冠状动脉时滞系统混沌同步算法研究

发布时间：2018-04-19 06:18

本文选题：稳定性分析 + 线性矩阵不等式　；参考：《天津工业大学》2017年硕士论文

【摘要】：冠状动脉是为心脏供给氧气和营养的动脉血管。临床上,冠状动脉的痉挛和阻塞会导致心肌梗死、心绞痛等疾病。近些年来,研究者用Duffing方程描述冠状动脉系统,并证明了其中含有混沌特性。因此,从混沌同步控制的角度出发,提出相关的控制策略,有一定的生物和临床医学价值。本文针对冠状动脉系统的混沌同步,进行了如下两方面研究:在实际治疗中,服用药物以及药物的吸收可能存在滞后。然而,现有的很多控制策略存在较大的保守性,甚至未考虑系统时滞。本文在考虑输入时滞的情况下,研究了冠状动脉的混沌同步问题。通过构造增广的Lyapunov-Krasovskii泛函,结合改进的Jensen不等式和Wirtinger型双重积分不等式,提出保守性较小的稳定性判据,在该稳定性判据的基础上设计带时滞的状态反馈控制器,从而实现冠状动脉系统的混沌同步。为了进一步减小保守性,采用分段时滞法,针对不同的分段区间构造不同的Lyapunov-Krasovskii泛函,得到了保守性更小的稳定性判据,并且将它用于冠状动脉时滞系统的混沌同步。冠状动脉系统是一个复杂的非线性系统。T-S模糊模型是对复杂非线性系统进行描述和分析的有力工具。本文提出了基于T-S模糊模型的冠状动脉系统模型。在将药物作用考虑成输入非线性的情况下,提出了参数自适应的控制策略,实现了冠状动脉系统的混沌同步控制。论文从以上两个方面对冠状动脉系统的混沌同步控制进行研究,为冠状动脉系统的相关研究提供了一种思路,丰富了已有的研究成果。
[Abstract]:The coronary artery is the artery that supplies oxygen and nutrition to the heart.Clinically, coronary artery spasm and obstruction can lead to myocardial infarction, angina and other diseases.In recent years, the Duffing equation has been used to describe the coronary artery system and it has been proved that there is chaos in it.Therefore, from the point of view of chaos synchronization control, the related control strategy is put forward, which has certain biological and clinical value.In this paper, the chaotic synchronization of coronary artery system has been studied as follows: in the actual treatment, drug taking and drug absorption may lag behind.However, many existing control strategies are conservative and do not even take time delay into account.In this paper, the chaotic synchronization of coronary artery is studied considering the input delay.By constructing the extended Lyapunov-Krasovskii functional, combining the improved Jensen inequality and the Wirtinger type double integral inequality, a less conservative stability criterion is proposed. Based on the stability criterion, a state feedback controller with time delay is designed.Thus the chaos synchronization of coronary artery system is realized.In order to further reduce the conservatism, the piecewise delay method is used to construct different Lyapunov-Krasovskii Functionals for different segmented intervals, and a less conservative stability criterion is obtained, which is applied to chaotic synchronization of coronary artery delay systems.Coronary artery system is a complex nonlinear system. T-S fuzzy model is a powerful tool for describing and analyzing complex nonlinear system.This paper presents a coronary artery system model based on T-S fuzzy model.When the drug action is considered as input nonlinearity, a parameter adaptive control strategy is proposed to realize chaotic synchronization control of coronary artery system.In this paper, the chaos synchronization control of coronary artery system is studied from the above two aspects, which provides a way of thinking for the research of coronary artery system, and enriches the existing research results.
【学位授予单位】：天津工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R54;TP13

【参考文献】