基于母函数的有限时域约束最优控制问题求解方法研究
发布时间：2018-11-15 14:52
【摘要】：最优控制作为现代控制理论的重要组成部分,在各工程领域中都得到了极大的应用和发展,然而随着系统复杂程度的提高以及由各种限制条件的约束,单纯用解析的方法已经很难求解此类控制问题。本文针对约束非线性系统最优控制问题,研究了一种数值算法,内容分成两个部分:第一部分是在哈密顿理论框架下考虑约束非线性系统最优控制的数值算法构造问题;第二部分是针对非线性约束的系统模型,应用本文提出的算法进行最优控制律设计。论文首先在分析了非线性最优控制问题的发展历程和国内外研究现状,然后介绍了将最优控制问题转化为两点边值问题的方法,并以此为基础,对含有状态或控制量约束的最优控制问题展开研究。解决这类含约束问题的难点在于它们在时间区间上分别包含了状态参数和控制参数的连续不等式约束,针对这类问题,本文运用内点惩罚函数思想将其转化为无约束的最优控制问题。最后,在母函数算法思想的基础上,采用双重母函数来实现两点边值问题的最优解逼近,并且实现程序仿真。基于所得到的含约束非线性系统最优控制问题的数值算法,本文将其应用于门式吊装系统控制以及近地圆轨道航天器模块分离问题当中。两者均为六阶系统的约束最优控制问题,在分别对两者模型中非线性参数近似处理后进行仿真分析,仿真结果显示控制律能够满足吊运过程中的小幅摆角限制以及航天器的小推力约束条件。
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：V448.2;O232
，
本文编号：2333615
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：V448.2;O232
，
本文编号：2333615
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