本文選題：切換系統(tǒng) + 平均駐留時間��； 參考：《哈爾濱工業(yè)大學(xué)》2016年博士論文

【摘要】：作為一類重要的混雜系統(tǒng),切換系統(tǒng)由若干個子系統(tǒng)以及一個協(xié)調(diào)各子系統(tǒng)之間切換的切換策略構(gòu)成,在自然科學(xué)、工程控制和社會系統(tǒng)等方面有著廣泛的應(yīng)用。近年來,學(xué)者們對切換系統(tǒng)進(jìn)行了深入的研究,取得了許多的研究成果。在對切換系統(tǒng)的控制問題進(jìn)行研究時,一般假設(shè)子系統(tǒng)和控制器同步運(yùn)行,然而,在實際工程控制中,系統(tǒng)在識別子系統(tǒng)和請求相應(yīng)的控制器時需要一段時間,控制器的切換相對于子系統(tǒng)的切換存在切換時延,從而產(chǎn)生異步切換。本文對幾類切換系統(tǒng)的異步控制問題進(jìn)行研究,主要內(nèi)容如下：對帶有非線性擾動的離散時間切換系統(tǒng),利用解分析法直接研究其動力學(xué)性質(zhì)。首先,通過迭代方法得到閉環(huán)切換系統(tǒng)的狀態(tài)解,利用平均駐留時間法對所得狀態(tài)解進(jìn)行分析,建立使得閉環(huán)切換系統(tǒng)指數(shù)穩(wěn)定的充分條件。其次,基于所得穩(wěn)定性條件,利用線性矩陣不等式方法,設(shè)計狀態(tài)反饋控制器。最后,給出求解狀態(tài)反饋控制器增益和最小平均駐留時間的最優(yōu)控制算法。這種解分析方法沒有使用任何李雅普諾夫函數(shù),為切換系統(tǒng)的研究提供了新的思路。對帶有非線性擾動的連續(xù)時間切換系統(tǒng),采用平均駐留時間方法,研究其有限時間異步控制問題�；陂]環(huán)切換系統(tǒng)的狀態(tài)解,使用Gronwall-Bellman不等式和平均駐留時間方法,建立使得閉環(huán)切換系統(tǒng)有限時間穩(wěn)定的判定條件。利用線性矩陣不等式法設(shè)計相應(yīng)的狀態(tài)反饋控制器,并給出求解狀態(tài)反饋控制器和平均駐留時間的算法。最后,通過具體仿真實例來驗證結(jié)論的正確性。對帶有時變時滯的切換系統(tǒng),基于模型依賴平均駐留時間方法,研究其異步H∞控制問題。所考慮的時變時滯不僅存在于系統(tǒng)狀態(tài)而且存在于系統(tǒng)的輸出。首先,將傳統(tǒng)的加權(quán)H∞性能的概念推廣到模型依賴平均駐留時間信號下的切換系統(tǒng)中,采用分段李雅普諾夫函數(shù)法,建立使得系統(tǒng)指數(shù)穩(wěn)定且具有H∞性能的判定準(zhǔn)則。其次,基于所選參數(shù)的數(shù)值,將子系統(tǒng)分成兩類進(jìn)行研究,設(shè)計兩類較平均駐留時間小的模型依賴平均駐留時間。最后,設(shè)計能夠保證閉環(huán)系統(tǒng)指數(shù)穩(wěn)定且具有H∞性能的動態(tài)輸出反饋控制器。給出動態(tài)輸出反饋控制器和模型依賴平均駐留時間的計算算法,并通過具體仿真實例來驗證算法的有效性。
[Abstract]:As an important hybrid system, the switched system is composed of several subsystems and a switching strategy to coordinate the switching between the subsystems. It has been widely used in natural science, engineering control and social systems. In recent years, scholars have carried on the thorough research to the switched system, obtained many research results. When studying the control problem of switching system, it is generally assumed that the subsystem and the controller run synchronously. However, in the actual engineering control, it takes some time for the system to identify the subsystem and request the corresponding controller. The handoff of controller has a handoff delay relative to the handoff of subsystem, which results in asynchronous handoff. In this paper, the asynchronous control problems of several switched systems are studied. The main contents are as follows: for discrete-time switched systems with nonlinear perturbations, the dynamic properties of the switched systems are studied directly by solution analysis. Firstly, the state solution of the closed-loop switched system is obtained by iterative method, and the obtained state solution is analyzed by the mean resident time method, and a sufficient condition for exponential stability of the closed-loop switched system is established. Secondly, based on the obtained stability conditions, a state feedback controller is designed by using linear matrix inequality (LMI) method. Finally, an optimal control algorithm for state feedback controller gain and minimum average dwell time is presented. This method does not use any Lyapunov functions and provides a new idea for the study of switched systems. For continuous-time switched systems with nonlinear perturbations, the finite time asynchronous control problem is studied by using the mean dwell time method. Based on the state solution of the closed-loop switched system, the Gronwall-Bellman inequality and the mean dwell time method are used to establish the criteria for the stability of the closed-loop switched system in finite time. The linear matrix inequality (LMI) method is used to design the corresponding state feedback controller, and an algorithm for solving the state feedback controller and the average dwell time is given. Finally, the correctness of the conclusion is verified by a specific simulation example. For switched systems with time-varying delays, the asynchronous H _ 鈭，

本文編號：1999577