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2019 | OriginalPaper | Buchkapitel

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

verfasst von : Olga Samsonyuk, Stepan Sorokin, Maxim Staritsyn

Erschienen in: Mathematical Optimization Theory and Operations Research

Verlag: Springer International Publishing

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Abstract

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.

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Vorheriges Kapitel Problems of Hard Control for a Class of Degenerate Fractional Order Evolution Equations

Nächstes Kapitel Semi-supervised Classification Using Multiple Clustering and Low-Rank Matrix Operations

Bressan, A., Rampazzo, F.: Impulsive control systems without commutativity assumptions. J. Optim. Theory Appl. 81(3), 435–457 (1994). https://doi.org/10.1007/BF02193094MathSciNetCrossRefMATH

Bressan, A., Mazzola, M.: Graph completions for impulsive feedback controls. J. Math. Anal. Appl. 412(2), 976–988 (2014). https://doi.org/10.1016/j.jmaa.2013.11.015MathSciNetCrossRefMATH

Bressan, A., Piccoli, B.: Introduction to the mathematical theory of control, AIMS Series on Applied Mathematics, vol. 2. American Institute of Mathematical Sciences (AIMS), Springfield (2007)

Bressan, A., Rampazzo, F.: On differential systems with quadratic impulses and their applications to Lagrangian mechanics. SIAM J. Control Optim. 31(5), 1205–1220 (1993). https://doi.org/10.1137/0331057MathSciNetCrossRefMATH

Clarke, F.H., Ledyaev, Yu. S., Stern, R.J., Wolenski, R.R.: Nonsmooth Analysis and Control Theory. Graduate Texts in Mathematics, vol. 178. Springer, New York (1998). https://doi.org/10.1007/b97650

Clarke, F.: Functional Analysis, Calculus of Variations and Optimal Control. Graduate Texts in Mathematics, vol. 264. Springer, London (2013). https://doi.org/10.1007/978-1-4471-4820-3CrossRefMATH

Dykhta, V.: Variational necessary optimality conditions with feedback descent controls for optimal control problems. Dokl. Math. 91(3), 394–396 (2015)MathSciNetCrossRef

Dykhta, V.: Positional strengthenings of the maximum principle and sufficient optimality conditions. Proc. Steklov Inst. Math. 293(1), S43–S57 (2016)CrossRef

Dykhta, V., Samsonyuk, O.: Optimal Impulsive Control with Applications, 2nd edn. Fizmatlit, Moscow (2003)MATH

10.

Dykhta, V., Samsonyuk, O.: Hamilton-\(\text{ J }\)acobi Inequalities and Variational Optimality Conditions. Irkutsk state university, Irkutsk (2015)

11.

Dykhta, V., Samsonyuk, O.: Optimality conditions with feedback controls for optimal impulsive control problems. IFAC-PapersOnLine 51(32), 509–514 (2018)CrossRef

12.

Fraga, S.L., Pereira, F.L.: Hamilton-Jacobi-Bellman equation and feedback synthesis for impulsive control. IEEE Trans. Autom. Control 57(1), 244–249 (2012). https://doi.org/10.1109/TAC.2011.2167822MathSciNetCrossRefMATH

13.

Gurman, V.: The Extension Principle in Optimal Control Problems, 2nd edn. Fizmatlit, Moscow (1997)MATH

14.

Karamzin, D., Oliveira, V., Pereira, F., Silva, G.: On some extension of optimal control theory. Eur. J. Control 20(6), 284–291 (2014)MathSciNetCrossRef

15.

Karamzin, D., Oliveira, V., Pereira, F., Silva, G.: On the properness of the extension of dynamic optimization problems to allow impulsive controls. ESAIM Control Optim. Calc. Var. 21(3), 857–875 (2015)MathSciNetCrossRef

16.

Miller, B.: The generalized solutions of nonlinear optimization problems with impulse control. SIAM J. Control Optim. 34, 1420–1440 (1996)MathSciNetCrossRef

17.

Miller, B., Rubinovich, E.: Discontinuous solutions in the optimal control problems and their representation by singular space-time transformations. Autom. Remote Control 74, 1969–2006 (2013)MathSciNetCrossRef

18.

Miller, B.M., Rubinovich, E.Y.: Impulsive Control in Continuous and Discrete-Continuous Systems. Kluwer Academic/Plenum Publishers, New York (2003). http://dx.doi.org/10.1007/978-1-4615-0095-7CrossRef

19.

Motta, M., Rampazzo, F.: Space-time trajectories of nonlinear systems driven by ordinary and impulsive controls. Differ. Integr. Equ. 8, 269–288 (1995)MathSciNetMATH

20.

Samsonyuk, O.: Invariant sets for nonlinear impulsive control systems. Autom. Remote Control 76(3), 405–418 (2015)MathSciNetCrossRef

21.

Sesekin, A., Zavalishchin, S.: Dynamic Impulse Systems: Theory and Applications. Kluwer Academic Publishers, Dordrecht (1997)MATH

22.

Sorokin, S., Staritsyn, M.: Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control. Numer. Algebra Control Optim. 7(2), 201–210 (2017)MathSciNetCrossRef

23.

Staritsyn, M., Sorokin, S.: On feedback strengthening of the maximum principle for measure differential equations. J. Glob. Optim. (2019). https://doi.org/10.1007/s10898-018-00732-3

24.

Vinter, R.: Optimal Control. Birkhauser, Berlin (2000)MATH

Titel: Feedback Optimality Conditions with Weakly Invariant Functions for Nonlinear Problems of Impulsive Control
verfasst von: Olga Samsonyuk
Stepan Sorokin
Maxim Staritsyn
Verlag: Springer International Publishing
Buch: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-22628-2

Electronic ISBN: 978-3-030-22629-9

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-22629-9_36

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