The control parameterization enhancing transform for constrained optimal control problems
The control parameterization enhancing transform for constrained optimal control problems
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DOI：
10.1017/s0334270000010936
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发表时间：
1999-01
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影响因子：
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通讯作者：
K. Teo;L. Jennings;H. Lee;V. Rehbock
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文献类型：
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作者：
K. Teo;L. Jennings;H. Lee;V. Rehbock
摘要 考虑一类典型形式的约束最优控制问题。使用经典的控制参数化技术，时间（规划）范围被划分为几个子区间。控制函数通过具有预先固定的切换时间的分段常数或分段线性函数来近似。然而，如果要获得的最优控制函数是分段连续的，则该逼近过程的精度很大程度上取决于划分的精细程度。另一方面，所使用的任何优化算法的性能都受到问题决策变量数量的限制。因此，时间范围不能被划分为任意多个子区间以达到所需的精度。为了克服这个困难，切换点也应该被视为决策变量。这是本文的主要动机。引入了一种新颖的变换，称为控制参数化增强变换，将具有可变切换时间的近似最优控制问题转换为涉及具有预先固定切换时间的分段常数或分段线性控制函数的等效标准最优控制问题。变换后的问题本质上是最优参数选择问题，因此可以通过各种现有算法来解决。为了便于说明，使用所提出的方法求解了两个重要的数值示例。
Abstract Consider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.