本文選題：脈沖隨機系統(tǒng) + 有限時間穩(wěn)定　； 參考：《安徽工業(yè)大學(xué)》2017年碩士論文

【摘要】：近年來,混雜系統(tǒng)受到越來越多學(xué)者的關(guān)注,原因在于它不僅能代表現(xiàn)實中很多復(fù)雜的系統(tǒng),而且有著重要的理論研究價值與工程實踐背景;脈沖隨機系統(tǒng)作為一類重要的混雜系統(tǒng),為系統(tǒng)工程和控制領(lǐng)域提供了許多豐富的研究課題,引起了國內(nèi)外眾多學(xué)者的研究興趣。此外,在工程應(yīng)用中,例如導(dǎo)彈系統(tǒng)、機器人操控系統(tǒng)、通信網(wǎng)絡(luò)系統(tǒng)等一些工作時間短、反應(yīng)快的系統(tǒng)中,有限時間穩(wěn)定性就顯得比漸近穩(wěn)定性更為重要。本文主要研究了脈沖隨機系統(tǒng)的有限時間穩(wěn)定性與控制設(shè)計問題,具體內(nèi)容如下:1.研究了一類線性脈沖隨機定常時滯系統(tǒng)的有限時間穩(wěn)定與控制問題。首先,基于有限時間穩(wěn)定性的概念,利用Lyapunov-Krasovskii泛函法和Lyapunov函數(shù)法,結(jié)合時滯微分不等式技巧以及相關(guān)引理,獲得了兩個基于平均脈沖區(qū)間約束下的系統(tǒng)有限時間均方穩(wěn)定充分條件。然后對兩種方法得到的穩(wěn)定充分條件進行了分析比較,并在有限時間穩(wěn)定充分條件的基礎(chǔ)上,以線性矩陣不等式(LMIs)形式給出了狀態(tài)反饋控制器的設(shè)計方案。最后,由數(shù)值例子和圖像仿真說明了結(jié)果的正確性。2.進一步討論了帶時變時滯的非線性脈沖隨機系統(tǒng)的有限時間穩(wěn)定與控制問題。首先,通過建立合適的時滯相關(guān)Lyapunov-Krasovskii泛函以及適當(dāng)?shù)牟坏仁椒趴s技巧,結(jié)合相關(guān)引理和平均脈沖區(qū)間的概念,并以LMIs形式給出系統(tǒng)有限時間均方穩(wěn)定的充分條件。然后基于所提出的穩(wěn)定條件,為系統(tǒng)設(shè)計了狀態(tài)反饋控制器,以保證相應(yīng)的閉環(huán)系統(tǒng)是有限時間均方穩(wěn)定的。最后,以數(shù)值例子和圖像仿真驗證了該部分結(jié)論的可行性。3.考慮到H∞控制理論在擾動抑制方面的重要作用,針對一類脈沖隨機系統(tǒng)的有限時間H∞控制問題進行了研究。首先,基于H∞控制理論以及Lyapunov函數(shù)法等,結(jié)合相關(guān)引理、矩陣分析以及平均脈沖區(qū)間的約束條件,以LMIs形式給出了系統(tǒng)有限時間均方穩(wěn)定以及均方有界的充分條件。然后分析了系統(tǒng)的有限時間H∞性能,并設(shè)計了有限時間H∞控制器保證閉環(huán)系統(tǒng)是有限時間均方有界的且滿足一定H∞性能指標(biāo)。最后,通過數(shù)值例子和圖像仿真驗證了所設(shè)計控制器的有效性。
[Abstract]:In recent years, hybrid systems have attracted more and more attention of scholars, because they not only represent many complex systems in reality, but also have important theoretical research value and engineering practice background. As an important class of hybrid systems, impulsive stochastic systems provide a lot of research topics for the system engineering and control fields, and have aroused the interest of many scholars at home and abroad. In addition, finite time stability is more important than asymptotic stability in engineering applications, such as missile system, robot control system, communication network system and so on. In this paper, the finite time stability and control design of impulsive stochastic systems are studied. The main contents are as follows: 1. In this paper, the finite time stability and control problems of a class of linear impulsive stochastic time-delay systems are studied. First of all, based on the concept of finite time stability, using Lyapunov-Krasovskii functional method and Lyapunov function method, combined with delay differential inequality techniques and related Lemma, Two sufficient conditions for the finite time mean square stability of the system based on the mean impulsive interval constraint are obtained. Then, the stability sufficient conditions obtained by the two methods are analyzed and compared. On the basis of the sufficient stability conditions in finite time, the design scheme of the state feedback controller is given in the form of linear matrix inequality (LMI). Finally, numerical examples and image simulations show the correctness of the results. The finite time stability and control of nonlinear impulsive stochastic systems with time-varying delays are discussed. Firstly, by establishing appropriate delay-dependent Lyapunov-Krasovskii Functionals and appropriate inequality scaling techniques, combining the concepts of correlation Lemma and mean impulsive interval, a sufficient condition for the finite time mean square stability of the system is given in the form of LMIs. Then a state feedback controller is designed for the system based on the proposed stability conditions to ensure that the closed-loop system is finite-time mean-square stable. Finally, the feasibility of the conclusion is verified by numerical examples and image simulations. Considering the important role of H 鈭，

本文編號：1950842