Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics

被引:28
|
作者
Sarychev, AV [1 ]
Torres, DFM [1 ]
机构
[1] Univ Aveiro, Dept Math, P-3810 Aveiro, Portugal
来源
APPLIED MATHEMATICS AND OPTIMIZATION | 2000年 / 41卷 / 02期
关键词
optimal control; Calculus of Variations; Pontryagin Maximum Principle; boundedness of minimizers; nonlinear control-affine systems; Lipschitzian regularity;
D O I
10.1007/s002459911013
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the Lagrange Problem of Optimal Control with a functional integral(a)(b) L (t, x (t), u (t)) dt and control-affine dynamics (x) over dot = f (t, x) + g (t, x)u and (a priori) unconstrained control u is an element of R-m. We obtain conditions under which the minimizing controls of the problem are bounded-a fact which is crucial for the applicability of many necessary optimality conditions, like, for example, the Pontryagin Maximum Principle. As a corollary we obtain conditions for the Lipschitzian regularity of minimizers of the Basic Problem of the Calculus of Variations and of the Problem of the Calculus of Variations with higher-order derivatives.
引用
收藏
页码:237 / 254
页数:18
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