带脉冲时间窗口的脉冲控制系统稳定性

发布时间：2018-01-03 19:01

本文关键词：带脉冲时间窗口的脉冲控制系统稳定性　出处：《西南大学》2016年博士论文　论文类型：学位论文

【摘要】：本文主要研究带脉冲时间窗口的脉冲控制系统的稳定性.目前关于脉冲系统的研究大多假设脉冲发生的时刻是预先指定的(这种系统称为固定时刻的脉冲系统),或者由系统轨迹与某一超平面碰撞的时刻确定(这种系统称为状态相关脉冲系统).因此,可以说:“经典的脉冲控制总是假定脉冲的发生时刻是固定的或者是可以计算出来的.”而我们知道没有任何机器能把脉冲毫无差错地输入到系统中去,因为在期望输入的脉冲时刻和真实的输入时刻总之间存在误差的.例如,我们计划在t时刻输入一个脉冲,但是机器的输入时刻可能是在一个小的脉冲时间窗口(t-α,t+α)之内,其中,α是一个小正数并被叫做脉冲时间窗口,并且,这种情况在我们的现实中是非常常见的.但是关于这方面的文献是非常少的.我们的系统与目前存在的脉冲系统比较的话,有非常有用的价值.所以,对于脉冲时间窗口的研究是非常有意义的.我们主要在脉冲控制理论的基础上把有时间窗口考虑进去,从中找到脉冲时间窗口对系统的影响.我们把这种系统叫做带脉冲时间窗口的脉冲控制系统.具体做法是首先确定一个控制周期,在控制周期上确定脉冲时间窗口,每个脉冲都随机地在脉冲时间窗口内发生,随着时间的推移实现对原系统的镇定.总体来说,我们的工作主要集中在以下方面.首先,我们引入了带脉冲时间窗口的线性脉冲控制系统,研究了不同情况下该系统的渐近稳定性,得到了一些稳定性的判据,并通过数值例子验证理论结果的有效性.其次,通过推广传统的脉冲控制理论,我们建立了该系统的比较系统,从理论上证明了带脉冲时间窗口的脉冲控制系统的稳定性能够由其对应的比较系统的稳定性决定.应用该比较方法,实现了洛伦兹系统的镇定.再次,建立了一类带脉冲时间窗口的每个周期包含多个脉冲的周期控制系统.我们提出了三类系统的新模型,即带脉冲时间窗口的单脉冲控制系统,带脉冲时间窗口的交替脉冲控制系统,以及带脉冲时间窗口的三明治脉冲控制系统.我们研究了它们的稳定性,给出了线性矩阵不等式形式的稳定性判据,并通过蔡氏振荡器系统的镇定验证了结论的有效性.第四,我们研究了带脉冲时间窗口的脉冲时滞线性系统.在该系统中,我们假设脉冲是依赖时滞的.通过构建一个李雅普诺夫函数我们得到了保证该系统一致稳定的一些条件,并给出了一个例子来验证结果的有效性.最后,我们把T-S模糊模型和带脉冲时间窗口的脉冲控制思想结合在一起,建立了忆阻蔡氏混沌系统的一个T-S模糊模型,用带脉冲时间窗口的周期单脉冲控制方法来控制这个T-S模糊模型,通过设计一个合适的控制器,实现了对该系统的控制.
[Abstract]:This paper mainly studies the stability of impulsive control system with pulse time window. The current research on impulsive systems assume that the pulse time is pre specified (this system is called pulse system fixed time), or by the system trajectory and a super plane collision time is determined (this system is called state dependent impulsive systems). Therefore, we can say: "pulse classic control pulse is always assumed time is fixed or can be calculated." and we know that no machine can make the pulse without error is inputted to the system, because the pulse time in the desired input and real time error exists between the total input for example, we plan to input a pulse at t time, but the time machine may be input in a small pulse time window (t- alpha, alpha t+), which is an alpha A small positive number and called the pulse time window, and this situation is very common in our reality. But on the literature in this area is very small. Compared with the present system of the pulse of our system, a very useful value. So, for the study of pulse time window is very meaningful. We mainly based on impulsive control theory on the time window is taken into account, find the influence of the system from the pulse time window. We call this system called the pulse control system with pulse time window. The specific approach is to first determine a control cycle, determining the pulse time window in the control period each pulse, random pulse occurs in the time window, with the passage of time for the stability of the original system. Overall, our work focused on the following aspects. First of all, I Have introduced the pulse control system with linear pulse time window, we study the asymptotic stability of the system under different conditions, some criteria of stability are obtained, and the validity of the theoretical results is tested by numerical examples. Secondly, through the promotion of pulse traditional control theory, we establish a comparison of the system theoretically. That determines the stability of the system stability of impulsive control systems with impulse time window can by the corresponding application. The comparison method, the stabilization of Lorenz system. Thirdly, set up a class with each pulse cycle time window comprises a plurality of pulse cycle control system. We propose a new model of the three kind the system, namely single pulse control system with pulse time window, alternating with pulse time window pulse control system, and the pulse time window three pulse Meiji Impulse control system. We study their stability, given the stability criterion of linear matrix inequalities, and the validity of the conclusion is verified by the stabilization of Chua's oscillator system. Fourth, we study the linear impulsive delay systems with impulsive time window. In this system, we assume that the pulse is delay dependent by. To construct a Lyapunov function we obtain some conditions to ensure uniform stability of the system, the effectiveness and an example is given to verify the results. Finally, we put the fuzzy T-S model with impulsive control theory of time window together, set up a T-S memristor Chua's chaotic system fuzzy model with periodic impulsive time window single pulse control method to control the T-S fuzzy model, by designing a suitable controller, the realization of the system control.

【学位授予单位】：西南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O231

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