General nonlinear impulsive control problems

In this concluding chapter, an extension of the classical control problem is given in the most general nonlinear case. The essential matter is that now the control variable is not split into conventional and impulsive types, while the dependence on this unified control variable is not necessarily affine. By combining the two approaches, the one based on the Lebesgue discontinuous time variable change, and the other based on the convexification of the problem by virtue of the generalized controls proposed by Gamkrelidze, a fairly general extension of the optimal control problem is constructed founded on the concept of generalized impulsive control. A generalized Filippov-like existence theorem for a solution is proved. The Pontryagin maximum principle for the generalized impulsive control problem with state constraints is presented. Within the framework of the proposed approach, a number of classic examples of essentially nonlinear problems of calculus of variations which allow for discontinuous optimal arcs are also examined. The chapter ends with seven exercises. © 2019, Springer Nature Switzerland AG.

Authors
Arutyunov A. 1, 2, 3 , Karamzin D. 4 , Lobo Pereira F.
Publisher
Springer Verlag
Language
English
Pages
153-172
Status
Published
Volume
477
Year
2019
Organizations
  • 1 Moscow State University, Moscow, Russian Federation
  • 2 Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russian Federation
  • 3 RUDN University, Moscow, Russian Federation
  • 4 Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russian Federation
  • 5 FEUP/DEEC, Porto University, Porto, Portugal
Keywords
Optimal control systems; Calculus of variations; Classical control; Control variable; Existence theorem; Impulsive controls; Nonlinear problems; Optimal control problem; State constraints; Calculations
Date of creation
04.02.2019
Date of change
04.02.2019
Short link
https://repository.rudn.ru/en/records/article/record/36163/
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Arutyunov A., Karamzin D., Lobo Pereira F.
Lecture Notes in Control and Information Sciences. Springer Verlag. Vol. 477. 2019. P. 1-18