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Deterministic Optimal Control: An Introduction for Scientists

by H. Gardner Moyer

182 pages; quality trade paperback (softcover); catalogue #02-1202; ISBN 1-55395-487-4; US$23.95, C$35.45, EUR23.10, £16.00

This textbook gives a geometric, visual presentation of optimal control. The material on conservation laws, geodesics on a Riemannian manifold, and the quantization of a Hamiltonian system are particularly valuable for physics students.

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about the book      about the author      sample excerpts or Table of Contents      catalogue info

About the Book This textbook is intended for physics students at the senior and graduate level. The first chapter employs Huygens' theory of wavefronts and wavelets to derive Hamilton's equations and the Hamilton-Jacobi equation. The final section presents a step-by-step precedure for the quanitzation of a Hamiltonian system. The remarkable congruence between particle dynaics and wave packets is shown. The second chapter presents sufficiency conditions for the standard case, broken, and singular extremals. Chapter III presents four schemes that can yield formal integrals of of Hamilton's equations- Killing's, Noether's, Poisson's, and Jacobi's. Chapter IV discusses iterative, numerical algorithms that converge to extremals. Three discontinuous problems are solved in Chapter V - refraction, jump discontinuities specified for state variables, and inequality contrainsts on state variables. The book contains many exercises and examples, in particular the geodesics of a Riemannian manifold.

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About the Author The author learned optimal control while working in the research department of Grumman Aerospace. He wrote computer programs for the flight paths of aircraft and the lunar lander rocket. He has authored numerous publications on the theory and applications of optimal control.

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Sample Excerpts or Table of Contents

CONTENTS CHAPTER I - THE PROPAGATION OF DISTURBANCES 1. Introduction 2. Huygens' Principle 3. Two Wavefront Normals 4. Boundary Conditions for the Normal Vector 5. The Hamilton-Jacobi Formula 6. Quantization     References CHAPTER II - SUFFICIENT CONDITIONS FOR A MAXIMUM 1. Introduction 2. The Standard Case 3. Broken Extremals 4. Singular Extremals 5. Abnormal Points and Extremals 6. Necessity of the Conditions     References CHAPTER III - FORMAL INTEGRALS 1. Killing's Method 2. Noether's Method 3. Poisson's Method 4. Jacobi's Method     References CHAPTER IV - NUMERICAL ALGORITHMS 1. Extremal Search 2. Gradient - Fixed Final Time, Final Point Open 3. Gradient - Minimum Time Approached from Below 4. Gradient - Minimum Time Approached from Above 5. Comparison of the Methods     References CHAPTER V - DISCONTINUOUS PROBLEMS 1. Refraction 2. Jump Discontinuities in the State Variables 3. State Variable Inequality Constraints     References GLOSSARY SYMBOLS FIGURES INDEX INDEX abnormal extremal abnormal point action principle adjoint variable Anderson J.L. balance function bang-bang control Bell, D.J. Beltrami, B. Bernoulli brothers Bliss, G.A. Bohm, D. Bolza, O. boundary of the reachable set de Broglie, L. broken extremal Bryson, A. E. calculus of variations canonical momentum Caratheodory, C. Carathoedory condition Cicala, P. Citron, S.J. Cole, K.C. comparison arc complementary variable conjugate point constraint holonomic constraint inequality     control variable     state variable control saturation control variable corner, extremal corner, wavefront Courant, R. Darboux, G. Dresden, A. Dyer, P. eikonal eikonal approximation Einstein, A. Elmore, W.C. equations of variaton Euler condition Euler equations Euler's rule excess function extremal extremal search method Fermat's principle field coordinates field, extremal first integral focal point Fomin, S.V. functional Gelfond, I.M. geodesics geodetic sphere Goldstein, H. gradient gradient method group velocity Halkin, H. Hamilton's formulas Hamilton's principle Hamilton-Jacobi formula Hamiltonian, control Hamiltonian, true Haynes, G.W. Head, M.A. Heisenberg, W. Hestenes, M.R. Hilbert, D Ho, Y-C hodograph space Huygens' principle ignored variable impulse response function indicatrix influence functions isochronal Jackson, J.D. Jacobi condition Jacobian Jacobi's identity Jacobi's method Jacobson, D.H. Keats, J. Kelley, H.J. Killing, H. Kneser, A. Knowles, G. Kopp, R.E. Lagrange bracket Lagrange form Lagrange multipliers Lagrangian Legendre-Clebsch condition Lele, M.M. Lewis, F.L. Lie bracket line element linear-quadratic problem Logan, J.D. max H iterative method maximum principle McReynolds, S.R. Mieli, A. min H iterative method, see max H     iterative method minimum principle Misner, C.W. Moiseiwitsch, B.L. Moyer, H.G. multistage rockets natural boundary conditions     transversatility navigation problems, Zermelo's Neuenschwander, D.E. Noether E. normal vector ordinary maximum problem penalty functions performance index perturbation system, see equations of     variation phase velocity pilot wave Planck's constant Poisson, S.D. Pontryagin, L.S. reciprocity regulators ridges, method of Riemann, G.F.B. see geodesics Robbins, H.M. rocket flight Rohrlich, F. Roxin, E.O. Schroedinger, E. Schutz, B.F. second integrals singular extremals Snell's law Speyer, J.L. Starkey, S.R. state variables steepest ascent strong variation Styer, D.F. switch function Syrmos, V.L Thorne, K.S. total internal reflection transversal surface transversatility Tsiotras, P. two-point boundary value problems uncertainty principle Warga, J. wave equation wavefront wavefront normal, see normal vector wavelet weak variation Weierstrass, K. Weierstrass-Erdmann corner     condition Wheeler, J.A. Whittaker, E.T. work integral Zermelo, E. see navigation problems

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Catalogue Information

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