随机时滞系统的有限时间随机性能优化与设计

Because of the high speed of response, the more tracking accuracy and the strength anti-interference etc., The finite-time stability and control problems for stochastic systems has been the current research hotspots.The stochastic finite-time stability and stabilization problems for stochastic time-delay systems are deeply studied, and the finite-time stochastic performance optimization and design problems, which are also the most important research problems, for stochastic time-delay systems are studied in this project. Firstly, based on the finite-time stability definition in the form of generalized KL functions, overcoming the effects of random factors and time-delay factors, the finite-time performance optimization index for stochastic time-delay systems including the definition of finite-time stochastic dissipativity and finite-time stochastic passivity are established. Then, On the basis of Lyapunov stochastic finite-time stability theorem, overcoming the effects of random factors and time-delay factors, the control theory of finite-time stochastic performance optimization for linear stochastic time-delay systems is developed in order that less time-delay conservativeness and more features on randomness are implied. And then, with the consideration of unknown parameters and nonlinear perturbances for stochastic time-delay systems, the state-feedback controller, stochastic dynamic output feedback controller and filter, which make the corresponding closed-loop control systems satisfying finite-time stochastic performance optimization index, are designed. Finally, we will apply the above theorems and approaches to the finite-time performance optimization and design for Ito type stochastic complex networks. The aim of this project is expanding the stochastic time-delay systems theory, and proposing the novel ways and approaches for this researches.

由于有限时间控制响应速度快，跟踪精度高，抗干扰性强等优点，随机系统有限时间稳定与控制已成为当前研究热点。本项目以随机时滞系统为研究对象,研究随机有限时间稳定与镇定，重点研究有限时间的随机性能优化与设计问题。首先,基于推广的KL函数形式有限时间稳定性定义,克服随机和时滞因素影响,建立随机时滞系统有限时间性能优化指标,包括有限时间随机耗散,无源等定义。然后,以Lyapunov随机有限时间稳定性理论为基础,克服随机与时滞的影响,以体现随机时滞系统特色、减少时滞的保守性为追求目标,建立线性随机时滞系统有限时间随机性能优化控制理论。进而,考虑随机时滞系统受到未知参数和非线性扰动等影响，设计状态反馈控制器、随机动态反馈控制器、滤波器等使系统满足有限时间随机性能优化指标。最后将上述理论与方法应用到Ito型随机复杂网络的有限时间性能优化与设计中。本项目旨在拓广随机时滞系统理论,为该研究提供新的途径与方法。

本项目以随机时滞系统为研究对象,研究随机有限时间稳定与镇定，重点研究有限时间的随机性能优化与设计问题。首先,基于推广的KL函数形式给出了有限时间稳定性定义,克服随机和时滞因素影响,建立随机时滞系统有限时间性能优化指标,包括有限时间随机耗散,无源等定义。然后,以Lyapunov随机有限时间稳定性理论为基础,以体现随机时滞系统特色、减少时滞的保守性为追求目标,建立线性随机时滞系统有限时间随机性能优化控制理论。最后将上述理论与方法应用到Ito型随机复杂网络的有限时间性能优化与设计中。围绕这一主题，在项目执行期间，在Applied Mathematics and Computation, Mathematical Problems in Engineering , Chinese Physics B,The Astronomical Journal, Acta Physica Sinica, 电子学报，ICACI，CCDC，数学杂志等国内外重要期刊或会议上发表论文16篇，其中SCI收录5篇，EI检索论文9篇，培养毕业研究生6人，在读研究生5名，实用性算法专利1项，参加国际国内学术会议50余人次。主要工作如下：.1.具有Markov切换和时滞的随机区间系统有限时间耗散控制与有限时间无源控制。针对具有Markov切换与时滞的随机区间系统，首先给出了有限时间随机有界，有限时间随机耗散，随机无源的定义，然后利用区间矩阵变换和Schur补定理，给出了若干充分条件，以及响应控制器的设计方法，并将结论运用到区间能量存储电路模型的控制中。.2.随机时滞神经网络的有限时间随机镇定控制器的设计。针对随机时滞惯性神经网络和随机时滞递归神经网络，借助Lyapunov理论和随机分析工具，给出了系统有限时间随机镇定的若干充分条件，进而设计了非线性时滞反馈控制器。.3.非线性随机时滞系统的鲁棒控制。针对一类具有Markov跳跃的离散时间随机时滞区间系统，利用矩阵变换给出了鲁棒时滞反馈控制器的设计方法，进而基于耗散性分析，给出了一类非线性鲁棒控制器的设计方法。.4.信号去噪方法与小波检测与谐波提取。通过计算无噪声脉冲信号的小波包系数分布特征，构造Laplace概率密度小波系数，获得经过消除的脉冲星信号无子采样小波包重建估计系数。提出了基于Synchroqueezing小波变换的一种谐波检测方法。