三角结构随机非线性系统的非光滑镇定研究

项目名称： 三角结构随机非线性系统的非光滑镇定研究

项目编号： No.61203054

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 马莉

作者单位： 江苏大学

项目金额： 24万元

中文摘要： 随机非线性系统是近年来的一个研究热点。针对此类系统的控制设计，目前主要考虑系统在满足局部Lipschitz连续条件下的光滑镇定。然而，注意到许多实际系统本身含有非光滑的非线性动态，或者在控制设计中引入了非光滑项，从而导致基于局部Lipschitz连续的光滑性方法无法运用。基于此，本项目针对一类典型的随机非线性系统-三角结构随机非线性系统，研究其非光滑镇定问题。首先，在非Lipschitz连续条件下，建立随机非线性系统依概率全局渐近稳定性理论。然后，基于上述稳定性理论，针对下三角随机非线性系统，在局部Lipschitz连续情况下，研究其依概率有限时间镇定问题；在非Lipschitz连续情况下，研究其非光滑镇定问题。最后，对具有高次非线性和含有低次非线性的上三角随机非线性系统，研究其非光滑镇定问题。本项目的研究将为完善随机非线性系统的控制理论提供坚实的基础。

中文关键词： 非光滑控制；随机系统；非线性系统；；

英文摘要： Recently, the stochastic nonlinear systems have received much attention. For the above kind of systems, the control design problem mainly considers the smooth stabilization under locally Lipschitz continuous condition. However, we note that many practical systems inherently contain non-smooth nonlinearities, or could introduce the non-smooth nonlinearities by control design, which yields that the smooth-based control method can not be applied. To this end, this proposal will focus the research on the non-smooth stabilization of a typical kind of stochastic nonlinear systems, i.e., the triangular stochastic nonlinear systems. First of all, under the non-Lipschitz continuous condition, we will establish the globally asymptotic stability theory in probability for stochastic nonlinear systems. Next, based on the above stability theory, we will study the finite-time stabilization problem in probability for locally Lipschitz continuous lower-triangular stochastic nonlinear systems and the non-smooth stabilization for non-Lipschitz continuous lower-triangular stochastic nonlinear systems. Finally, we will consider the problem of non-smooth stabilization of upper-triangular stochastic nonlinear systems with higher-order nonlinearities and lower-order nonlinearities, respectively. This proposal could provide the solid th

英文关键词： nonsmooth control；stochastic systems；nonliear systems；；