双线性系统的迭代学习控制

发布时间：2018-04-13 18:21

本文选题：双线性系统 + 迭代学习控制　；参考：《广西科技大学》2017年硕士论文

【摘要】：双线性系统(Bilinear Control Systems)是结构简单的非线性系统,并且是最接近于线性系统的非线性系统。双线性系统的主要特点是含有状态变量和控制变量的乘积项,因此整体上是非线性系统,尽管对状态变量、控制变量分别是线性的。正是由于双线性系统存在这些显著的优点,使得双线性系统成为控制领域研究的热点之一。迭代学习控制是一种具有严格数学描述的智能控制方法,适用于有限区间上具有重复运动特性的被控系统。它的研究对建模复杂、系统具有不确定性及具有较强的非线性耦合等动力学系统有着重要的意义。本文针对几种不同模型的双线性系统讨论迭代学习控制算法的收敛性,并对其进行相关的理论分析,最后给出相应实例的数值仿真。本文由以下五部分构成:1.介绍了双线性系统的研究背景及意义、数学模型和研究现状,并概述了迭代学习控制的基本原理和研究现状,以及简单介绍了本文的主要工作和论文框架。2.针对一类连续双线性系统,设计了对数型迭代学习误差以及D型迭代学习控制律,并给出了迭代学习误差的收敛条件。通过严格的数学证明讨论了该控制算法的收敛性问题,最后通过仿真实例验证了其算法的有效性。3.考虑一类齐次输入离散双线性系统,提出了对数型迭代学习误差和指数型迭代学习律,给出了系统学习误差收敛的充分条件。通过严格的数学证明对算法的收敛性进行研究,最后通过实例仿真验证了将迭代学习控制算法应用到齐次输入的离散双线性系统的有效性。4.本章研究了一阶双曲型分布参数的双线性系统迭代学习控制问题,设计了闭环P型迭代学习控制器。通过和开环型迭代学习律的仿真结果进行对比,可看出闭环型迭代学习控制律具有更快的收敛速度。最后,对本文研究成果进行了总结,并探讨了在未来本文仍需进行深入研究的问题。
[Abstract]:Bilinear system Bilinear Control Systems is a simple nonlinear system and is the closest nonlinear system to the linear system.The main feature of bilinear systems is that they contain product terms of state variables and control variables, so they are nonlinear systems as a whole, although for state variables, control variables are linear.Because of these remarkable advantages, bilinear systems have become one of the hotspots in the field of control.Iterative learning control (ILC) is an intelligent control method with strict mathematical description. It is suitable for the controlled systems with repetitive motion in finite interval.Its research is of great significance to dynamic systems such as complex modeling, uncertain systems and strong nonlinear coupling.In this paper, the convergence of iterative learning control algorithm is discussed for bilinear systems with different models, and the relevant theoretical analysis is carried out. Finally, numerical simulation of corresponding examples is given.This article consists of the following five parts: 1.This paper introduces the research background and significance, mathematical model and research status of bilinear systems, summarizes the basic principle and research status of iterative learning control, and briefly introduces the main work of this paper and the framework of the paper .2.For a class of continuous bilinear systems, the logarithmic iterative learning error and D-type iterative learning control law are designed, and the convergence conditions of iterative learning errors are given.The convergence problem of the control algorithm is discussed by strict mathematical proof. Finally, the effectiveness of the algorithm is verified by a simulation example.In this paper, the logarithmic iterative learning error and exponential iterative learning law are proposed for a class of homogeneous input discrete bilinear systems, and the sufficient conditions for the convergence of learning errors are given.The convergence of the algorithm is studied by strict mathematical proof. Finally, the effectiveness of applying the iterative learning control algorithm to the homogeneous input discrete bilinear system is verified by an example.In this chapter, the iterative learning control problem for bilinear systems with first order hyperbolic distribution parameters is studied, and a closed loop P-type iterative learning controller is designed.By comparing with the simulation results of open-loop iterative learning law, it can be seen that the closed-loop iterative learning control law has faster convergence speed.Finally, this paper summarizes the research results and discusses the problems that need to be further studied in the future.
【学位授予单位】：广西科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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