發(fā)布時間：2018-02-17 05:25

  本文關(guān)鍵詞： Markov 跳變系統(tǒng) 模型預(yù)測控制 不變集 硬約束概率軟約束 時滯 類周期系統(tǒng)　出處：《上海交通大學(xué)》2015年博士論文　論文類型：學(xué)位論文

【摘要】：Markov跳變系統(tǒng)是指結(jié)構(gòu)發(fā)生隨機(jī)性突變的系統(tǒng),如經(jīng)濟(jì)系統(tǒng)、飛行器控制系統(tǒng)、通信系統(tǒng)以及太陽能加熱系統(tǒng)中都會出現(xiàn)這樣的情況,它是一類非常重要的系統(tǒng)。在Markov跳變系統(tǒng)中,由于物理限制的存在或者經(jīng)濟(jì)、性能的要求總是不可避免地存在約束。在處理約束時,模型預(yù)測控制由于其獨特的滾動時域運行機(jī)制,相比于其他控制方法通常更有優(yōu)勢。因此Markov跳變系統(tǒng)的模型預(yù)測控制是一個非常有意義的研究課題。約束的存在給Markov跳變系統(tǒng)預(yù)測控制器的設(shè)計帶來了困難。在約束存在的情形下設(shè)計具有遞歸可行性保證以及良好控制性能的預(yù)測控制器是Markov跳變系統(tǒng)預(yù)測控制研究的一個關(guān)鍵問題。本論文針對以上問題,對Makrov跳變系統(tǒng)不同情形下約束預(yù)測控制器的設(shè)計展開研究,主要內(nèi)容和成果如下。?針對加性擾動的約束Markov跳變系統(tǒng),給出了求解該系統(tǒng)最大允許集的高效算法。?針對具有硬約束的Markov跳變系統(tǒng),基于橢圓集給出了無約束、約束多步控制器的設(shè)計,證明了算法的遞歸可行性和閉環(huán)系統(tǒng)的均方穩(wěn)定性。為了提高算法的在線計算效率,進(jìn)一步給出了降低其在線計算量的預(yù)測控制器設(shè)計。?針對具有硬約束的Markov跳變系統(tǒng),為了克服上面算法不能有效處理非對稱約束的缺點,基于最大允許集(多面體集)給出了一般插值、具有線性目標(biāo)和基于精確約束處理的插值預(yù)測控制器設(shè)計,證明了算法的遞歸可行性和閉環(huán)系統(tǒng)的均方穩(wěn)定性。?針對具有概率軟約束的Markov跳變系統(tǒng),分兩種情形:擾動能量有界和持續(xù)擾動的情形,基于最大允許集給出了相應(yīng)的預(yù)測控制器的設(shè)計,證明了算法的遞歸可行性和閉環(huán)系統(tǒng)的均方穩(wěn)定性。?針對時滯建模為Markov鏈的結(jié)構(gòu)不確定系統(tǒng),采用狀態(tài)增廣的方式將系統(tǒng)轉(zhuǎn)化為標(biāo)準(zhǔn)的結(jié)構(gòu)不確定時滯Markov跳變系統(tǒng),給出了預(yù)測控制器的設(shè)計,并給出了降低其在線計算量的預(yù)測控制器設(shè)計。?針對具有類周期特性和期望約束的Markov跳變系統(tǒng),分別給出了魯棒控制器、隨機(jī)控制器以及預(yù)測控制器的設(shè)計。證明了在以上控制器作用下的約束滿足性以及閉環(huán)系統(tǒng)的穩(wěn)定性。
[Abstract]:Markov jump systems are systems in which the structure changes at random, such as economic systems, aircraft control systems, communications systems, and solar heating systems. It is a very important system. In Markov jump system, because of the existence of physical limitation or economy, the performance requirement inevitably exists. Model Predictive Control (MPC), due to its unique rolling time-domain operation mechanism, Compared with other control methods, the model predictive control of Markov jump system is a very meaningful research topic. The existence of constraints makes the design of predictive controller for Markov jump system difficult. The design of predictive controller with recursive feasibility and good control performance is a key problem in the study of predictive control for Markov jump systems. The design of constrained predictive controller for Makrov jump system under different conditions is studied. The main contents and results are as follows. For an additive perturbed constrained Markov jump system, an efficient algorithm for solving the maximum allowable set of the system is presented. For Markov jump systems with hard constraints, the design of unconstrained and constrained multistep controllers based on elliptic sets is presented. The recursive feasibility of the algorithm and the mean square stability of closed loop systems are proved. Furthermore, the design of a predictive controller to reduce the amount of on-line calculation is given. For Markov jump systems with hard constraints, in order to overcome the disadvantage that the above algorithm can not deal with asymmetric constraints effectively, a general interpolation method based on the maximum allowable set (polyhedron set) is presented. The design of interpolation predictive controller with linear target and precise constraint processing proves the recursive feasibility of the algorithm and the mean square stability of the closed-loop system. For Markov jump systems with probabilistic soft constraints, the corresponding predictive controllers are designed on the basis of the maximum allowable set. The recursive feasibility of the algorithm and the mean square stability of the closed-loop system are proved. For structured uncertain systems with time-delay modeling as Markov chains, the system is transformed into a standard structured uncertain time-delay Markov jump system by state expansion, and the design of predictive controller is presented. The design of a predictive controller to reduce the amount of calculation on line is also given. The design of robust controller, stochastic controller and predictive controller for Markov jump systems with quasi-periodic characteristics and expected constraints are presented, and the constraint satisfaction and the stability of closed-loop systems are proved.
【學(xué)位授予單位】：上海交通大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：O211.62;O231

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 李德偉;席裕庚;;基于多步控制集的魯棒預(yù)測控制器設(shè)計(英文)[J];自動化學(xué)報;2009年04期

，

本文編號：1517321