The Directed Control Of Complex Network And Tracking Control Of Elastic System

In this paper, the classical elastic string equation, Euler-Bernoulli beam equation and schrodinger equation are studied. Using different methods and different control strategy to study tracking control problem of schrodinger equation and Euler-Bernoulli beam equation with uncertain internal disturbance. The boundary disturbance of Euler-Bernoulli system is talked due to the ease of implementation in the engineering. And then the topic of directed control of string network is introduced, using the spectral method and Lyapunov function to study the simple tree-shaped wave network.The paper consists of two parts that tracking, anti-disturbance control and the directed control of network. The tracking and anti-disturbance control mainly for the single system.A class of tracking control problem for the schrodinger equation with uncertain disturbance is shown, assume that disturbance is uniformly bounded in the meaning of L2 space. The unit vector controller with adaptive gain is designed to reject disturbance by sliding mode control technology. The adaptive rate is positive definite as the change of time. By constructing Lyapunov function to prove the asymptotic stability of the error system, That's tracking system can track the target trajectory asymptotically. Then consider the tracking control problem of Euler-Bernoulli beam equation with uncertain internal disturbance,the tracking problem can be transferred into stability of error system between the original tracking problem and the target system. To reject disturbance by designing a nonlinear controller. Finally, we prove that the closed loop system is exponential stability in a certain area for each initial value.Furthermore, analysing the problem of boundary disturbance and promote the LionsLax-Milgram theorem to semilinear case and prove the solvability of closed loop system.On the other hand, the thought of Lasalle Invariant set is applied to prove the local asymptotic stability.Finally, we study the directed control problem of tree-shaped wave network. First,a new controller is designed by the information of target network to stable specific part of network and have no effect on the rest of the system. When the information of target system is unknown, we regard it as a unknown disturbance, by designing the disturbance identifier to estimate the unknown disturbance and the stability of error system is proved by Lyapunov method.