Feedback Optimality Conditions with Weakly Invariant Functions for Nonlinear Problems of Impulsive Control

  • Olga Samsonyuk
  • Stepan SorokinEmail author
  • Maxim Staritsyn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)


We consider a broad class of optimal control problems for nonlinear measure-driven equations. For such problems, we propose necessary optimality conditions, which are based on a specific procedure of “feedback variation” of a given, reference impulsive control. The approach is based on using impulsive feedback controls designed by means of “weakly invariant functions”. The concept of weakly invariant function generalizes the notion of weakly monotone function. In the paper, we discuss the advantages of this approach and some perspectives of designing, on its base, nonlocal numeric algorithms for optimal impulsive control.


Measure differential equations Impulsive control Feedback control Optimality condition Functions of Lyapunov type 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control TheoryIrkutskRussia

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