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首页> 外文期刊>SIAM Journal on Control and Optimization >Lipschitz continuity of optimal controls for state constrained problems
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Lipschitz continuity of optimal controls for state constrained problems

机译：状态约束问题的最优控制的Lipschitz连续性

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摘要

This paper provides new conditions under which optimal controls are Lipschitz continuous for dynamic optimization problems with functional inequality constraints, a control constraint expressed in terms of a general closed convex set and a coercive cost function. It is shown that the linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition that requires linear independence merely with respect to nonnegative weighting parameters. Smoothness conditions on the data, imposed in earlier work, are also relaxed. The new conditions for Lipschitz continuity of optimal controls are obtained by a detailed analysis of the implications of first order optimality conditions in the form of a nonsmooth maximum principle. [References: 12]
机译：本文为具有功能不等式约束，以一般闭合凸集和强制成本函数表示的控制约束的动态优化问题提供了最优控制为Lipschitz连续的新条件。结果表明，较早文献中存在的关于活动状态约束的线性独立性条件可以替换为一个限制性较小的正线性独立性条件，该条件仅对非负加权参数需要线性独立性。先前工作中施加的数据平滑度条件也得到了放松。最优控制的Lipschitz连续性的新条件是通过以非光滑最大原理的形式对一阶最优条件的含义进行详细分析而获得的。 [参考：12]

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