| The analysis and control of stochastic systems have always been a hot topic in the control field,in which the control input can be divided into continuous control input(the control signal is executed continuously)and discontinuous control input(the control signal is executed discontinuously,like intermittent control,impulsive control,sliding mode control,sampling-data control etc.)In some applications,such as refrigerator refrigeration,air conditioning temperature adjustment,wind power generation,satellite orbit transfer,sterilization process,etc.,discontinuous control is more advantageous and can reduce control consumption.This thesis will focus on dynamic behaviors of several stochastic systems under intermittent control or impulsive control.The main content is summarized as follows:Firstly,the stabilization problem of nonlinear stochastic delayed systems via aperiodically intermittent control is studied.The average control rate and average control period are proposed to describe the characteristics of aperiodically intermittent control.By employing the Lyapunov method,inequalities techniques and the inductive method,we obtain the stability conditions of the closed-loop systems under the cases that the delay is strictly less than the average control interval length or the delay can be larger than the average control interval length,respectively.Simultaneously,we give the estimate for the lower bound of average control rate.The theoretical results are applied to stochastic delayed neural networks.The numerical simulations illustrate the effectiveness and superiority.Secondly,the stabilization problem of discrete-time stochastic delayed neural networks by aperiodically intermittent control is investigated.By applying the Lyapunov method,discrete-time inequalities techniques as well as the inductive method,we obtain the stability conditions of the closed-loop systems under the cases that the delay is strictly less than the average control interval length or the delay can be larger than the average control interval length,respectively.Simultaneously,we give the estimate for the lower bound of average control rate and the design for the controller gain matrix.Finally,the numerical example verifies the effectiveness of the theoretical results.Thirdly,the asynchronously intermittent control for the synchronization of stochastic complex networks with delays is studied,where the control/rest times of subsystems’ controllers are independent of each other.First,we design an auxiliary timer for each subsystem to compensate for the control time and rest time.Then we apply graph-theoretic techniques to deal with cross terms between subsystems.We obtain a synchronization criterion which is independent of the upper bound of delay.Simultaneously,we give the design for controller gain matrices.Finally,the numerical example verifies the effectiveness of the theoretical results.Fourthly,the input-to-state stability of nonlinear impulsive stochastic systems is investigated.Based on the non-exponential Lyapunov function and average dwell-time condition,we obtain the sufficient conditions for studied system to achieve the input-tostate stability under impulsive disturbance or impulsive control,respectively.At the same time,by combining graph-theoretic techniques,we also study the input-to-state stability of impulsive stochastic complex networks.Finally,we apply the theoretical results to spring-mass-damper system and coupled spring-mass-damper systems,respectively.The numerical simulations illustrate the effectiveness of the theoretical results.Finally,the input-to-state stability of mild solutions to infinite-dimensional impulsive stochastic systems is studied.By constructing a family of Yosida strong solution approximation systems and applying the non-exponential Lyapunov function,we obtain the sufficient conditions for studied system to achieve the input-to-state stability under impulsive disturbance or impulsive control,respectively.Simultaneously,we obtain the average dwell time for impulsive sequences.Furthermore,by combining graph-theoretic techniques,we also study the input-to-state stability of infinite-dimensional impulsive stochastic complex networks.Finally,we apply the theoretical results to the impulsive stochastic Korteweg-de Vries equation and the impulsive coupled stochastic reactiondiffusion neural networks. |
