The existence, uniqueness, globally exponential stability andspeed of exponential convergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concis...The existence, uniqueness, globally exponential stability andspeed of exponential convergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concise conditions, and theorems for estimating the global convergence speed approaching the equilibrium and criteria for its globally exponential stability are derived, Considering synapse time delay, by constructing appropriate Lyapunov functional, the existence of a unique equilibrium and its global stability for the delayed network are also proved. The results, which do not require the cloning template to be symmetric, are easy to use in network design.展开更多
PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID ...PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain systems.This paper continues the previous researches towards establishing a theoretical foundation of PID control,by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic systems.To be specific,a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion terms.It will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control,whenever the controller parameters are chosen from the constructed parameter set.Moreover,similar results can also be obtained for PD(PI)control in some special cases.A numerical example will be provided to illustrate the theoretical results.展开更多
基金This work was supported by the National Natural Science Foundation of China ( Grant No. 69871005) .
文摘The existence, uniqueness, globally exponential stability andspeed of exponential convergence for a class of cellular neural networks are investigated. The existence of a unique equilibrium is proved under very concise conditions, and theorems for estimating the global convergence speed approaching the equilibrium and criteria for its globally exponential stability are derived, Considering synapse time delay, by constructing appropriate Lyapunov functional, the existence of a unique equilibrium and its global stability for the delayed network are also proved. The results, which do not require the cloning template to be symmetric, are easy to use in network design.
基金supported by the National Natural Science Foundation of China under Grant No.12288201.
文摘PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain systems.This paper continues the previous researches towards establishing a theoretical foundation of PID control,by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic systems.To be specific,a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion terms.It will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control,whenever the controller parameters are chosen from the constructed parameter set.Moreover,similar results can also be obtained for PD(PI)control in some special cases.A numerical example will be provided to illustrate the theoretical results.
