Optimal Control Theory for Applications

Optimization, the area of mathematics concerned with finding the "best" points, curves, surfaces, etc., has many uses in engineering research and applications. Optimal Control Theory for Applications teaches analytical optimization at the graduate level. To make the material accessible to a wide audience, the prerequisites are limited to calculus and differential equations. Example problems are not tied to any engineering discipline. This material will benefit and interest both beginning engineering graduate students, as well as practicing engineers with the same background.

From the reviews:

"It presents a unified approach to the conversion of nonlinear optimal control problems into parameter optimizations for numerical solutions. the book is written in a way that is very accessible to the audience. The selection of topics is useful and coherent, and the book is well organized. is highly effective in explaining basic ideas of optimal control. It can also be a useful reference to engineers and researchers who want to use applied optimal control theories for solving engineering problems ." (Yiyuan J. Zhao, International Journal of Robust and Nonlinear Control, Vol. 15 (17), 2005)

Auteur
Optimization, the area of mathematics concerned with finding the "best" points, curves, surfaces, etc., has many uses in engineering research and applications. Optimal Control Theory for Applications teaches analytical optimization at the graduate level. To make the material accessible to a wide audience, the prerequisites are limited to calculus and differential equations. Example problems are not tied to any engineering discipline. This material will benefit and interest both beginning engineering graduate students, as well as practicing engineers with the same background.

Résumé
Mechanical engineering, an engineering discipline born of the needs of the in­ dustrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in con­ temporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on page ii of this volume. The areas of concentration are applied mathematics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Austin, Texas Frederick F. Ling Preface Optimization is an area of mathematics that is concerned with finding the "best" points, curves, surfaces, and so on. "Best" is determined by minimizing some measure of performance subject to equality and inequality constraints. Points are constrained by algebraic equations; curves are constrained by or­ dinary differential equations and algebraic equations; surfaces are constrained by partial differential equations, ordinary differential equations, and algebraic equations.

Contenu
1 Introduction to Optimization.- I. Parameter Optimization.- 2 Unconstrained Minimization.- 3 Constrained Minimization: Equality Constraints.- 4 Constrained Minimization: Inequality Constraints.- 5 Minimization Using Matrix Notation.- II. Optimal Control Theory.- 6 Differentials in Optimal Control.- 7 Controllability.- 8 Simplest Optimal Control Problem.- 9 Fixed Final Time: First Differential.- 10 Fixed Final Time: Tests for a Minimum.- 11 Fixed Final Time: Second Differential.- 12 Fixed Final Time Guidance.- 13 Free Final Time.- 14 Parameters.- 15 Free Initial Time and States.- 16 Control Discontinuities.- 17 Path Constraints.- III. Approximate Solutions.- 18 Approximate Solutions of Algebraic Equations.- 19 Approximate Solutions of Differential Equations.- 20 Approximate Solutions of Optimal Control Problems.- 21 Conversion into a Parameter Optimization Problem.- Appendix: A First and Second Differentials by Taylor Series Expansion.- References.