Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of c...Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of chaos in the unified chaotic system using only a single variable feedback. The present controller, to our knowledge, is the simplest control scheme for controlling a unified chaotic system.展开更多
In tracking test, discharge is a complicated process and comparative tracking index (CTI) has wide varia-tion. To evaluate tracking resistance, the chaos analysis of discharge current is presented based on the trackin...In tracking test, discharge is a complicated process and comparative tracking index (CTI) has wide varia-tion. To evaluate tracking resistance, the chaos analysis of discharge current is presented based on the tracking test of phenolic resin in accordance with IEC60112. According to the characteristics of statistical self-similarity and complexity of discharge current, the largest Lyapunov exponent is calculated, and the 2-dimensional attractor of discharge current is reconstructed. Moreover, the attractors of discharge current and recurrence plots of different discharge states are reconstructed. The results indicate that the chaos attractors have different characteristics in evo-lutionary tracks, the topological structure and grain direction of recurrence plots show significant differences. The chaos attractor can describe the tracking process, the recurrence plot can identify the tracking state clearly, while its arithmetic is simple.展开更多
Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was...Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme.展开更多
We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states.The quantizer adopted in this paper takes finite many values.In particular,one zoomer is placed ...We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states.The quantizer adopted in this paper takes finite many values.In particular,one zoomer is placed at the input terminal of the quantizer,and another zoomer is located at the output terminal of the quantizer.The zoomers possess a common adjustable time-varying parameter.By using the adaptive laws for the time-varying parameter and estimating boundary error of values of quantization,the stabilization feedback controller with the quantized state measurements is proposed for a class of chaotic systems.Finally,some numerical examples are given to demonstrate the validity of the proposed methods.展开更多
文摘Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of chaos in the unified chaotic system using only a single variable feedback. The present controller, to our knowledge, is the simplest control scheme for controlling a unified chaotic system.
基金Supported by National Natural Science Foundation of China (No.50777048).
文摘In tracking test, discharge is a complicated process and comparative tracking index (CTI) has wide varia-tion. To evaluate tracking resistance, the chaos analysis of discharge current is presented based on the tracking test of phenolic resin in accordance with IEC60112. According to the characteristics of statistical self-similarity and complexity of discharge current, the largest Lyapunov exponent is calculated, and the 2-dimensional attractor of discharge current is reconstructed. Moreover, the attractors of discharge current and recurrence plots of different discharge states are reconstructed. The results indicate that the chaos attractors have different characteristics in evo-lutionary tracks, the topological structure and grain direction of recurrence plots show significant differences. The chaos attractor can describe the tracking process, the recurrence plot can identify the tracking state clearly, while its arithmetic is simple.
文摘Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme.
基金Supported by the National Science Foundation of China under Grant No.11172017the Guangdong Natural Science Foundation under Grant No.8151009001000061Natural Science Joint Research Program Foundation of Guangdong Province under Grant No.8351009001000002
文摘We investigate asymptotical stabilization for a class of chaotic systems by means of quantization measurements of states.The quantizer adopted in this paper takes finite many values.In particular,one zoomer is placed at the input terminal of the quantizer,and another zoomer is located at the output terminal of the quantizer.The zoomers possess a common adjustable time-varying parameter.By using the adaptive laws for the time-varying parameter and estimating boundary error of values of quantization,the stabilization feedback controller with the quantized state measurements is proposed for a class of chaotic systems.Finally,some numerical examples are given to demonstrate the validity of the proposed methods.
