Abstract:
In this work, generalized solutions to optimal control problems are discussed. A notion of generalized impulsive control is introduced. Some extension is proposed for a constrained control problem governed by the dynamics of a general type. A corresponding existence theorem is formulated within the class of discontinuous arcs. The presented extension is smaller than those previously derived in literature for this type of problems, as it contains less generalized impulsive controls, and, correspondingly, less trajectories. This is achieved by rejecting the problem convexification. As the main tool for investigation, the generally known Lebesgue discontinuous time variable change is employed. It is important noting that the obtained existence theorem is not always applicable. Therefore, a task of finding more subtle conditions for the existence of a solution arises. In this regard, a number of classical variational calculus problems are discussed in the context of presented nonlinear impulsive extension. This article is dedicated to the memory of Vladimir Alexandrovich Dykhta.
Keywords:optimal impulsive control, generalized solutions, existence theorems.
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