adaptive adjustment. Sufficient conditions are derived to guarantee chaos control from Lyapunov stability theory. The proposed approach offers a systematic design procedure for stabilizing a large class of chaotic systems in the literature about chaos research. The simulation results on Rossler＇s system verify the effectiveness of the proposed methods.
文摘Attitude identification method for unmanned helicopter based on fuzzy model at hovering is presented. The dynamical attitude model is considered as basis for attitude control and it is very complex. To reduce the complexity of model, nonlinear model of unmanned helicopter with unknown parameters are to be determined by fuzzy system first and then derivative based gradient method is used to identify unknown parameters of model. Gradient method is used due to ability that fuzzy system is not necessarily to be linear in parameters, therefore all fuzzy sets for input and output can be adjusted. The validity of the proposed model was verified using experimental data obtained by the commercially available flight simulator X-Plane. The simulation results showed high accuracy of the modeling method and attitude dynamics data matched well with experimental data.
文摘恒功率负载(constant power loads, CPL)的负阻抗特性是引起前端独立运行能够稳定的变换器带负载时却失去稳定的主要原因,由于电路状态方程的非线性,难以得到状态变量的时域解来判断系统稳定性。基于小信号线性化、以特征根的分布来评估系统稳定性的方法,需要在平衡点处线性化并以数值方法求解特征根,且无法描述出大信号扰动时的渐近稳定范围。针对并网型三电平整流器直接带恒功率负载和以LC滤波器连接恒功率负载的2种系统,使用Takagi-Sugeno(TS)模糊推理模型方法建立考虑主电路参数和控制器参数的全阶模型,以线性矩阵不等式(linear matrix inequality,LMI)的半正定规划是否能够求解作为系统稳定判据,从而能够分析系统参数与稳定区间之间的关系。同时构造的Lyapunov备选函数能够绘制出稳定吸引域(stability domain of attraction,DOA),实现大扰动情况下的稳定性分析。仿真和实验验证了该方法的有效性和实用性。
