基于时间网格重构的多重打靶最优控制策略研究

发布时间：2018-05-17 02:07

本文选题：最优控制 + 多重打靶法　；参考：《浙江大学》2017年硕士论文

【摘要】：最优控制,或称为动态优化,作为现代控制理论的核心,目前已经被广泛应用于石油化工、生物医学、通信网络等社会生活和工业领域中。通过最优控制算法求解得到受控系统的最优操作策略,可以实现系统的节能降耗和挖潜增效等目标。直接法是最优控制问题的一类常用解法,即将无限维的原问题近似转换为有限维的静态优化问题。多重打靶法作为直接法中的一种代表性方法,能求解含高度非线性动态方程组的最优控制问题,具有求解精度高且容易实现等优点。本文主要针对多重打靶法数值计算中求解精度与计算成本之间的矛盾,提出了相应的解决方案,实现了对时间网格进行重构的改进多重打靶算法,并使用改进算法对经典的最优控制问题进行求解,获得了良好的结果。本文的主要工作及贡献有:(1)针对优化迭代过程中非常耗时的微分方程组求解,引入Runge-Kutta公式在参数化时间网格上进行数值积分,实现了对微分方程组的快速求解,保证精度的同时节省时间成本;(2)针对不等式路径约束处理的困难,使用光滑化惩罚函数法,将约束条件使用光滑化函数近似,并作为惩罚项增广进问题的目标函数,测试实例验证了方法的有效性;(3)针对时间网格分辨率与计算成本之间的矛盾,提出一种基于控制参数曲线斜率分析的时间网格重构方法,通过不断插入或删除时间节点,根据控制轨迹实现对网格的自适应调整;(4)针对固定时间网格的缺陷,提出一种可变时间节点的改进多重打靶方法,在求解最优控制参数的迭代过程中同时获取最优的网格划分,并与国际上著名的Time-Scaling方法进行对比研究,实例求解结果证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.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O232

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