本文選題：不確定離散系統(tǒng)　切入點(diǎn)：預(yù)見(jiàn)控制　出處：《北京科技大學(xué)》2017年博士論文　論文類(lèi)型：學(xué)位論文

【摘要】：確定性系統(tǒng)的預(yù)見(jiàn)控制理論的研究已經(jīng)取得了很大的進(jìn)展.然而對(duì)預(yù)見(jiàn)控制系統(tǒng),不可避免地會(huì)存在某些不確定性,因此將預(yù)見(jiàn)控制理論和不確定系統(tǒng)相結(jié)合,研究魯棒預(yù)見(jiàn)控制問(wèn)題就自然地成為一個(gè)新的課題.本文主要作了以下幾方面的研究工作:1.研究了范數(shù)有界不確定性的離散時(shí)間系統(tǒng)魯棒預(yù)見(jiàn)控制問(wèn)題.為了克服經(jīng)典的差分方法無(wú)法推廣到不確定系統(tǒng)中的困難,本文采用一種輔助方法構(gòu)造擴(kuò)大誤差系統(tǒng).然后利用線(xiàn)性矩陣不等式(LMI)技巧將增益矩陣的求解問(wèn)題轉(zhuǎn)換為一個(gè)凸優(yōu)化問(wèn)題,分解代回原系統(tǒng)便得到預(yù)見(jiàn)控制器.2.研究了變時(shí)滯不確定離散時(shí)間系統(tǒng)的魯棒預(yù)見(jiàn)控制問(wèn)題.首先利用模型變換的方法將系統(tǒng)中的變時(shí)滯項(xiàng)連同不確定項(xiàng)從形式上提取出來(lái),并將上述的構(gòu)造方法推廣過(guò)來(lái).然后運(yùn)用標(biāo)度小增益定理給出預(yù)見(jiàn)控制器的設(shè)計(jì)方法.最后數(shù)值仿真表明預(yù)見(jiàn)控制器的優(yōu)越性.3.考慮了一類(lèi)參數(shù)不確定離散時(shí)間系統(tǒng)的參數(shù)依賴(lài)的預(yù)見(jiàn)控制器設(shè)計(jì)問(wèn)題.將經(jīng)典的差分方法運(yùn)用到不確定離散時(shí)間系統(tǒng)中,構(gòu)造出包含未來(lái)目標(biāo)值信號(hào)的信息的擴(kuò)大誤差系統(tǒng),將跟蹤問(wèn)題轉(zhuǎn)化為調(diào)節(jié)問(wèn)題;然后結(jié)合LMI的方法和參數(shù)依賴(lài)的思想,設(shè)計(jì)了參數(shù)依賴(lài)預(yù)見(jiàn)控制器.4.研究了時(shí)變參數(shù)不確定離散時(shí)間系統(tǒng)的魯棒預(yù)見(jiàn)控制.首先利用輔助變量的構(gòu)造方法和狀態(tài)增廣技術(shù)推導(dǎo)出擴(kuò)大誤差系統(tǒng).然后利用參數(shù)依賴(lài)的Lyapunov穩(wěn)定性理論和LMI方法,得到了保證閉環(huán)系統(tǒng)漸近穩(wěn)定的充分條件.接著,通過(guò)求解有限個(gè)線(xiàn)性不等式,得到預(yù)見(jiàn)控制器的增益矩陣.5.研究了不確定離散時(shí)間系統(tǒng)的輸出反饋預(yù)見(jiàn)控制問(wèn)題.首先構(gòu)造出不確定離散時(shí)間系統(tǒng)的擴(kuò)大誤差系統(tǒng);然后針對(duì)擴(kuò)大誤差系統(tǒng),改寫(xiě)輸出方程,使得充分利用可預(yù)見(jiàn)信號(hào)的信息.最后利用魯棒控制的有關(guān)理論方法求解出輸出反饋增益矩陣.上述所有的情況都對(duì)定理成立的條件給出了嚴(yán)格的數(shù)學(xué)證明.
[Abstract]:Great progress has been made in the study of predictive control theory for deterministic systems. However, some uncertainties inevitably exist in the predictive control systems, so the theory of predictive control is combined with uncertain systems. The study of robust foresight control problem has naturally become a new subject. In this paper, the following research work is done: 1. The problem of robust predictive control for discrete-time systems with norm-bounded uncertainties is studied in order to solve the problem of robust foresight control in discrete-time systems with norm-bounded uncertainties. The classical difference method can not be extended to the difficulties of uncertain systems. In this paper, an auxiliary method is used to construct the extended error system, and then the problem of solving the gain matrix is transformed into a convex optimization problem by using the LMI (linear matrix inequality) technique. The problem of robust predictive control for uncertain discrete-time systems with variable time-delay is studied. Firstly, the variable time-delay term and the uncertain term in the system are extracted from the formal form by the method of model transformation. Then the design method of the predictive controller is given by using the scalar small gain theorem. Finally, the numerical simulation shows the superiority of the predictive controller. 3. A class of parameter uncertain discrete time is considered. The classical difference method is applied to uncertain discrete-time systems. An extended error system containing the information of the future target signal is constructed, and the tracking problem is transformed into an adjustment problem, and then the method of LMI and the idea of parameter dependence are combined. A parameter-dependent predictive controller .4.The robust predictive control for time-varying uncertain discrete-time systems is studied. Firstly, the extended error system is derived by using the construction method of auxiliary variables and the state augmentation technique. Using parameter-dependent Lyapunov stability theory and LMI method, Sufficient conditions for the asymptotic stability of closed-loop systems are obtained. Then, by solving finite linear inequalities, The gain matrix of the predictive controller is obtained. 5. The output feedback foresight control problem of uncertain discrete time system is studied. Firstly, the extended error system of uncertain discrete time system is constructed, and then the output equation is rewritten for the extended error system. Finally, the output feedback gain matrix is solved by using the theory of robust control. All the above cases give strict mathematical proof for the condition that the theorem holds.
【學(xué)位授予單位】：北京科技大學(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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