本文選題：最優(yōu)控制 + 多重打靶法��； 參考：《浙江大學(xué)》2017年碩士論文

【摘要】：最優(yōu)控制,或稱為動態(tài)優(yōu)化,作為現(xiàn)代控制理論的核心,目前已經(jīng)被廣泛應(yīng)用于石油化工、生物醫(yī)學(xué)、通信網(wǎng)絡(luò)等社會生活和工業(yè)領(lǐng)域中。通過最優(yōu)控制算法求解得到受控系統(tǒng)的最優(yōu)操作策略,可以實(shí)現(xiàn)系統(tǒng)的節(jié)能降耗和挖潛增效等目標(biāo)。直接法是最優(yōu)控制問題的一類常用解法,即將無限維的原問題近似轉(zhuǎn)換為有限維的靜態(tài)優(yōu)化問題。多重打靶法作為直接法中的一種代表性方法,能求解含高度非線性動態(tài)方程組的最優(yōu)控制問題,具有求解精度高且容易實(shí)現(xiàn)等優(yōu)點(diǎn)。本文主要針對多重打靶法數(shù)值計算中求解精度與計算成本之間的矛盾,提出了相應(yīng)的解決方案,實(shí)現(xiàn)了對時間網(wǎng)格進(jìn)行重構(gòu)的改進(jìn)多重打靶算法,并使用改進(jìn)算法對經(jīng)典的最優(yōu)控制問題進(jìn)行求解,獲得了良好的結(jié)果。本文的主要工作及貢獻(xiàn)有:(1)針對優(yōu)化迭代過程中非常耗時的微分方程組求解,引入Runge-Kutta公式在參數(shù)化時間網(wǎng)格上進(jìn)行數(shù)值積分,實(shí)現(xiàn)了對微分方程組的快速求解,保證精度的同時節(jié)省時間成本;(2)針對不等式路徑約束處理的困難,使用光滑化懲罰函數(shù)法,將約束條件使用光滑化函數(shù)近似,并作為懲罰項(xiàng)增廣進(jìn)問題的目標(biāo)函數(shù),測試實(shí)例驗(yàn)證了方法的有效性;(3)針對時間網(wǎng)格分辨率與計算成本之間的矛盾,提出一種基于控制參數(shù)曲線斜率分析的時間網(wǎng)格重構(gòu)方法,通過不斷插入或刪除時間節(jié)點(diǎn),根據(jù)控制軌跡實(shí)現(xiàn)對網(wǎng)格的自適應(yīng)調(diào)整;(4)針對固定時間網(wǎng)格的缺陷,提出一種可變時間節(jié)點(diǎn)的改進(jìn)多重打靶方法,在求解最優(yōu)控制參數(shù)的迭代過程中同時獲取最優(yōu)的網(wǎng)格劃分,并與國際上著名的Time-Scaling方法進(jìn)行對比研究,實(shí)例求解結(jié)果證明本文提出的方法是可行的。
[Abstract]:As the core of modern control theory, optimal control, or dynamic optimization, has been widely used in petrochemical, biomedical, communication network and other social and industrial fields. The optimal operation strategy of the controlled system can be obtained by solving the optimal control algorithm, which can achieve the goals of saving energy and reducing consumption and tapping potential and increasing efficiency of the system. Direct method is a kind of commonly used solution for optimal control problem, that is to say, the original problem of infinite dimension is approximately transformed into a static optimization problem of finite dimension. As a representative method of direct method, multiple target shooting method can solve the optimal control problem with highly nonlinear dynamic equations. It has the advantages of high precision and easy realization. Aiming at the contradiction between the precision and the cost in the numerical calculation of multiple target shooting, this paper proposes a corresponding solution, and realizes the improved multiple target shooting algorithm to reconstruct the time grid. The improved algorithm is used to solve the classical optimal control problem and good results are obtained. The main work and contribution of this paper are as follows: (1) in view of the time-consuming solution of differential equations in the optimization iteration process, the Runge-Kutta formula is introduced to carry out numerical integration on the parameterized time grid, and the fast solution of the differential equation system is realized. Aiming at the difficulty of dealing with the path constraint of inequality, the smoothing penalty function method is used to approximate the constraint condition with smoothing function, and it is regarded as the objective function of increasing penalty term into the problem. A test example is given to verify the effectiveness of the method. Aiming at the contradiction between time grid resolution and computational cost, a new time grid reconstruction method based on slope analysis of control parameter curve is proposed. Time nodes are inserted or deleted continuously. Aiming at the defects of fixed time grid, an improved multiplex shooting method for variable time nodes is proposed, which can obtain the optimal mesh division in the iterative process of solving the optimal control parameters. Compared with the famous Time-Scaling method in the world, the results show that the method proposed in this paper is feasible.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O232

【參考文獻(xiàn)】

相關(guān)期刊論文 前5條

1 李國棟;劉興高;;一種求解最優(yōu)控制問題的變時間節(jié)點(diǎn)控制向量參數(shù)化方法[J];化工學(xué)報;2015年02期

2 胡云卿;劉興高;薛安克;;解非線性動態(tài)優(yōu)化問題的一種改進(jìn)的控制矢量迭代方法.Ⅱ.帶路徑約束問題(英文)[J];Chinese Journal of Chemical Engineering;2014年02期

3 胡云卿;劉興高;薛安克;;非線性動態(tài)優(yōu)化問題的改進(jìn)控制矢量迭代法(Ⅰ)無路徑約束問題(英文)[J];Chinese Journal of Chemical Engineering;2012年06期

4 張曉東;李樹榮;雷陽;張強(qiáng);;一種可變時間節(jié)點(diǎn)的控制向量參數(shù)化方法[J];化工學(xué)報;2012年09期

5 屈香菊;;直接多重打靶法在軌跡優(yōu)化方面的應(yīng)用[J];飛行力學(xué);1992年01期

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本文編號：1899413