Optimality-based grid adaptation for input-affine optimal control problems
Optimality-based grid adaptation for input-affine optimal control problems
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DOI：
10.1016/j.compchemeng.2016.04.041
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Fady Assassa;W. Marquardt
中科院分区：
文献类型：
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作者：
Fady Assassa;W. Marquardt
本文研究了直接单次打靶法与连续最优控制问题（OCP）的解的精度。首先，通过一个算例分析了非线性规划解与连续最优控制问题解之间的收敛关系。这个例子表明，庞特里亚金的最小值原理不能用作基于最优控制网格自适应的停止准则。因此，引入了一种新的网格细化策略，这是相当基于开关功能，从而限制到类的输入仿射OCP。网格点被删除和插入，这样的OCP的最优性条件的近似，阐明了开关功能，得到改善。所建议的方法进行说明，并通过两个反应堆优化问题与不同的解决方案的特点，以前出版的基于小波的自适应方法进行比较。
This paper studies the solution accuracy of direct single-shooting in comparison to the solution of the continuous optimal control problem (OCP). First, a convergence relation between the solution of the nonlinear program and that of continuous OCP is analyzed by means of an exemplary problem. This example reveals that Pontryagin's minimum principle cannot be used as a stopping criterion for optimality-based control grid adaptation. Consequently, a novel grid refinement strategy is introduced, which is rather based on the switching function and thus limited to the class of input-affine OCPs. Grid points are eliminated and inserted such that the approximation of the optimality condition of the OCP, elucidated by the switching function, is improved. The suggested methodology is illustrated and compared to a previously published wavelet-based adaptation approach by means of two reactor optimization problems with different solution characteristics.