Cauchy problem for linearized system of two - dimensional isentropic flow with axisymmetrical initial data in gas dynamics 二維等熵流的線性化方程的具軸對稱初值的柯西問題
In this method , the feedback linearization method is used to convert the nonlinear system into the linearized system , for which the tracking controller is designed , by this way , the nonlinear chaotic system can be forced to track variable reference input 在該方法中,首先采用反饋線性化方法將非線性系統轉化為線性系統,再針對反饋線性化后的線性系統設計軌跡跟蹤控制器,實現被控對象對于連續變化給定信號的跟蹤控制。
Two illustrative examples , a duffing oscillator subject to a harmonic parametric control and a driven murali - lakshmanan - chua ( mlc ) circuit imposed with a weak harmonic control , are presented here to show that the random phase plays a decisive role for control function . the method for computing the top lyapunov exponent is based on khasminskii ' s formulation for linearized systems . then , the obtained results are further verified by the poincare map analysis on dynamical behavior of the system , such as stability , bifurcation and chaos 通過兩個實例,即一類參激激勵作用下的duffing系統和一類murali - lakshmanan - chua ( mlc )電路,考察隨機相位在非反饋混沌控制中的影響與作用,利用最大lyapunov指數和poincare截面分析法證實了隨機相位確實可以用來調節系統的混沌行為,即一個小的隨機相位的擾動可能導致系統從有序轉變為無序,也可能使得系統從無序轉變為有序。
Third , controlling chaos in the chaotic n - scroll chua ' s circuit is studied . the approach taken is to use feedback of a single state variable in a simple pd ( proportional and differential ) format . first , the unstable fixed points in the n - scroll chua ' s circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized system matrix at the fixed points 第三,研究了多渦卷chua電路中不動點處jacobian矩陣特征根的性質,并據此將不動點分成兩類,應用變量的比例微分反饋法分別對這兩類不動點的可控性進行了研究,研究發現該法只能實現第一類不動點及其相應子空間的混沌控制,而不能完成第二類不動點的混沌控制,并給出了數值模擬結果,理論分析和數值模擬證實了該方法的有效性。
The main contributions of this dissertation are summarized as follows : for the exponential stability of neural networks , many existing results are related to local exponential stability . since the local exponential stability of a nonlinear system is equivalent to that of its linearized system , it can be easily obtained 目前許多文獻中有關指數穩定性的研究都是針對局部指數穩定性展開的,由于非線性系統的局部指數穩定性可以通過其相應的線性化系統得到,因此比較容易分析,而全局指數穩定性則不然。