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Optimal Control: Calculus of Variations, Optimal Control Theory and Numerical Methods
Name: Optimal Control: Calculus of Variations, Optimal Control Theory and Numerical Methods
Pages: 352
Year: 1993
Language: English
File Size: 22.1 MB
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Editors Prof. Dr. R. Bulirsch Mathematisches Institut THMiinchen Postfach 20 24 20 0 80290 Miinchen 2 Germany Prof. Dr. J. Stoer Inst. f. Angewandte Mathematik u. Statistik Am Hubland 0 97074 Wiirzburg Germany Library of Congress Cataloging in Publication Data Dr. A. Miele Dept. of Mechanical Engineering and Materials Science Post Office Box 1892 Houston, Texas 77251 1892 USA Prof. Dr. K. Well Inst. f. Flugmechanik u. Flugregelung Universitlit Stuttgart Forststr. 86 0 70176 Stuttgart Germany Optimal control: calculus of variations, optimal control theory, and numerical methods I edited by R. Bulirsch ... let al.]. p. em. (International series of numerical mathematics: vol. 111) 1. Calculus of variations Congresses. 2. Control theory Congesses. 3. Mathematical optimization Congresses. I. Bulirsch, Roland. II. Series: International series of numerical mathematics; v. 111. QA315.068 1993 003'.5 dc20 Deutsche Bibliothek Cataloging in Publication Data Optimal Control: calculus of variations, optimal control theory and numerical methods I ed. by R. Bulirsch ... Basel; Boston ; Berlin: Birkhliuser, 1993 (International series of numerical mathematics; Vol. 111) ISBN 978 3 0348 7541 7 ISBN 978 3 0348 7539 4 (eBook) DOI 10.1007/978 3 0348 7539 4 NE: Bulirsch, Roland ; GT This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use the permission of the copyright owner must be obtained. 1993 Birkhauser Verlag, P.O. Box 133, CH 4010 Basel, Switzerland Camera ready copy prepared by the editors Printed on acid free paper produced from chlorine free pulp Cover design: Heinz Hiltbrunner, Basel 987654321


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Contents Foreword ..................................................................... VIII Participants .................................................................. IX Preface....................................................................... XI Optimality Conditions and Algorithms Tent Method in Optimal Control Theory V.G. Boltyanski ............................................................... 3 Pontryagin's Maximum Principle for Multidimensional Control Problems R. Klotzler, S. Pickenhain ..................................................... 21 An Algorithm for Abstract Optimal Control Problems Using Maximum Principles and Applications to a Class of Distributed Parameter Systems H. Benker, M. Handschug ..................................................... 31 Convexification of Control Problems in Evolution Equations W. Kampowsky, U. Raitums .................................................. 43 Semidiscrete Ritz Galerkin Approximation of Nonlinear Parabolic Boundary Control Problems F. TroItzsch .................................................................. 57 Iterative Methods for Optimal Control Processes governed by Integral Equations W.H. Schmidt ................................................................ 69 Solving Equations a Problem of Optimal Control L. Bittner .................................................................... 83 On the Minimax Optimal Control Problem and Its Variations P. Lu, N.X. Vinh ............................................................. 99 Numerical Methods Trajectory Optimization Using Sparse Sequential Quadratic Program ming J. T. Betts .................................................................... 115


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VI Numerical Solution of Optimal Control Problems by Direct Collocation O. v. Stryk .................................................................... 129 Reduced SQP Methods for Nonlinear Heat Conduction Control Problems F. S. Kupfer, E. W. Sachs ..................................................... 145 Analysis and Synthesis of Nonlinear Systems Decomposition and Feedback Control of Nonlinear Dynamic Systems F.L. Chernousko .............................................................. 163 A Discrete Stabilizing Study Strategy for a Student Related Problem under Uncertainty G. Leitmann, C.S. Lee ........................................................ 173 Stability Conditions in Terms of Eigenvalues of a Nonlinear Optimal Controlled System H. Bourdache Siguerdidjane ................................................... 187 Program Positional Optimization for Dynamic Systems R. Gabasov, F.M. Kirillova, N. V. Balashevich ......... . . . . . . . . . . . . . . . . . . . . . . . .. 195 Synthesis of Bilinear Controlled Systems with Delay V. Kolmanovskii, N. Koroleva ................................................. 207 Constructing Feedback Control in Differential Games by Use of "Central" Trajectories G. Sonnevend ................................................................. 221 Applications to Mechanical and Aerospace Systems Singular Pertubation Time Optimal Controller on Disk Drives M.D. Ardema, E. Cooper ..................................................... 251 Optimal Design of Elastic Bars L. Mikulski ................................................................... 265 Combining Indirect and Direct Methods in Optimal Control: Range Max imization of a Hang Glider R. Bulirsch, E. Nerz, H.J. Pesch, O. v. Stryk ................................... 273 Periodic Optimal Trajectories with Singular Control for Aircraft with High Aerodynamic Efficiency G. Sachs, K. Lesch, H.G. Bock, M. Steinbach ................................. 289


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Foreword The conference on Optimal Control Variationsrechnung und Optimalsteuerungen was held at the Mathematisches Forschungsinstitut of the University of Freiburg during the period May 26 to June 1, 1991. It was the second conference with this title in Oberwolfach, the first one took place in 1986. There were 52 participants, 8 from the United States of America, 6 from Russia and Byelorussia, several from France, Poland, and Austria, and many from Germany the first time from a unified Germany. In comparison to the material covered during the first meeting, this manuscript contains new theoretical and practical advances for analyzing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations. New necessary and sufficient conditions for optimality are given. Recent advances in numerical methods are due to new techniques for solving large sized nonlinear programs with sparse Hessians and due to a combination of direct and indirect methods for solv ing the multi point boundary value problem associated with the optimization problem. The construction of feedback controls for nonlinear systems is the third major contri bution of this book. Recent advances in the theory of problems with uncertainty, on decomposition methods of nonlinear systems, and on new techniques for constructing feedback controls for state and control constrained linear quadratic systems are pre sented. The book has solutions for many complex practical optimal control problems. The authors gratefully acknowlege the assistance of the reviewers and the help of Mr. Tilmann Raible, who combined the various UTEX files into their present form. Roland Bulirsch Mathematisches Institut TU Miinchen Postfach 202420 8000 Miinchen 2 Germany Josef Stoer Angewandte Mathematik und Statistik Universitiit Wiirzburg Am Hubland 8700 Wiirzburg Germany Angelo Miele Department of Mechanical Engineering and Material Sciences P.O.Box 1892 Houston, Texas 77251 1892 USA Klaus H. Well Institut fr Flugmechanik und Flugregelung Universitiit Stuttgart ForststraBe 86 7000 Stuttgart 1 Germany


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