Convex duality and nonlinear optimal control
Convex duality and nonlinear optimal control
复制标题
凸对偶性与非线性最优控制
DOI：
10.1137/0331024
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发表时间：
1993
影响因子：
2.2
通讯作者：
R. Vinter
中科院分区：
文献类型：
--
作者：
R. Vinter
非线性最优控制中的问题可以重新表述为线性函数向量空间上的凸优化问题。这样，凸分析方法就可以承担表征此类问题的解决方案的任务。结果是最优性的充分必要条件，它概括了动态规划中众所周知的充分条件，称为验证定理；作为副产品，我们获得了用 Hamilton-Jacobi 方程子解的上包络表示的最小成本。它生动地说明了凸分析，特别是凸对偶性适用的广泛问题。该方法应用于变分法中的参数问题，由 L. C. Young 首创 [Lectures on the Calculus of Variations and Optimal Control Theory, W. B. Saunders, Philadelphia, PA, 1969]。然而，正如最近的工作所表明的那样，当应用于最优控制时，它同样富有成效。蒂...
Problems in nonlinear optimal control can be reformulated as convex optimization problems over a vector space of linear functionals. In this way, methods of convex analysis can be brought to bear on the task of characterizing solutions to such problems. The result is a necessary and sufficient condition of optimality that generalizes well-known sufficient conditions, referred to as verification theorems, in dynamic programming; as a byproduct, we obtain a representation of the minimum cost in terms of the upper envelope of subsolutions to the Hamilton–Jacobi equation. It is a striking illustration of the wide range of problems to which convex analysis, and, in particular, convex duality, is applicable. The approach, applied to parametric problems in the calculus of variations, was pioneered by L. C. Young [Lectures on the Calculus of Variations and Optimal Control Theory, W. B. Saunders, Philadelphia, PA, 1969]. As recent work has shown, however, it is equally fruitful when applied in optimal control. Thi...