【摘要】：最優(yōu)控制作為現(xiàn)代控制理論的重要組成部分,在各工程領(lǐng)域中都得到了極大的應(yīng)用和發(fā)展,然而隨著系統(tǒng)復(fù)雜程度的提高以及由各種限制條件的約束,單純用解析的方法已經(jīng)很難求解此類(lèi)控制問(wèn)題。本文針對(duì)約束非線性系統(tǒng)最優(yōu)控制問(wèn)題,研究了一種數(shù)值算法,內(nèi)容分成兩個(gè)部分:第一部分是在哈密頓理論框架下考慮約束非線性系統(tǒng)最優(yōu)控制的數(shù)值算法構(gòu)造問(wèn)題;第二部分是針對(duì)非線性約束的系統(tǒng)模型,應(yīng)用本文提出的算法進(jìn)行最優(yōu)控制律設(shè)計(jì)。論文首先在分析了非線性最優(yōu)控制問(wèn)題的發(fā)展歷程和國(guó)內(nèi)外研究現(xiàn)狀,然后介紹了將最優(yōu)控制問(wèn)題轉(zhuǎn)化為兩點(diǎn)邊值問(wèn)題的方法,并以此為基礎(chǔ),對(duì)含有狀態(tài)或控制量約束的最優(yōu)控制問(wèn)題展開(kāi)研究。解決這類(lèi)含約束問(wèn)題的難點(diǎn)在于它們?cè)跁r(shí)間區(qū)間上分別包含了狀態(tài)參數(shù)和控制參數(shù)的連續(xù)不等式約束,針對(duì)這類(lèi)問(wèn)題,本文運(yùn)用內(nèi)點(diǎn)懲罰函數(shù)思想將其轉(zhuǎn)化為無(wú)約束的最優(yōu)控制問(wèn)題。最后,在母函數(shù)算法思想的基礎(chǔ)上,采用雙重母函數(shù)來(lái)實(shí)現(xiàn)兩點(diǎn)邊值問(wèn)題的最優(yōu)解逼近,并且實(shí)現(xiàn)程序仿真�；谒玫降暮s束非線性系統(tǒng)最優(yōu)控制問(wèn)題的數(shù)值算法,本文將其應(yīng)用于門(mén)式吊裝系統(tǒng)控制以及近地圓軌道航天器模塊分離問(wèn)題當(dāng)中。兩者均為六階系統(tǒng)的約束最優(yōu)控制問(wèn)題,在分別對(duì)兩者模型中非線性參數(shù)近似處理后進(jìn)行仿真分析,仿真結(jié)果顯示控制律能夠滿足吊運(yùn)過(guò)程中的小幅擺角限制以及航天器的小推力約束條件。
[Abstract]:As an important part of modern control theory, optimal control has been greatly applied and developed in various engineering fields. However, with the increase of the complexity of the system and the constraints of various constraints, It is difficult to solve this kind of control problem simply by analytic method. In this paper, a numerical algorithm for optimal control of constrained nonlinear systems is studied. The content is divided into two parts: the first part is the construction of numerical algorithms for optimal control of constrained nonlinear systems under the framework of Hamiltonian theory; In the second part, the optimal control law is designed by applying the proposed algorithm to the nonlinear constrained system model. Firstly, the paper analyzes the development of nonlinear optimal control problem and the current research situation at home and abroad, then introduces the method of transforming the optimal control problem into a two-point boundary value problem. The optimal control problem with state or control constraints is studied. The difficulty of solving this kind of constrained problems is that they contain continuous inequality constraints of state parameters and control parameters in the time interval respectively. In this paper, the idea of interior point penalty function is used to transform it into an unconstrained optimal control problem. Finally, on the basis of the idea of generating function algorithm, the double generating function is used to achieve the optimal solution approximation of the two-point boundary value problem, and the program simulation is realized. Based on the numerical algorithm of the optimal control problem for nonlinear systems with constraints, this paper applies it to the control of portal hoisting systems and to the separation of spacecraft modules in low Earth orbit. Both of them are constrained optimal control problems for sixth order systems. After approximate treatment of nonlinear parameters in the two models, simulation analysis is carried out. The simulation results show that the control law can satisfy the small swing angle limit and the small thrust constraint condition of spacecraft during hoisting.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：V448.2;O232
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本文編號(hào)：2333615