基于提升隐式积分器的微分代数系统最优控制快速求解算法

发布时间：2018-01-31 23:09

本文关键词： 最优控制微分代数方程隐式龙格库塔积分时间尺度变换敏感性更新　出处：《合肥工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着现代社会生产及科学技术的快速发展,人们研究的系统对象的规模在逐渐增大、结构也愈加复杂。许多动态系统的状态运动受到限制,采用常微分方程对它们进行建模并不是最为方便的。本论文采用微分代数方程代替常微分方程对受限动态系统进行建模。在此基础上,讨论指标-1微分代数方程初值问题的快速求解,以及这类系统最优控制问题的高效序列式求解算法。首先,基于时间尺度变换技术,将控制变量描述为幅值和切换时间可变的分段连续函数。与等间隔分段的控制参数化相比,增加的这一切换时刻自由度扩大了问题解的可行域。其次,对于控制参数化得到的非线性规划问题,文中提出了一种基于隐式龙格库塔积分的函数评价算法,利用隐函数理论和算法微分技术进行高效的敏感性计算。在此基础上,通过引入一种预测校正策略,使得改进的函数评价算法的牛顿迭代次数大大减少。最后,本文将该算法与非线性规划问题求解软件Ipopt结合,设计实现了最优控制问题的求解器,并以Delta机器人点对点最优控制问题为例对求解器的高效性进行了验证。数值仿真和理论分析表明该算法可以有效提高求解速度。
[Abstract]:With the rapid development of modern social production and scientific and technological system, object of study on the size of the structure increases gradually, become more and more complex. The state of motion in many dynamic systems is limited, they are not the most convenient for modeling by ordinary differential equations. This paper uses differential algebraic equations instead of differential equations modeling the limited dynamic system. Based on this, discuss the fast solution of -1 differential algebraic equations of initial value index, and efficient sequence of this kind of system optimal control problem solving algorithm. Firstly, the time scale transformation based on the technology of control variables is described as piecewise continuous function with variable amplitude and switching time. Compared with the control parameters the increase of piecewise interval, the switching time freedom expanded feasible solution of the problem. Secondly, the nonlinear programming control parameters obtained is asked Questions, this paper proposes an algorithm evaluation function implicit Runge Kutta integration based on efficient sensitivity is calculated by using the implicit function theory and algorithm of differential technology. On this basis, through the introduction of a prediction correction method, the Newton iteration algorithm for function evaluation improved greatly reduced. Finally, this paper will solve the software Ipopt with the algorithm of nonlinear programming problems with the design and implementation of solving optimal control problems, and taking the Delta robot point to the optimal control problem is proposed for efficient cases solver. Numerical simulation and theoretical analysis show that the algorithm can effectively improve the speed of solution.

【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.8;O232

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