非线性时滞广义Markov跳跃系统的分析与控制

项目名称： 非线性时滞广义Markov跳跃系统的分析与控制

项目编号： No.61473173

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 马树萍

作者单位： 山东大学

项目金额： 82万元

中文摘要： 非线性时滞广义Markov跳跃系统是子系统为非线性时滞广义系统的一类随机混杂系统，广泛存在于混合动力电动汽车、经济等实际系统中。这类系统不仅含有非线性、时滞、随机切换，且具有脉冲行为，结构复杂，其性能分析和控制设计都极具挑战性。本项目拟在非线性满足一定条件下，利用系统等价变换和隐函数定理等分析非线性时滞广义Markov跳跃系统存在无脉冲唯一解的条件，并基于广义随机Lyapunov泛函、线性和非线性矩阵不等式等给出随机稳定性判据，进而利用非线性控制-状态对变换、奇异值分解等研究镇定控制、H∞控制，鲁棒稳定性、鲁棒控制问题，以及不定号二次指标最优控制及保性能控制等问题。并探讨系统在混合动力电动汽车建模和控制中的应用。项目首次探讨这类系统的随机切换时刻无脉冲条件和不定号最优控制问题。本项目的实施将建立非线性时滞广义Markov跳跃系统的基础理论体系，为相关实际系统提供有效的控制方法。

中文关键词： 非线性时滞广义Markov跳跃系统；无脉冲与随机稳定性；控制设计；鲁棒稳定与镇定；不定号二次指标最优控制

英文摘要： Nonlinear time-delay descriptor Markov jump systems are a class of stochastic hybrid systems whose subsystems are nonlinear time-delay descriptor systems, and they widely exist in practical systems, such as hybrid electric vehicle, economic systems and so on. The structures of this kind of systems are very complex, which not only contain nonlinearities, time-delays and random switchings, but also have impulsive behavior, and hence the performance analysis and control design for the systems are all challenge problems. In this project, under the nonlinearities satisfying some conditions, the existence condition of unique impulse-free solutions of nonlinear time-delay descriptor Markov jump systems will be analyzed by using system equivalent transformation and implicit function theorem, and based on the descriptor stochastic Lyapunov functional, linear matrix inequality and nonlinear matrix inequality methods, stochastic stability criterions of this kind of systems will be given. Then, by using nonlinear control-state pair transformation, singular value decomposition, some control problems for nonlinear time-delay descriptor Markov jump systems, such as stabilization, H-infinity control, robust stability and robust control problem, indefinite quadratic cost optimal control and indefinite quadratic guaranteed cost control and so on, will be researched. Finally,the applications for nonlinear time-delay descriptor Markov jump systems in modeling and controlling of hybrid electric vehicles will be discussed. In this project, inpulse-free conditions at random switching instants and the indefinite quadratic cost optimal control problem for nonlinear time-delay descriptor Markov jump systems will be discussed for the first time. According to the research for the project, the basic theoretical system of nonlinear time-delay descriptor Markov jump systems will be developed, and the effective control methods for corresponding practical systems will be provided.

英文关键词： nonlinear time-delay descriptor Markov jump systems;impulse-free and stochastic stability;control design;robust stability and stabilization;indefinite quadratic cost optimal control