Abstract

For a class of nonlinear nonconvex impulsive control problems with states of bounded variation driven by Borel measures, we derive a new type non-local necessary optimality condition, named impulsive feedback maximum principle. This optimality condition is expressed completely within the objects of the impulsive maximum principle (IMP), while employs certain “feedback variations” of impulsive control. The obtained optimality condition is shown to, potentially, discard non-optimal IMP-extrema, and can be viewed as a deterministic non-local iterative algorithm for optimal impulsive control.

中文翻译：

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关于测量微分方程最大值原理的反馈加强

摘要

对于一类由Borel测度驱动的带界变化状态的非线性非凸脉冲控制问题，我们推导了一种新型的非局部必要最优性条件，称为脉冲反馈最大原理。最优条件完全体现在脉冲最大原理（IMP）的目标之内，同时采用了脉冲控制的某些“反馈变化”。所获得的最优性条件可能会丢弃非最优的IMP极值，并且可以看作是用于最优脉冲控制的确定性非局部迭代算法。