Optimal Control Problems with Vector-Valued Impulse Controls and Time Delays
研究以向量值测度为控制、状态含时滞的非线性系统，引入不连续有界变差解概念并建立等价表示，进而证明解适定性并推导最优控制的最大值原理。
Abstract We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a concept of discontinuous, bounded variation solution associated with this system and establish an equivalent representation formula for it, inspired by the approach known in delay-free impulsive control as the ‘graph completion’ method. Then, thanks to this equivalent formulation, we prove well-posedness properties of these solutions and also derive necessary optimality conditions in the form of a Maximum Principle for an associated optimization problem.