【摘要】：脈沖微分系統(tǒng)作為刻畫突變現(xiàn)象的一類數(shù)學模型,在工業(yè)、經(jīng)濟等領(lǐng)域得到了諸多應用。迭代學習控制技術(shù)作為跟蹤問題的一類解決方案,在設(shè)備制造、機器運行等工業(yè)領(lǐng)域得到了廣泛應用。為解決某些帶有瞬時突變的運動軌線的有限時間跟蹤問題,本文研究了脈沖微分系統(tǒng)的迭代學習控制問題。主要內(nèi)容如下：首先,將跟蹤連續(xù)運動軌線的經(jīng)典方法和結(jié)果,延拓到跟蹤不連續(xù)運動軌線,針對一類非線性脈沖微分系統(tǒng),設(shè)計帶有初態(tài)學習的開環(huán)、閉環(huán)P型學習律,綜合利用脈沖Gronwall不等式,Holder不等式等方法,在L2范數(shù)意義下,給出初態(tài)偏移情形下的收斂性充分條件。通過數(shù)值算例,驗證了理論結(jié)果的有效性。其次,考慮到D型控制器具有前瞻、預測的特性,針對一類非線性脈沖微分系統(tǒng),設(shè)計帶有初態(tài)學習的開環(huán)、閉環(huán)PD型學習律,在λ范數(shù)意義下,給出初態(tài)偏移情形下的收斂性的充分條件。通過數(shù)值算例,驗證了理論結(jié)果的有效性。最后,為了讓控制器具有更靈活的控制手段,針對一類非線性脈沖微分系統(tǒng),設(shè)計帶有初態(tài)學習的開環(huán)、閉環(huán)PDDα型學習律,利用分數(shù)階分部積分公式,給出λ范數(shù)意義下,帶有初態(tài)偏移情形下的收斂性充分條件。通過數(shù)值算例,驗證了理論結(jié)果的有效性。通過在仿生機器魚速度控制的應用,驗證了PDDα型學習律在迭代速度和收斂精度方面,明顯優(yōu)于P型學習律和PD型學習律。
[Abstract]:As a kind of mathematical model, impulsive differential system (PDS) has been applied in many fields such as industry, economy and so on. As a kind of solution to tracking problem, iterative learning control technology has been widely used in equipment manufacturing, machine operation and other industrial fields. In order to solve the finite time tracking problem of some trajectory with instantaneous abrupt changes, the iterative learning control problem for impulsive differential systems is studied in this paper. The main contents are as follows: firstly, the classical methods and results of tracking continuous motion trajectory are extended to track discontinuous motion trajectory. For a class of nonlinear impulsive differential systems, an open-loop, closed-loop P-type learning law with initial learning is designed. By means of impulsive Gronwall inequality, Holder inequality and so on, the sufficient conditions of convergence in the case of initial state migration are given in the sense of L 2 norm. The validity of the theoretical results is verified by numerical examples. Secondly, considering the prospective and predictive characteristics of D-type controllers, an open-loop, closed-loop PD learning law with initial state learning is designed for a class of nonlinear impulsive differential systems. In the sense of 位 norm, Sufficient conditions for convergence in the case of initial state migration are given. The validity of the theoretical results is verified by numerical examples. Finally, for a class of nonlinear impulsive differential systems, an open-loop, closed-loop PDD 偽 learning law with initial state learning is designed for a class of nonlinear impulsive differential systems. In the sense of 位 norm, the fractional partial integral formula is used to design the open loop and closed loop PDD 偽 learning law for a class of nonlinear impulsive differential systems. Sufficient conditions for convergence with initial state migration. The validity of the theoretical results is verified by numerical examples. It is proved that PDD 偽 learning law is superior to P type learning law and PD type learning law in iterative speed and convergence accuracy through the application of speed control in bionic robot fish.
【學位授予單位】：貴州大學
【學位級別】：碩士
【學位授予年份】：2016
【分類號】：O175;O231
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本文編號：2407646