具有凸多面体不确定性的混杂随机微分方程的镇定分析

发布时间：2018-05-14 23:40

本文选题：混杂随机系统 + 凸多面体不确定性　；参考：《东华大学》2017年硕士论文

【摘要】：近年来,随着实际应用对系统的复杂程度要求越来越高,学者们纷纷开始关注具有凸多面体不确定的随机系统的稳定性以及稳定化问题,这类随机系统常见于元件随机故障及维修、互联子系统、环境突变等模型中,有广泛的研究价值。论文主要研究了基于离散观测数据的具有凸多面体不确定性的混杂随机系统的稳定化问题。论文主要包括两个部分。第一部分中,研究当具有凸多面体不确定性的混杂系统不稳定时,在系统的漂移项和扩散项上同时添加基于离散观测的状态反馈控制器,使得控制系统均方指数稳定,该控制系统是不带时滞的混杂系统,通过添加控制器引入了时滞量?(t)。该部分还结合Lyapunov函数对控制系统进行分析,建立了控制系统的稳定条件以及时滞量的确定准则。第二部分中,基于第一部分的基础,考虑了可变时滞的问题,即在带有变时滞的不稳定混杂系统中,在漂移项和扩散项添加带有时滞的控制器,使得混杂系统是指数稳定的。该系统中的可变时滞是t的有界函数,应用Razumikhin方法,求得介于两个连续状态观测之间的?的最佳边界,该部分中证明了时滞独立以及依赖于状态两种情况下的准则。论文应用LMI方法对控制项的系数矩阵进行求解,针对第一部分以及第二部分中时滞独立于状态的情况给出了相同的算例对结论进行验证,在相同的数值算例中,第一部分中需??0.0008132,第二部分中??0.09418。论文把凸多面体不确定性引入带有马尔科夫切换的随机微分方程中,这类系统可以更精确地描述现实生活中的部分系统,更能准确地反映系统的微小变化。在控制器的设计过程中,一般的方法是采用连续的观测数据,而论文是基于离散观测数据设计了反馈控制器,这种方法在实际应用里更加经济有效。
[Abstract]:In recent years, with the increasing demand for the complexity of the system, scholars have begun to pay attention to the stability and stability of stochastic systems with convex polyhedron uncertainty. This kind of stochastic system is widely used in the model of random failure and maintenance of components, interconnected subsystems, and environmental catastrophe. This paper mainly deals with the stabilization problem of hybrid stochastic systems with convex polyhedron uncertainty based on discrete observation data. The thesis mainly includes two parts. In the first part, when the hybrid system with convex polyhedron uncertainty is unstable, the discrete observation is added to the drift term and the diffusion term of the system simultaneously. The state feedback controller makes the mean square exponent of the control system stable. The control system is a hybrid system without delay. By adding a controller, the time lag is introduced (T). This part also combines the Lyapunov function to analyze the control system, and establishes the stability conditions of the control system and the determination criteria of the time delay quantity. In the second part, the system is based on the control system. In the first part, the problem of variable delay is considered, that is, in an unstable hybrid system with variable delay, a controller with time delay is added to the drift term and diffusion term. The hybrid system is exponentially stable. The variable delay in the system is a bounded function of t. The Razumikhin method should be used to obtain two continuous states of state. The best boundary between the measurements? In this part, the time delay independence and the two conditions dependent on the state are proved. The paper uses the LMI method to solve the coefficient matrix of the control term. The same numerical example is given to verify the conclusion for the first part and the second part of the time delay independent of the state. In the case of value calculation, the first part is required in the first part of the 0.0008132, the second part???? 0.09418. paper introduces the convex polyhedron uncertainty into the stochastic differential equation with Markoff switching. This kind of system can more accurately describe the part of the system in real life, more accurately reflect the small changes of the system. The general method is to use continuous observation data, and the paper is based on the discrete observation data to design the feedback controller. This method is more economical and effective in practical application.

【学位授予单位】：东华大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63

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