Cauchy problem for linearized system of two - dimensional isentropic flow with axisymmetrical initial data in gas dynamics 二維等熵流的線(xiàn)性化方程的具軸對(duì)稱(chēng)初值的柯西問(wèn)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(xiàn)性化方法將非線(xiàn)性系統(tǒng)轉(zhuǎn)化為線(xiàn)性系統(tǒng),再針對(duì)反饋線(xiàn)性化后的線(xiàn)性系統(tǒng)設(shè)計(jì)軌跡跟蹤控制器,實(shí)現(xiàn)被控對(duì)象對(duì)于連續(xù)變化給定信號(hào)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(guò)兩個(gè)實(shí)例,即一類(lèi)參激激勵(lì)作用下的duffing系統(tǒng)和一類(lèi)murali - lakshmanan - chua ( mlc )電路,考察隨機(jī)相位在非反饋混沌控制中的影響與作用,利用最大lyapunov指數(shù)和poincare截面分析法證實(shí)了隨機(jī)相位確實(shí)可以用來(lái)調(diào)節(jié)系統(tǒng)的混沌行為,即一個(gè)小的隨機(jī)相位的擾動(dòng)可能導(dǎo)致系統(tǒng)從有序轉(zhuǎn)變?yōu)闊o(wú)序,也可能使得系統(tǒng)從無(wú)序轉(zhuǎn)變?yōu)橛行颉?
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(dòng)點(diǎn)處jacobian矩陣特征根的性質(zhì),并據(jù)此將不動(dòng)點(diǎn)分成兩類(lèi),應(yīng)用變量的比例微分反饋法分別對(duì)這兩類(lèi)不動(dòng)點(diǎn)的可控性進(jìn)行了研究,研究發(fā)現(xiàn)該法只能實(shí)現(xiàn)第一類(lèi)不動(dòng)點(diǎn)及其相應(yīng)子空間的混沌控制,而不能完成第二類(lèi)不動(dòng)點(diǎn)的混沌控制,并給出了數(shù)值模擬結(jié)果,理論分析和數(shù)值模擬證實(shí)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(xiàn)中有關(guān)指數(shù)穩(wěn)定性的研究都是針對(duì)局部指數(shù)穩(wěn)定性展開(kāi)的,由于非線(xiàn)性系統(tǒng)的局部指數(shù)穩(wěn)定性可以通過(guò)其相應(yīng)的線(xiàn)性化系統(tǒng)得到,因此比較容易分析,而全局指數(shù)穩(wěn)定性則不然。