000 04474nam a22005775i 4500
001 978-1-4614-3834-2
003 DE-He213
005 20140220083249.0
007 cr nn 008mamaa
008 120626s2012 xxu| s |||| 0|eng d
020 _a9781461438342
_9978-1-4614-3834-2
024 7 _a10.1007/978-1-4614-3834-2
_2doi
050 4 _aQA315-316
050 4 _aQA402.3
050 4 _aQA402.5-QA402.6
072 7 _aPBKQ
_2bicssc
072 7 _aPBU
_2bicssc
072 7 _aMAT005000
_2bisacsh
072 7 _aMAT029020
_2bisacsh
082 0 4 _a515.64
_223
100 1 _aSchättler, Heinz.
_eauthor.
245 1 0 _aGeometric Optimal Control
_h[electronic resource] :
_bTheory, Methods and Examples /
_cby Heinz Schättler, Urszula Ledzewicz.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2012.
300 _aXIX, 640 p. 118 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInterdisciplinary Applied Mathematics,
_x0939-6047 ;
_v38
505 0 _aThe Calculus of Variations: A Historical Perspective -- The Pontryagin Maximum Principle: From Necessary Conditions to the Construction of an Optimal Solution -- Reachable Sets of Linear Time-Invariant Systems: From Convex Sets to the Bang-Bang Theorem -- The High-Order Maximum Principle: From Approximations of Reachable Sets to High-Order Necessary Conditions for Optimality -- The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum -- Synthesis of Optimal Controlled Trajectories: FromLocal to Global Solutions -- Control-Affine Systems in Low Dimensions: From Small-Time Reachable Sets to Time-Optimal Syntheses -- References -- Index.
520 _aThis book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including  the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of  Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.
650 0 _aMathematics.
650 0 _aDifferential Equations.
650 0 _aGlobal differential geometry.
650 0 _aMathematical optimization.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
650 2 4 _aControl.
650 2 4 _aDifferential Geometry.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
700 1 _aLedzewicz, Urszula.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461438335
830 0 _aInterdisciplinary Applied Mathematics,
_x0939-6047 ;
_v38
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-3834-2
912 _aZDB-2-SMA
999 _c101451
_d101451