03495nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050000900153050001900162072001700181072002300198072001600221100007600237245013300313250001800446264007900464300006400543336002600607337002600633338003600659347002400695490006200719505051400781520118601295650001902481650002002500650003102520650002302551650002902574650001802603650002302621700008102644710003402725773002602759776003602785776003602821776003602857830006202893856004602955978-3-031-64124-4DE-He21320251030113054.0cr nn 008mamaa240919s2024    sz |    s    |||| 0|eng d  a97830316412447 a10.1007/978-3-031-64124-42doi 4aQ295 4aQA402.3-402.37 7aGPFC2bicssc 7aSCI0640002bisacsh 7aGPFC2thema1 aMiller, Boris.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aOptimization of Dynamical Systems with Impulse Controls and Shocksh[electronic resource] /cby Boris Miller, Evgeny Rubinovich.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2024.  aXV, 624 p. 70 illus., 14 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSystems & Control: Foundations & Applications,x2324-97570 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.  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. 0aSystem theory. 0aControl theory. 0aMathematical optimization. 0aDynamical systems.14aSystems Theory, Control.24aOptimization.24aDynamical Systems.1 aRubinovich, Evgeny.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303164123708iPrinted edition:z978303164125108iPrinted edition:z9783031641268 0aSystems & Control: Foundations & Applications,x2324-975740uhttps://doi.org/10.1007/978-3-031-64124-4