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020 _a9783031641244
_9978-3-031-64124-4
024 7 _a10.1007/978-3-031-64124-4
_2doi
050 4 _aQ295
050 4 _aQA402.3-402.37
072 7 _aGPFC
_2bicssc
072 7 _aSCI064000
_2bisacsh
072 7 _aGPFC
_2thema
100 1 _aMiller, Boris.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984663
245 1 0 _aOptimization of Dynamical Systems with Impulse Controls and Shocks
_h[electronic resource] /
_cby Boris Miller, Evgeny Rubinovich.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2024.
300 _aXV, 624 p. 70 illus., 14 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSystems & Control: Foundations & Applications,
_x2324-9757
505 0 _aPreface -- Introduction -- Discrete-continuous systems with impulse control -- Optimal impulse control problem with restricted number of impulses -- Generalized solutions of nonlinear differential equations -- Optimal generalized solutions in control problems -- The maximum principle in problems of generalized optimal control -- Observations control in discrete-continuous stochastic systems -- Impulsive control in shock mechanics -- Appendix. Differential equations with measures -- Index -- Bibliography.
520 _aThis text explores the state-of-the-art in the rapidly developing theory of impulse control and introduces the theory of singular space-time transformations, a new method for studying shock mechanical systems. Two approaches in the theory of impulse control are presented: The first, more traditional approach defines the impulsive action as a discontinuity of phase coordinates depending on the current time, the state preceding the action, and its magnitude. The second requires the use of modern methods for describing dynamical systems - differential equations with measures. The impulse is treated as an idealization of a very short action of high magnitude, which produces an almost abrupt change of phase coordinates. The relation between these two approaches is also discussed, and several applications, both traditional and emerging, are considered. This text is intended for graduate students and researchers in control engineering and optimal control theory for dynamical systems. Readers are assumed to be familiar with the theory of ODEs, optimal control, and functional analysis, though an appendix is included that covers many of the necessary mathematical concepts.
650 0 _aSystem theory.
_966519
650 0 _aControl theory.
_968675
650 0 _aMathematical optimization.
_965522
650 0 _aDynamical systems.
650 1 4 _aSystems Theory, Control.
_968676
650 2 4 _aOptimization.
_965528
650 2 4 _aDynamical Systems.
700 1 _aRubinovich, Evgeny.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984664
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031641237
776 0 8 _iPrinted edition:
_z9783031641251
776 0 8 _iPrinted edition:
_z9783031641268
830 0 _aSystems & Control: Foundations & Applications,
_x2324-9757
_979787
856 4 0 _uhttps://doi.org/10.1007/978-3-031-64124-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c63546
_d63546