03864nam a22005775i 4500 978-3-031-64124-4 DE-He213 20251030113054.0 cr nn 008mamaa 240919s2024 sz | s |||| 0|eng d 9783031641244 978-3-031-64124-4 10.1007/978-3-031-64124-4 doi Q295 QA402.3-402.37 GPFC bicssc SCI064000 bisacsh GPFC thema Miller, Boris. author. aut http://id.loc.gov/vocabulary/relators/aut 84663 Optimization of Dynamical Systems with Impulse Controls and Shocks [electronic resource] / by Boris Miller, Evgeny Rubinovich. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. XV, 624 p. 70 illus., 14 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Systems & Control: Foundations & Applications, 2324-9757 Preface -- 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. This 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. System theory. 66519 Control theory. 68675 Mathematical optimization. 65522 Dynamical systems. Systems Theory, Control. 68676 Optimization. 65528 Dynamical Systems. Rubinovich, Evgeny. author. aut http://id.loc.gov/vocabulary/relators/aut 84664 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031641237 Printed edition: 9783031641251 Printed edition: 9783031641268 Systems & Control: Foundations & Applications, 2324-9757 79787 https://doi.org/10.1007/978-3-031-64124-4 ZDB-2-SMA ZDB-2-SXMS 63546 63546