复杂网络的定向控制及弹性系统的追踪控制

发布时间：2018-05-15 23:40

本文选题：定向控制 + 追踪控制　；参考：《天津大学》2015年硕士论文

【摘要】：本文对经典的弹性系统弦方程,欧拉梁方程和薛定谔方程进行研究。分别采用不同的方法,不同的控制策略对内部含有不确定干扰的薛定谔方程和欧拉梁方程进行研究。在工程上,由于边界控制的易实现性,本文也对欧拉梁边界干扰问题进行了讨论。最后对波网络的定向控制问题,运用谱方法和李雅普诺夫函数方法对简单的树形波网络进行研究。文章主要由两部分组成:跟踪与抗干扰控制和网络定向控制。跟踪与抗干扰控制主要研究单个系统的跟踪或抗干扰问题。讨论了一类薛定谔方程的追踪控制问题,假定系统内部带有不确定干扰,干扰的L2范数是一致有界的。利用滑模控制技术,设计了带有自适应增益的单位向量滑模控制器抵抗干扰,其中自适应率随着时间的变化是半正定的。通过构造李雅普诺夫函数证明了误差系统的渐近稳定性,即追踪系统能够渐近追踪到目标信号。进一步考虑了具有不确定内部干扰的欧拉梁方程的追踪控制问题。将追踪问题转化为追踪系统和目标信号的误差系统的稳定性问题。通过设计非线性控制器来抵抗干扰。证明了对任意的初值在某个区域闭环系统的能量是指数衰减的。对欧拉梁方程边界干扰问题进行分析,将Lions-Lax-Milgram定理推广到半线性的情形证明系统的可解性问题,然后运用拉塞尔不变集的思想证明了系统的局部渐近稳定性。最后,研究了树形波网络的定向控制问题。运用目标系统的信息设计了一种新的控制器以稳定系统的特定部分而对网络的其他部分没有影响。当目标系统的信息未知时,将其当做未知干扰进行处理,设计干扰辨识器对未知干扰进行估计。最后运用Lyapunov方法证明误差系统的稳定性。
[Abstract]:In this paper, the classical string equation, Euler beam equation and Schrodinger equation of elastic system are studied. The Schrodinger equation and Euler beam equation with uncertain interference are studied by different methods and different control strategies. In engineering, the boundary interference of Euler beam is also discussed because of the easiness of boundary control. Finally, a simple tree-wave network is studied by using spectral method and Lyapunov function method. This paper mainly consists of two parts: tracking and anti-jamming control and network orientation control. Tracking and anti-jamming control mainly study the single system tracking or anti-jamming problem. In this paper, the tracking control problem for a class of Schrodinger equations is discussed. It is assumed that there is an uncertain disturbance in the system, and the L 2 norm of the disturbance is uniformly bounded. Using sliding mode control technique, a unit vector sliding mode controller with adaptive gain is designed to resist interference, in which the adaptive rate is positive semidefinite with time. The asymptotic stability of the error system is proved by constructing Lyapunov function, that is, the tracking system can asymptotically track the target signal. Furthermore, the tracking control problem of Euler beam equation with uncertain internal disturbance is considered. The tracking problem is transformed into the stability of the tracking system and the error system of the target signal. A nonlinear controller is designed to resist interference. It is proved that the energy of a closed loop system with arbitrary initial values in a region is exponentially attenuated. The boundary disturbance problem of Euler beam equation is analyzed. The Lions-Lax-Milgram theorem is extended to the semi-linear case to prove the solvability of the system. Then the local asymptotic stability of the system is proved by using the idea of Russell invariant set. Finally, the directional control problem of tree wave network is studied. Using the information of the target system, a new controller is designed to stabilize the specific parts of the system without affecting the other parts of the network. When the information of the target system is unknown, it is treated as an unknown interference, and an interference identifier is designed to estimate the unknown interference. Finally, the Lyapunov method is used to prove the stability of the error system.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5;O231

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