LEADER 05698nam 22007455 450 001 9910483429703321 005 20200701044723.0 010 $a9783030447786 010 $a3030447782 024 7 $a10.1007/978-3-030-44778-6 035 $a(CKB)5310000000016714 035 $a(MiAaPQ)EBC6232563 035 $a(DE-He213)978-3-030-44778-6 035 $a(PPN)248602179 035 $a(MiAaPQ)EBC31886933 035 $a(Au-PeEL)EBL31886933 035 $a(OCoLC)1499720661 035 $a(EXLCZ)995310000000016714 100 $a20200620d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Control Theory $eAn Introduction /$fby Jerzy Zabczyk 205 $a2nd ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020. 215 $a1 online resource (347 pages) 225 1 $aSystems & Control: Foundations & Applications,$x2324-9749 311 08$a9783030447762 311 08$a3030447766 327 $aPreface -- Preface to the second edition -- Introduction -- Part I. Elements of Classical Control Theory -- Chapter 1. Controllability and Observability -- Chapter 2. Stability and Stabilizability -- Chapter 3. Controllability with Vanishing Energy -- Chapter 4. Systems with Constraints -- Chapter 5. Realization Theory -- Part II. Nonlinear Control Systems -- Chapter 6. Controllability and Observability of Nonlinear Systems -- Chapter 7. Stability and Stabilizability -- Chapter 8. Realization Theory -- Part III. Optimal Control -- Chapter 9. Dynamic Programming -- Chapter 10. Viscosity Solutions of Bellman Equations -- Chapter 11. Dynamic Programming for Impulse Control -- Chapter 12. The Maximum Principle -- Chapter 13. The Existence of Optimal Strategies -- Part IV. Infinite-Dimensional Linear Systems -- Chapter 14. Linear Control Systems -- Chapter 15. Controllability -- Chapter 16. Stability and Stabilizability -- Chapter 17. Linear Regulators in Hilbert Spaces -- Chapter 18. Boundary Control Systems -- Appendix -- References -- Notations -- Index. 330 $aThis textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. This second edition includes new chapters that introduce a variety of topics, such as controllability with vanishing energy, boundary control systems, and delayed systems. With additional proofs, theorems, results, and a substantially larger index, this new edition will be an invaluable resource for students and researchers of control theory. Mathematical Control Theory: An Introduction will be ideal for a beginning graduate course in mathematical control theory, or for self-study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. From reviews of the first edition: At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone. Gian-Carlo Rota, The Bulletin of Mathematics Books It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory. Bulletin of the AMS Indeed, for mathematicians who look for the basic ideas or a general picture about the main branches of control theory, I believe this book can provide an excellent bridge to this area. IEEE Control Systems Magazine. 410 0$aSystems & Control: Foundations & Applications,$x2324-9749 606 $aSystem theory 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aCalculus of variations 606 $aAutomatic control 606 $aRobotics 606 $aMechatronics 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aControl, Robotics, Mechatronics$3https://scigraph.springernature.com/ontologies/product-market-codes/T19000 615 0$aSystem theory. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aCalculus of variations. 615 0$aAutomatic control. 615 0$aRobotics. 615 0$aMechatronics. 615 14$aSystems Theory, Control. 615 24$aApplications of Mathematics. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aControl, Robotics, Mechatronics. 676 $a629.8312 700 $aZabczyk$b Jerzy$4aut$4http://id.loc.gov/vocabulary/relators/aut$041807 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483429703321 996 $aMathematical Control Theory$9349266 997 $aUNINA