本文選題：隨機系統(tǒng) + 穩(wěn)定性　； 參考：《哈爾濱工業(yè)大學(xué)》2015年博士論文

【摘要】：隨著科技的進步,在實際應(yīng)用中對所建立的系統(tǒng)模型的精確度要求越來越高,傳統(tǒng)的確定性系統(tǒng)模型顯然已經(jīng)不能滿足這種高精度需求。另一方面,隨機因素和時滯又時常會破壞系統(tǒng)的性能和穩(wěn)定性,所以對隨機時滯系統(tǒng)的穩(wěn)定性研究和控制器設(shè)計就成為了一個亟待解決的問題。自適應(yīng)估計是估計系統(tǒng)中未知參數(shù)非常有效的方法,但由于隨機因素的影響,對帶有未知參數(shù)的非線性隨機系統(tǒng)進行參數(shù)估計和自適應(yīng)控制是很有難度的。本文利用隨機Lyapunov穩(wěn)定性理論、隨機積分性質(zhì)定理、線性矩陣不等式(LMI)以及參數(shù)分離理論對非線性隨機系統(tǒng)的穩(wěn)定性及控制器設(shè)計問題進行了研究。其主要研究內(nèi)容以及得到的結(jié)果包含以下幾個方面:利用Lyapunov-Krasovskii泛函結(jié)合線性矩陣不等式方法,基于單邊Lips-chitz條件和二次內(nèi)有界條件提出了一個新的時滯相關(guān)穩(wěn)定性判據(jù),由線性矩陣不等式給出了不確定隨機非線性系統(tǒng)保守性較小的穩(wěn)定性條件。設(shè)計了一個非脆弱狀態(tài)反饋控制器以保證閉環(huán)系統(tǒng)是魯棒隨機穩(wěn)定的,并且提出了H∞魯棒控制器設(shè)計方法,以確保閉環(huán)系統(tǒng)滿足一定的H∞性能。研究了Lipschitz隨機離散系統(tǒng)的觀測器設(shè)計。由于廣義Lipschitz條件能夠更好的利用非線性部分的結(jié)構(gòu)信息,所以將廣義Lipschitz條件引入到一類非線性隨機離散系統(tǒng)的觀測器設(shè)計中。對于非線性系統(tǒng)中不含有隨機因素的情形,給出了全階及降階觀測器設(shè)計方法,進而將其理論推廣至非線性隨機離散系統(tǒng),給出了非線性隨機離散系統(tǒng)的穩(wěn)定性判據(jù)和觀測器設(shè)計條件。利用LMI技術(shù)和二次穩(wěn)定性理論導(dǎo)出了新的觀測器合成方法�？紤]了一類非線性隨機(連續(xù)及離散)系統(tǒng)的自適應(yīng)觀測器設(shè)計。系統(tǒng)中未知常數(shù)參數(shù)假設(shè)為實范數(shù)有界的。將廣義Lipschitz條件引入到非線性隨機系統(tǒng)的自適應(yīng)觀測器設(shè)計中,可以更充分的利用非線性部分所提供的的結(jié)構(gòu)信息。基于Lyapunov-Krasovskii泛函方法和隨機Lyapunov穩(wěn)定性理論,設(shè)計出了一個新的使得誤差系統(tǒng)在均方意義下一致指數(shù)有界的自適應(yīng)觀測器設(shè)計條件。研究了一類帶有確定性擾動及隨機擾動的非線性隨機系統(tǒng)的自適應(yīng)估計及控制器設(shè)計問題。提出了一個新的設(shè)計分析方法構(gòu)造自適應(yīng)控制器。利用隨機Lyapunov理論,狀態(tài)反饋增益和觀測器增益設(shè)計的分離理論設(shè)計了自適應(yīng)狀態(tài)及參數(shù)估計器,以保證閉環(huán)系統(tǒng)是隨機穩(wěn)定的。并且把研究方法推廣至隨機時滯系統(tǒng),得到了參數(shù)估計器存在的充分條件。最后,給出了本文的總結(jié)及研究發(fā)展前景。
[Abstract]:With the development of science and technology, the accuracy of the established system model is becoming more and more high in practical application. The traditional deterministic system model obviously can not meet this kind of high precision demand. On the other hand, stochastic factors and delays often destroy the performance and stability of the system, so the stability research and controller design of stochastic time-delay systems become an urgent problem to be solved. Adaptive estimation is an effective method for estimating unknown parameters in the system. However, due to the influence of random factors, it is very difficult to estimate and control the parameters of nonlinear stochastic systems with unknown parameters. In this paper, the stability and controller design of nonlinear stochastic systems are studied by means of stochastic Lyapunov stability theory, stochastic integral property theorem, linear matrix inequality (LMI) and parameter separation theory. The main research contents and results are as follows: using Lyapunov-Krasovskii functional and linear matrix inequality method, a new delay-dependent stability criterion is proposed based on one-sided Lips-chitz condition and quadratic inner bounded condition. The stability conditions of uncertain stochastic nonlinear systems with less conservatism are given by using linear matrix inequalities (LMIs). In this paper, a non-fragile state feedback controller is designed to ensure that the closed-loop system is robust stochastic stable, and an H _ 鈭，

本文編號：1970279