Stabilization And Control Theory Of Stochastic Differential Equations Under G-expectation And Jump Diffusion Systems

This thesis investigates the stabilization and control problems of stochastic differential equations under G-expectation and jump diffusion systems which include exponential stabilization of stochastic differential equations driven by G-Brownian motion(G-SDEs)under discrete time and delayed feedback control,stability of stochastic delay differential equations driven by G-Brownian motion(G-SDDEs)and large scale G-SDE,stabilization and optimal control of jump diffusion systems.It consists of six chapters.In the first chapter,we outline the background of the research and recall the related theories for G-Brownian motion process,G-SDE,jump diffusion system.Meanwhile,the main results and innovative contributions of this thesis are introduced.In the second chapter,we firstly analyze the p-th moment and quasi sure exponential stabilization of linear G-SDE with discrete time feedback control by using the comparative method,and then study the mean square exponential and quasi sure exponential stabilization of G-SDE under global uniform Lipschitz conditions(nonlinear case)with discrete time feedback control.Secondly,we give the quasi sure exponential stabilization of linear systems with discrete time stochastic feedback induced by G-Brownian motion under 0<p<1.In the third chapter,a feasible criterion for exponential stabilization of G-SDE under the delayed feedback control is given by comparison method,and a new criterion for mean square exponential stabilization of G-SDDE is established.In the fourth chapter,we firstly construct an auxiliary G-SDE and establish the coefficient connection relation with large-scale G-SDE,and give the sufficient condition for the exponential stability of large-scale G-SDE.Secondly,we study the necessary and sufficient conditions for the path exponential stability of some triangle G-SDE by using exponential martingale inequality.In the fifth chapter,stabilization,instability and inverse optimal control of jump diffusion systems are studied.Firstly,for periodic intermittent stochastic feedback systems induced by Levy noise,on the one hand,sufficient conditions for system stabilization are given by using exponential martingale inequality with jump.On the other hand,sufficient conditions for system instability are given by using the law of large numbers of local martingales.Secondly,we use the Legendrel-Fenchel transformation method to design the inverse pre-optimal controller to obtain the inverse optimal stabilization strategy for the regime-switching jump diffusion systems.In the last chapter,a brief summary of the dissertation and some possible problems for further research are given.