本文選題：靜態(tài)輸出反饋 + 廣義系統(tǒng)　； 參考：《青島大學(xué)》2017年博士論文

【摘要】：近些年來(lái),作為控制理論和應(yīng)用中的重要方法,靜態(tài)輸出反饋控制得到了普遍的關(guān)注。這是由于系統(tǒng)的狀態(tài)經(jīng)常是不可測(cè)的,但是系統(tǒng)的輸出是可測(cè)的。另一方面,靜態(tài)輸出反饋控制方法簡(jiǎn)單,實(shí)施方便。實(shí)際系統(tǒng)中不可避免的包含了多種復(fù)雜動(dòng)態(tài),存在著脈沖行為、時(shí)滯、強(qiáng)耦合等。此時(shí),廣義系統(tǒng)、矩形系統(tǒng)、時(shí)滯系統(tǒng)、模糊系統(tǒng)、切換系統(tǒng)等能夠更好地描述這些含有復(fù)雜動(dòng)態(tài)的實(shí)際過(guò)程。本文在總結(jié)幾種復(fù)雜動(dòng)態(tài)系統(tǒng)的靜態(tài)輸出反饋控制研究基礎(chǔ)上,應(yīng)用Lyapunov穩(wěn)定性理論,結(jié)合各種不等式技巧,深入地研究了線性系統(tǒng)、廣義系統(tǒng)、時(shí)滯系統(tǒng)、矩形系統(tǒng)及混合系統(tǒng)的分析與靜態(tài)輸出反饋控制,發(fā)展了新的穩(wěn)定性理論和靜態(tài)輸出反饋控制方法,本文的主要研究成果如下:1.研究線性系統(tǒng)的靜態(tài)輸出反饋控制方法。針對(duì)原有的路徑追蹤算法中的不收斂的問(wèn)題,我們提出一個(gè)新的線性化方法,得到了改進(jìn)的路徑追蹤算法,并證明了其收斂性。針對(duì)路徑追蹤算法是局部算法,求解能力依賴于初始值的問(wèn)題,我們通過(guò)對(duì)能穩(wěn)性條件的等價(jià)變化,得到了初始值優(yōu)化算法,將其與改進(jìn)的路徑追蹤算法相結(jié)合,可大大提高算法的尋優(yōu)能力。另外,通過(guò)對(duì)Lyapunov函數(shù)的結(jié)構(gòu)的等價(jià)變換,得到一個(gè)新的能穩(wěn)性條件,該條件仍舊是BMI問(wèn)題,但是只需固定少量變量,就可以將該條件轉(zhuǎn)化為L(zhǎng)MI問(wèn)題。將初始值優(yōu)化算法和新的能穩(wěn)性條件相結(jié)合,又構(gòu)造出一個(gè)求解靜態(tài)輸出反饋控制問(wèn)題的新方法。以上方法都分別給出了連續(xù)系統(tǒng)和離散系統(tǒng)的不同形式。2.分別針對(duì)連續(xù)和離散兩類(lèi)系統(tǒng),研究了廣義系統(tǒng)的靜態(tài)輸出反饋控制問(wèn)題。由于廣義系統(tǒng)的穩(wěn)定性條件中的Lyapunov矩陣不再是嚴(yán)格的正定矩陣,線性系統(tǒng)靜態(tài)輸出反饋的某些算法,例如初始值優(yōu)化算法,無(wú)法直接應(yīng)用到該系統(tǒng)中,需要研究新的有效方法。對(duì)于連續(xù)系統(tǒng),我們研究了廣義系統(tǒng)與馬爾可夫跳躍系統(tǒng)結(jié)合在一起的混合系統(tǒng),提出了求解該系統(tǒng)的靜態(tài)輸出反饋控制器的新的路徑追蹤算法。該算法的Step 1僅通過(guò)求解一個(gè)LMI優(yōu)化問(wèn)題就可以得到一個(gè)較好的初始值,從而避免了應(yīng)用初始值優(yōu)化算法。對(duì)于離散系統(tǒng),我們將廣義系統(tǒng)與模糊系統(tǒng)相結(jié)合,也給出靜態(tài)輸出反饋控制的新充分條件,基于該條件,構(gòu)造了改進(jìn)的錐補(bǔ)線性化算法。3.研究連續(xù)和離散時(shí)滯系統(tǒng)的穩(wěn)定性分析和靜態(tài)輸出反饋控制問(wèn)題。對(duì)于連續(xù)的T-S模糊時(shí)滯系統(tǒng),通過(guò)構(gòu)造新的增強(qiáng)型Lyapunov-Krasovskii泛函和應(yīng)用保守性較低的Wirthinger-based積分不等式,得到新的穩(wěn)定性判據(jù)。對(duì)于連續(xù)的廣義時(shí)滯系統(tǒng),我們研究其混合H∞和無(wú)源控制問(wèn)題,通過(guò)應(yīng)用文獻(xiàn)[83]中的積分不等式,得到新的穩(wěn)定性和能穩(wěn)性判據(jù),從而構(gòu)造出求解靜態(tài)輸出反饋控制器的新算法。對(duì)于離散時(shí)滯系統(tǒng),我們首先給出兩個(gè)新的有限和不等式,得到離散時(shí)滯系統(tǒng)的新的保守性更低的穩(wěn)定性和能穩(wěn)性條件。應(yīng)用初始值優(yōu)化算法和改進(jìn)的路徑追蹤算法求解靜態(tài)輸出反饋控制器。最后,對(duì)于離散的廣義T-S模糊時(shí)滯系統(tǒng),應(yīng)用其中一個(gè)新的有限和不等式和增強(qiáng)型Lyapunov-Krasovskii泛函,得到新的穩(wěn)定性判據(jù)和能穩(wěn)性條件,并構(gòu)造改進(jìn)的錐補(bǔ)線性化算法求解。4.研究矩形時(shí)滯T-S模糊系統(tǒng)的正則化和能穩(wěn)性問(wèn)題。我們?yōu)殡x散的矩形時(shí)滯系統(tǒng)設(shè)計(jì)了動(dòng)態(tài)補(bǔ)償器,可使得閉環(huán)系統(tǒng)是方形的。給出了判斷是否存在動(dòng)態(tài)補(bǔ)償器使得閉環(huán)系統(tǒng)是正則的,因果的充分必要條件。此外,給出兩個(gè)判斷閉環(huán)系統(tǒng)穩(wěn)定的判據(jù),并提出求解的算法。
[Abstract]:In recent years, as an important method in the control theory and application, static output feedback control has received widespread attention. This is because the state of the system is often inmeasurable, but the output of the system is measurable. On the other hand, the static output feedback control method is simple and convenient. In complex dynamics, there are impulse behavior, time delay, strong coupling and so on. At this time, generalized systems, rectangular systems, time-delay systems, fuzzy systems, switching systems and so on can better describe these complex dynamic processes. Based on the study of the static output feedback control of several complex dynamic systems, this paper applies the Lyapunov stability theory. On the basis of various inequality techniques, the analysis and static output feedback control of linear systems, generalized systems, time-delay systems, rectangular systems and hybrid systems are studied, and new stability theory and static output feedback control methods are developed. The main achievements of this paper are as follows: 1. the static output feedback control of linear systems is studied. Method. In view of the problem of non convergence in the original path tracking algorithm, we propose a new linearization method and obtain an improved path tracking algorithm, and prove its convergence. For the path tracking algorithm is a local algorithm, the solution ability depends on the initial value, and we get the equivalent change of the stability condition. The initial value optimization algorithm, combining it with the improved path tracking algorithm, can greatly improve the optimization ability of the algorithm. In addition, a new stability condition is obtained by the equivalent transformation of the structure of the Lyapunov function. The condition is still a BMI problem, but only a small number of variables are fixed, and the condition can be converted to the LMI problem. A new method for solving the static output feedback control problem is constructed by combining the initial value optimization algorithm with the new stability condition. The above methods have given the two kinds of continuous and discrete two classes of continuous and discrete systems respectively, respectively, and study the static output feedback control problem of the broad sense system. The Lyapunov matrix in the stability condition of the generalized system is no longer a strict positive definite matrix, and some algorithms of the static output feedback of the linear system, such as the initial value optimization algorithm, can not be applied directly to the system. We need to study the new effective method. For the continuous system, we study the combination of the generalized system and the Markov jump system. In a hybrid system, a new path tracking algorithm for the static output feedback controller of the system is proposed. The Step 1 of the algorithm can get a better initial value only by solving a LMI optimization problem, thus avoiding the application of the initial value optimization algorithm. For discrete systems, we have generalized system and fuzzy system. In addition, a new sufficient condition for the static output feedback control is also given. Based on this condition, an improved cone complement linearization algorithm.3. is constructed to study the stability analysis of continuous and discrete time-delay systems and the static output feedback control problem. For continuous T-S fuzzy time delay systems, a new enhanced Lyapunov-Krasovskii functional is constructed. A new stability criterion is obtained by applying the low conservative Wirthinger-based integral inequality. For continuous generalized time-delay systems, we study its mixed H infinity and passive control problems. By applying the integral inequality in the literature [83], we obtain new stability and stability criteria, thus constructing a static output feedback controller. For discrete time delay systems, we first give two new finite and inequalities, get the new stability and stability conditions of the discrete time-delay systems, and apply the initial value optimization algorithm and the improved path tracking algorithm to solve the static output feedback controller. Finally, the discrete generalized T-S fuzzy time fuzzy system is used. With a new finite and inequality and enhanced Lyapunov-Krasovskii functional, a new stability criterion and a stable condition are obtained, and an improved cone complement linearization algorithm is constructed to solve.4.'s regularization and stability problems for the T-S fuzzy systems with rectangular delay. We have designed the dynamics for a discrete rectangular delay system. The compensator can make the closed loop system square. It gives the sufficient and necessary condition for judging whether the dynamic compensator is regular and causality whether the dynamic compensator exists. In addition, two criteria to judge the stability of the closed loop system are given, and the algorithm for solving it is proposed.
【學(xué)位授予單位】：青島大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：TP13

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