冠状动脉系统建模及其高阶滑模控制研究

Nonlinear science combined with biomedical engineering has yielded major advances in many areas of biological and medical research. The death rate of cardio and cerebrovascular diseases are the leading in all causes of deaths of residents. So, it is necessary to study the coronary artery system mathematical models to reveal the internal mechanism of the system. Firstly, it establishes a improved biomathema-tical model of coronary artery system. A qualitative and quantitative method will be used to analysis characteristics of chaotic dynamics which will find the way to chaos and the states of related variables when being at chaos．Due to the nonlinear differences between changes in vessel diameter, the behaviors of this system are highly complex in diseases such as vasospasm and myocardial infarction. Therefore, understanding its nonlinear behavior and suppressing undesired chaotic motion in coronary artery systems when it occurs are essential tasks. A higher order sliding mode adaptive control method is used to design a chaos suppression controller to tracking the control problem of chaotic coronary systems with dynamic uncertainties and unknown parameters. Hard constraints on the inputs can lead to performance degradation and even instability. Anti-windup control based on high order sliding control provides a method for resisting this performance degradation and helping to avoid the onset of instability. A higher order sliding mode control method is used to design a chaos suppression controller to deal with the control problem of chaotic coronary time-delay systems when the patients of cardio and cerebrovascular diseases are in drug absorption. From theory, the proposed controller drives the abnormal system to synchronize with the normal system despite different initial conditions and external disturbances. Finaly, it provides a theoretical basis and reference on prevention and curing some disease such as myocardial infarction and vasospasm. Finally a virtual simulation is build to verification the effectiveness of the proposed method.

非线性科学与生物医学工程的结合极大的推动生物医药领域的研究。由于心脑血管疾病死亡率占居人口总死亡率首位，有必要研究冠状动脉系统数学模型揭示系统内部机制。本项目建立改进的冠状动脉系统模型，定性和定量分析混沌动态特性，去探索发现系统走向混沌的过程和出现混沌时相应参变量状态。因为血管参数的变化会引起不同的非线性特点，如血管痉挛或者心肌梗死，所以，了解其非线性特性抑制有害的混沌行为显得至关重要。冠状动脉系统存在动态不确定和未知参数条件下设计高阶滑模自适应控制器；当执行机构控制信号受到硬约束时会导致吸能性能下降甚至不稳定，设计抗饱和高阶滑模控制器提高稳定性能；当心脑血管疾病病人对药物吸收各有不同时，研究冠状动脉时滞系统高阶滑模控制算法理论。从理论上验证处于血管痉挛时的运动可以与正常血管运动达到混沌同步，为有效防治和治疗心肌梗死和血管痉挛等疾病提供一定的理论依据及参考，最后采用虚拟仿真进行算法验证。

本课题探讨冠状动脉系统混沌同步控制相关问题，研究偏微分方程方法在冠状动脉系统低剂量CT图像去噪问题。在各向异性扩散模型基础上，提出了改进的4邻域偏微分降噪算法。将PMG模型与PMC模型进行融合，得到PMGC模型，以进一步提高降噪算法处理后的冠状动脉图像质量水平。计算机仿真和冠状动脉CT扫描数据实验结果显示，改进算法能够获得更高质量的重建图像，并具有较好的运算效率。此基础上研究了几种冠状动脉系统控制问题，首先，针对冠状动脉系统混沌同步问题，系统模型受到有界但未知的不确定干扰条件下,利用几何齐次性理论和积分滑模面设计高阶滑模自适应控制器，使响应系统在有限时间内跟踪驱动系统，该方法无需提前预知扰动边界。其次，考虑输入饱和限制的情况下，针对冠状动脉时滞混沌系统，提出一种带有输入饱和因子的 同步控制方法。基于李雅普稳定性理论和局部扇区条件，构造Lyapunov-Krasovskii泛函，推出冠状动脉混沌系统同步饱和控制条件。再次，考虑不同病人药物吸收时间不同，使用模糊控制和自由权积分不等式、Wirtinger双重积分不等式、改进的交互凸组合和变时滞划分的方法，设计冠状动脉系统混沌同步时滞系统控制器。最后，考虑系统状态不可测和外界不确定的情况下，针对冠状动脉时滞混沌系统，提出一种基于观测器的 同步控制策略,通过设计一个Luenberger状态观测器，实现健康冠状动脉系统的状态重构，基于李雅普稳定性理论，通过构造合适的Lyapunov-Krasovskii泛函，推导出基于观测器的同步控制条件为临床分析提供了有效的理论支持。. 在本课题的资助下，共发表论文20篇，其中SCI论文14篇，EI论文4篇，培养了硕士研究生8名。