本文選題：穩(wěn)定性分析 + 線性矩陣不等式　； 參考：《天津工業(yè)大學(xué)》2017年碩士論文

【摘要】：冠狀動脈是為心臟供給氧氣和營養(yǎng)的動脈血管。臨床上,冠狀動脈的痙攣和阻塞會導(dǎo)致心肌梗死、心絞痛等疾病。近些年來,研究者用Duffing方程描述冠狀動脈系統(tǒng),并證明了其中含有混沌特性。因此,從混沌同步控制的角度出發(fā),提出相關(guān)的控制策略,有一定的生物和臨床醫(yī)學(xué)價值。本文針對冠狀動脈系統(tǒng)的混沌同步,進行了如下兩方面研究:在實際治療中,服用藥物以及藥物的吸收可能存在滯后。然而,現(xiàn)有的很多控制策略存在較大的保守性,甚至未考慮系統(tǒng)時滯。本文在考慮輸入時滯的情況下,研究了冠狀動脈的混沌同步問題。通過構(gòu)造增廣的Lyapunov-Krasovskii泛函,結(jié)合改進的Jensen不等式和Wirtinger型雙重積分不等式,提出保守性較小的穩(wěn)定性判據(jù),在該穩(wěn)定性判據(jù)的基礎(chǔ)上設(shè)計帶時滯的狀態(tài)反饋控制器,從而實現(xiàn)冠狀動脈系統(tǒng)的混沌同步。為了進一步減小保守性,采用分段時滯法,針對不同的分段區(qū)間構(gòu)造不同的Lyapunov-Krasovskii泛函,得到了保守性更小的穩(wěn)定性判據(jù),并且將它用于冠狀動脈時滯系統(tǒng)的混沌同步。冠狀動脈系統(tǒng)是一個復(fù)雜的非線性系統(tǒng)。T-S模糊模型是對復(fù)雜非線性系統(tǒng)進行描述和分析的有力工具。本文提出了基于T-S模糊模型的冠狀動脈系統(tǒng)模型。在將藥物作用考慮成輸入非線性的情況下,提出了參數(shù)自適應(yīng)的控制策略,實現(xiàn)了冠狀動脈系統(tǒng)的混沌同步控制。論文從以上兩個方面對冠狀動脈系統(tǒng)的混沌同步控制進行研究,為冠狀動脈系統(tǒng)的相關(guān)研究提供了一種思路,豐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.
【學(xué)位授予單位】：天津工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：R54;TP13

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