研究了一类线性高维奇异摄动最优控制问题的空间对照结构解,利用\ k+\sigma 交换引理证明了空间对照结构解的存在性. 同时,利用边界层函数法基础上发展起来的直接展开法构造了该问题一致有效的形式渐近解.最后, 通过例子验证了主要结果.
In this paper, a class of linear high-dimensional singularly perturbed optimal control problem is discussed. By means of k+\sigma exchange lemma, we prove the existence\linebreak of contrast structure solution for the singularly perturbed optimal control problem. Meanwhile, by virtue of the direct scheme method which is based on boundary function method, we construct the uniformly valid formal asymptotic solution. Finally, an example is presented to illustrate the main results.
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