Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz co...Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz condition. The main purpose of this paper is to take a step towards nonlinear growth rate for second-order systems. The control law is designed based on least squares （LS） algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems.展开更多
We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） ...We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.展开更多
This paper is concerned with the stability characteristics of nonlinear surface waves propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. These characteristics have been simulated numeri...This paper is concerned with the stability characteristics of nonlinear surface waves propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. These characteristics have been simulated numerically by using the perturbation method. The growth rate of perturbation is computed by solving the dispersion equation of perturbation. I found that the stability of nonlinear surface waves is affected by the frequency dependence of the electric permittivity εh and magnetic permeability μh of the LHM. The spatial evolution of the steady state field amplitude is determined by using computer simulation method. The calculations show that with increasing the effective refractive index nx at fixed saturation parameter μp, the field distribution is sharpened and concentrated in the nonlinear medium. The waves are stable of forward and backward behavior. At higher values of nx, attenuated backward waves are observed.展开更多
基金the National Natural Science Foundation of China (Grant Nos. 60204010 and 60474499)the Aviation Foundation of China(Grant No. 00E51083)
文摘Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz condition. The main purpose of this paper is to take a step towards nonlinear growth rate for second-order systems. The control law is designed based on least squares （LS） algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems.
基金supported by NSFC(11201380)the Fundamental Research Funds for the Central Universities(XDJK2012B007)+1 种基金Doctor Fund of Southwest University(SWU111021)Educational Fund of Southwest University(2010JY053)
文摘We consider the growth rate and quenching rate of the following problem with singular nonlinearityfor some positive constants b：, b2 （see Theorem 3.3 for the parametersfor some constantsHence, the solution （u, v） quenches at the originx = 0 at the same time ＇1＇ （see Theorem 4.3）. We also tind various other conditions tor the solution to quench in a finite time and obtain the corresponding decay rate of the solution near the quenching time.
基金National Natural Science Foundation of China （60674036, 60974003）, the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China （JQ200919）, the Program for New Century Excellent Talents in University of China （NCET-07-0513）, the Key Science and Technique Foundation of Ministry of Education of China （108079）, the Excellent Young and Middle-Aged Scientist Award Grant of Shandong Province of China （2007BS01010）
文摘This paper is concerned with the stability characteristics of nonlinear surface waves propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. These characteristics have been simulated numerically by using the perturbation method. The growth rate of perturbation is computed by solving the dispersion equation of perturbation. I found that the stability of nonlinear surface waves is affected by the frequency dependence of the electric permittivity εh and magnetic permeability μh of the LHM. The spatial evolution of the steady state field amplitude is determined by using computer simulation method. The calculations show that with increasing the effective refractive index nx at fixed saturation parameter μp, the field distribution is sharpened and concentrated in the nonlinear medium. The waves are stable of forward and backward behavior. At higher values of nx, attenuated backward waves are observed.
基金supported by the National Natural Science Foundations of China(61325016,61273084,and 61233014)the National Science foundation of Distinguished Young Scholar of Shandong Province of China(JQ200919)the Independent Innovation Foundation of Shandong University of China(2012JC014)
