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Author(s) Bulirsch, R. (ed.)
Miele, A. (ed.)
Stoer, J. (ed.)
Well, K.H. (ed.)
Title Optimal Control, Calculus of Variations, Optimal Control Theory and Numerical Methods
Publisher Birkhäuser
Year of publication 1993
Reviewed by Vasile Postolica

This proceedings volume is a collection of research works in the Conference on Optimal Control-Variationsrechnung und Optimalsteuerungen at the Mathematisches Forschungsinstitut of the University of Freiburg during the period May 26 to June 1, 1991.

This second international conference having the above title was devoted to new theoretical and practical advances for analysing and synthesizing optimal controls of dynamical systems governed by partial and ordinary differential equations.

The first chapter entitled "Optimality Conditions and Algorithms" contains: V.G Boltyanski "Tent Method in Optimal Control Theory", R. Klötzler and S. Pickenhain "Pontryagin's Maximum Principle for Multidimensional Control Problems", H. Benker and M. Handschug "An Algorithm for Abstract Optimal Control Problems using Maximum Principles and Applications to a Class of Distributed Parameter Systems", W. Kampowsky and U. Raitums "Convexification of Control Problems in Evolution Equations", F. Tröltzsch "Semidiscrete Ritz-Galerkin Approximation of Nonlinear Parabolic Boundary Control Problems", W.H. Schmidt "Iterative Methods for Optimal Control Processes Governed by Integral Equations", L. Bittner "Solving Equations - A Problem of Optimal Control" and Ping Lu and Nguyen X. Vinh "On the Minimax Optimal Control Problem and Its Variations".

In the second chapter "Numerical Methods" we find: J.T. Betts "Trajectory Optimization using Sparse Sequential Quadratic Programming", Oskar von Stryk "Numerical Solution of Optimal Control Problems by Direct Collocation" and F.-S. Kupfer and E.W. Sachs "Reduced SQP Methods for Nonlinear Heat Conduction Control Problems".

The third chapter "Analysis and Synthesis of Nonlinear Systems" is devoted to: F.L. Chernouske "Decomposition and Feedback Control of Nonlinear Dynamic Systems", G. Leitmann and C.S. Lee "A Discrete Stabilizing Study Strategy for a Student Related Problem under Uncertainty", H. Bourdache-Siguerdidjane "Stability Conditions in Terms of Eigenvalues of a Nonlinear Optimal Controlled System", R. Gabasov, F.M. Kirillova and N.V. Balashevich "Program-Positional Optimization for Dynamic Systems", V. Kolmanovskii and Natalia Koroleva "Synthesis of Bilinear Controlled Systems with Delay" and G.Sonnevend "Constructing Feedback Control in Differential Games by Use of "Central" Trajectories".

The last chapter contains "Applications to Mechanical and Aerospace Systems". M.D. Ardema and E. Cooper "Singular Perturbation Time-Optimal Controller for Disk Drives", L. Mikulski "Optimal Design of Elastic Bars", R. Bulirsch, E. Nerz, H.J. Pesch and O. von Stryk "Combining Direct and Indirect Methods in Optimal Control: Range Maximization of a Hang Glider", G. Sachs, K. Lesch, H.G. Bock and M Steinbach 'Periodic Optimal Trajectories with Singular Control for Aircraft with High Aerodynamic Efficiency", W. Grimm "Optimal Flight Paths with Constrained Dynamic Pressure", K. Chudej "Optimal Ascent of a Hypersonic Space Vehicle", B. Kugelmann and H.J. Pesch "Controllability Investigations of a Two-Stage-To-Orbit Vehicle and R. Callies "Optimal Design of a Mission to Neptune".

Thanks to its valuable content which also links pure mathematics with applied mathematics and offers solutions to many practical optimal control problems, the book is an excellent scientific foundation of source of information for all research workers in the field of optimal control.