基于收缩理论的非线性控制及在无人机中的应用研究

发布时间：2018-05-14 00:41

本文选题：收缩理论 + 反步控制　；参考：《天津大学》2016年硕士论文

【摘要】：非线性系统是科学研究及现实生活各个领域内普遍存在的现象,因此非线性系统的控制研究,有着重要的理论和实际意义,并成为控制理论研究的热点之一。在传统非线性分析中,李雅普诺夫分析是常用的一种研究方法,该理论着重讨论的是平衡点的稳定性,即当系统受到轻微作用后,能否自动恢复到平衡点的能力。近年来,收缩理论作为一种研究非线性系统收敛性的新方法被提出并得到了广泛的应用。作为一个非线性系统的稳定性理论,收缩分析是基于连续介质力学和微分几何的,并不需要知道系统标称状态或者平衡点的具体信息,因此是一种更有前景的分析方法。本论文针对基于收缩理论的非线性控制以及在无人机中的应用展开以下三个方面的研究:针对一般的非线性参数严反馈系统,从系统轨迹收敛性角度出发,提出了一种基于收缩理论的自适应反步跟踪控制方法,首先为了保证收缩性,根据子系统的分层联接方式对虚拟及实际控制输入进行了设计,然后针对不确定性参数,利用收缩自适应设计了自适应估计律,并依据收缩自适应引理确保闭环系统轨迹的渐近收敛性以及估计值的有界性。针对一类不确定非线性参数严反馈系统,提出了基于收缩理论的自适应动态面控制方法。动态面控制器设计保证各子系统关于状态误差部分收缩;对于不确定参数构造收缩自适应律;并利用收缩下的奇异摄动分析降阶处理子系统,确保降阶前后状态误差间的偏差及滤波误差有界;通过分层子系统的收缩鲁棒性分析,证明了原闭环系统状态半全局收敛到以期望轨迹为中心的球域内,保证了跟踪误差及自适应估计有界。针对无扰动的无人机姿态角模型,在拉格朗日意义下引入多变量收缩反步法,结合收缩法的特征值分析方法,对单无人机的姿态模型进行了控制器设计并对其稳定性进行了详细的证明,然后在此基础上,考虑最基本的通信拓扑图,将多变量的收缩反步法扩展到多无人机姿态角模型的同步控制上,最后进行仿真实例验证,说明了此方法的有效性。
[Abstract]:Nonlinear system is a common phenomenon in various fields of scientific research and real life. Therefore, the study of nonlinear system control has important theoretical and practical significance, and has become one of the hotspots of control theory research. In the traditional nonlinear analysis, Lyapunov analysis is a common research method. This theory focuses on the stability of the equilibrium point, that is, the ability to automatically recover to the equilibrium point when the system is subjected to slight action. In recent years, contraction theory as a new method to study the convergence of nonlinear systems has been proposed and widely applied. As the stability theory of a nonlinear system, contraction analysis is based on continuum mechanics and differential geometry, and it does not need to know the specific information of the nominal state or equilibrium point of the system, so it is a more promising analysis method. In this paper, the nonlinear control based on contraction theory and its application in UAV are studied in the following three aspects: for the general nonlinear parametric strict feedback system, the trajectory convergence of the system is considered. In this paper, an adaptive backstepping tracking control method based on contraction theory is proposed. Firstly, virtual and actual control inputs are designed according to the hierarchical connection of subsystems, and then the uncertain parameters are designed. The adaptive estimation law is designed by using the contraction adaptive method, and the asymptotic convergence and boundedness of the estimated value are ensured according to the contraction adaptive Lemma. An adaptive dynamic surface control method based on contraction theory is proposed for a class of uncertain nonlinear parametric strict feedback systems. The dynamic surface controller is designed to guarantee the partial contraction of the subsystems about the state error, to construct the contraction adaptive law for the uncertain parameters, and to use the singular perturbation analysis of the contraction to reduce the order of the subsystem. It is proved that the state of the original closed-loop system converges semi-globally to the spherical domain centered on the desired trajectory through the analysis of the contraction robustness of the hierarchical subsystem. The tracking error and adaptive estimation are guaranteed to be bounded. In view of the attitude angle model of unmanned aerial vehicle (UAV) without disturbance, the multivariable contractile backstepping method is introduced in the sense of Lagrange, and the eigenvalue analysis method of the contraction method is combined. In this paper, the attitude model of single UAV is designed and its stability is proved in detail. Based on this, the most basic communication topology is considered. The multivariable contractile backstepping method is extended to the synchronization control of the multi-UAV attitude angle model. Finally, a simulation example is given to illustrate the effectiveness of the method.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：V279

【相似文献】