Globally Asymptotic Stability And Risk-sensitive Control Design Of Stochastic Nonlinear Systems

As is well known, there are rich results on stochastic systems and they have been widely applied in many fields such as mechanics, physics, economic, finance, engi-neering, machinery, power, control, etc. The stability is the most important topic in the field of stochastic systems since it is the premise condition of all the normal-work systems. By constructing a novel Lyapunov function and proposing a new control design, we study the globally asymptotic stability for a class of stochastic nonlinear systems with strict feedback forms, and the problem of the risk-sensitivity for a class of large-scale interconnected systems with time-varying delays.We now introduce our main results as follows:Firstly, we study the globally asymptotic stability for stochastic nonlinear sys-tems in strict-feedback form.In this part, we mainly discuss the stochastic nonlinear systems in strict-feedback form. By constructing a new Lyapunov function and designing the improved control, we prove that the globally asymptotic stability for the considered system can be guar-anteed by a smooth control without the condition of the smooth coefficients. The key of this problem is to find an appropriate Lyapunov function and apply the Ito formu-la and some important inequalities in stochastic differential equations to construct a control input such that the negative of the infinitesimal generator.Secondly, we deal with the decentralized risk-sensitivity for a class of large-scale stochastic interconnected systems with time-varying delays.In this part, we deal with the risk-sensitivity for a class of large-scale intercon-nected systems under the disturbance of the time-varying delays in the drift and d-iffusion coefficients. On one hand, the drift coefficients are considered under the condition of less than or equal to the unknown constants multiply by polymerization which is quite different from the known constants in the traditional works. On the other hand, the time-varying delays, which exist in both the drift coefficients and the diffusion coefficients, add difficulties to theoretical analysis. But it is widely used in real lives.Finally, we present some unsolved problems.