非线性时滞广义Markov跳跃系统的分析与控制

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.

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。

非线性（时滞）广义Markov跳跃系统是一类重要的随机混杂系统，广泛存在于混合动力电动汽车、经济等实际系统中。这类系统结构复杂，不仅含有非线性、时滞、随机切换，且具有脉冲行为，分析其特性及控制问题都极具挑战性，具有重要理论意义和应用价值。.项目基于非线性广义Markov跳跃系统的本质特性，开展相关研究工作，取得了一系列重要的基础性研究成果。在非线性满足Lipschitz条件下，利用系统等价变换和隐函数定理分析了非线性连续广义半Markov跳跃系统的正则性、无脉冲性、解的存在唯一性、随机稳定性，并给出充分性条件；利用奇异值分解、矩阵解耦技术，研究了非线性连续广义半Markov跳跃系统的状态反馈镇定，鲁棒H∞和有限时间H∞状态反馈控制，有限时间H∞滤波问题，利用线性矩阵不等式（LMI），给出控制器及滤波器存在的条件及设计方法；研究了非线性时变时滞广义Markov跳跃系统的鲁棒H∞滤波问题，给出全维和降维滤波器设计方法。研究了连续广义半Markov跳跃系统的饱和控制和饱和H∞控制，不定号保性能控制问题，给出控制器存在条件及设计方法。基于T-S模糊模型，研究了（时变时滞）非线性连续广义半Markov跳跃系统的可靠性估计和有限时间输出反馈H∞控制问题，给出估计器和控制器存在的条件和设计方法。研究了单边Lipschitz非线性连续广义Markov跳跃系统的降阶未知输入及H∞观测器设计问题，利用矩阵广义逆及LMI，给出观测器设计方法。当转移概率为时变时，研究了非线性离散广义Markov跳跃系统有限时间稳定与镇定、基于观测器的有限时间H∞丢包控制，非线性广义非齐次Markov跳跃系统的有限时间H∞滤波，广义Markov跳跃系统的异步丢包H∞状态估计问题，给出控制器及估计器的设计方法。.上述研究成果发展和完善了非线性广义Markov跳跃系统理论体系，具有重要的科学意义，为实际应用提供理论支撑。