几类动态系统的静态输出反馈控制

发布时间：2018-05-28 08:58

本文选题：静态输出反馈 + 广义系统　；参考：《青岛大学》2017年博士论文

【摘要】：近些年来,作为控制理论和应用中的重要方法,静态输出反馈控制得到了普遍的关注。这是由于系统的状态经常是不可测的,但是系统的输出是可测的。另一方面,静态输出反馈控制方法简单,实施方便。实际系统中不可避免的包含了多种复杂动态,存在着脉冲行为、时滞、强耦合等。此时,广义系统、矩形系统、时滞系统、模糊系统、切换系统等能够更好地描述这些含有复杂动态的实际过程。本文在总结几种复杂动态系统的静态输出反馈控制研究基础上,应用Lyapunov稳定性理论,结合各种不等式技巧,深入地研究了线性系统、广义系统、时滞系统、矩形系统及混合系统的分析与静态输出反馈控制,发展了新的稳定性理论和静态输出反馈控制方法,本文的主要研究成果如下:1.研究线性系统的静态输出反馈控制方法。针对原有的路径追踪算法中的不收敛的问题,我们提出一个新的线性化方法,得到了改进的路径追踪算法,并证明了其收敛性。针对路径追踪算法是局部算法,求解能力依赖于初始值的问题,我们通过对能稳性条件的等价变化,得到了初始值优化算法,将其与改进的路径追踪算法相结合,可大大提高算法的寻优能力。另外,通过对Lyapunov函数的结构的等价变换,得到一个新的能稳性条件,该条件仍旧是BMI问题,但是只需固定少量变量,就可以将该条件转化为LMI问题。将初始值优化算法和新的能稳性条件相结合,又构造出一个求解静态输出反馈控制问题的新方法。以上方法都分别给出了连续系统和离散系统的不同形式。2.分别针对连续和离散两类系统,研究了广义系统的静态输出反馈控制问题。由于广义系统的稳定性条件中的Lyapunov矩阵不再是严格的正定矩阵,线性系统静态输出反馈的某些算法,例如初始值优化算法,无法直接应用到该系统中,需要研究新的有效方法。对于连续系统,我们研究了广义系统与马尔可夫跳跃系统结合在一起的混合系统,提出了求解该系统的静态输出反馈控制器的新的路径追踪算法。该算法的Step 1仅通过求解一个LMI优化问题就可以得到一个较好的初始值,从而避免了应用初始值优化算法。对于离散系统,我们将广义系统与模糊系统相结合,也给出静态输出反馈控制的新充分条件,基于该条件,构造了改进的锥补线性化算法。3.研究连续和离散时滞系统的稳定性分析和静态输出反馈控制问题。对于连续的T-S模糊时滞系统,通过构造新的增强型Lyapunov-Krasovskii泛函和应用保守性较低的Wirthinger-based积分不等式,得到新的稳定性判据。对于连续的广义时滞系统,我们研究其混合H∞和无源控制问题,通过应用文献[83]中的积分不等式,得到新的稳定性和能稳性判据,从而构造出求解静态输出反馈控制器的新算法。对于离散时滞系统,我们首先给出两个新的有限和不等式,得到离散时滞系统的新的保守性更低的稳定性和能稳性条件。应用初始值优化算法和改进的路径追踪算法求解静态输出反馈控制器。最后,对于离散的广义T-S模糊时滞系统,应用其中一个新的有限和不等式和增强型Lyapunov-Krasovskii泛函,得到新的稳定性判据和能稳性条件,并构造改进的锥补线性化算法求解。4.研究矩形时滞T-S模糊系统的正则化和能稳性问题。我们为离散的矩形时滞系统设计了动态补偿器,可使得闭环系统是方形的。给出了判断是否存在动态补偿器使得闭环系统是正则的,因果的充分必要条件。此外,给出两个判断闭环系统稳定的判据,并提出求解的算法。
[Abstract]:In recent years, as an important method in the control theory and application, static output feedback control has received widespread attention. This is because the state of the system is often inmeasurable, but the output of the system is measurable. On the other hand, the static output feedback control method is simple and convenient. In complex dynamics, there are impulse behavior, time delay, strong coupling and so on. At this time, generalized systems, rectangular systems, time-delay systems, fuzzy systems, switching systems and so on can better describe these complex dynamic processes. Based on the study of the static output feedback control of several complex dynamic systems, this paper applies the Lyapunov stability theory. On the basis of various inequality techniques, the analysis and static output feedback control of linear systems, generalized systems, time-delay systems, rectangular systems and hybrid systems are studied, and new stability theory and static output feedback control methods are developed. The main achievements of this paper are as follows: 1. the static output feedback control of linear systems is studied. Method. In view of the problem of non convergence in the original path tracking algorithm, we propose a new linearization method and obtain an improved path tracking algorithm, and prove its convergence. For the path tracking algorithm is a local algorithm, the solution ability depends on the initial value, and we get the equivalent change of the stability condition. The initial value optimization algorithm, combining it with the improved path tracking algorithm, can greatly improve the optimization ability of the algorithm. In addition, a new stability condition is obtained by the equivalent transformation of the structure of the Lyapunov function. The condition is still a BMI problem, but only a small number of variables are fixed, and the condition can be converted to the LMI problem. A new method for solving the static output feedback control problem is constructed by combining the initial value optimization algorithm with the new stability condition. The above methods have given the two kinds of continuous and discrete two classes of continuous and discrete systems respectively, respectively, and study the static output feedback control problem of the broad sense system. The Lyapunov matrix in the stability condition of the generalized system is no longer a strict positive definite matrix, and some algorithms of the static output feedback of the linear system, such as the initial value optimization algorithm, can not be applied directly to the system. We need to study the new effective method. For the continuous system, we study the combination of the generalized system and the Markov jump system. In a hybrid system, a new path tracking algorithm for the static output feedback controller of the system is proposed. The Step 1 of the algorithm can get a better initial value only by solving a LMI optimization problem, thus avoiding the application of the initial value optimization algorithm. For discrete systems, we have generalized system and fuzzy system. In addition, a new sufficient condition for the static output feedback control is also given. Based on this condition, an improved cone complement linearization algorithm.3. is constructed to study the stability analysis of continuous and discrete time-delay systems and the static output feedback control problem. For continuous T-S fuzzy time delay systems, a new enhanced Lyapunov-Krasovskii functional is constructed. A new stability criterion is obtained by applying the low conservative Wirthinger-based integral inequality. For continuous generalized time-delay systems, we study its mixed H infinity and passive control problems. By applying the integral inequality in the literature [83], we obtain new stability and stability criteria, thus constructing a static output feedback controller. For discrete time delay systems, we first give two new finite and inequalities, get the new stability and stability conditions of the discrete time-delay systems, and apply the initial value optimization algorithm and the improved path tracking algorithm to solve the static output feedback controller. Finally, the discrete generalized T-S fuzzy time fuzzy system is used. With a new finite and inequality and enhanced Lyapunov-Krasovskii functional, a new stability criterion and a stable condition are obtained, and an improved cone complement linearization algorithm is constructed to solve.4.'s regularization and stability problems for the T-S fuzzy systems with rectangular delay. We have designed the dynamics for a discrete rectangular delay system. The compensator can make the closed loop system square. It gives the sufficient and necessary condition for judging whether the dynamic compensator is regular and causality whether the dynamic compensator exists. In addition, two criteria to judge the stability of the closed loop system are given, and the algorithm for solving it is proposed.
【学位授予单位】：青岛大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13

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