Optimization of Dynamic Systems (Solid Mechanics and Its Applications, 70)

This textbook deals with optimization of dynamic systems. The motivation for undertaking this task is as follows: There is an ever increasing need to produce more efficient, accurate, and lightweight mechanical and electromechanical de­ vices. Thus, the typical graduating B.S. and M.S. candidate is required to have some familiarity with techniques for improving the performance of dynamic systems. Unfortunately, existing texts dealing with system improvement via optimization remain inaccessible to many of these students and practicing en­ gineers. It is our goal to alleviate this difficulty by presenting to seniors and beginning graduate students practical efficient techniques for solving engineer­ ing system optimization problems. The text has been used in optimal control and dynamic system optimization courses at the University of Deleware, the University of Washington and Ohio University over the past four years. The text covers the following material in a straightforward detailed manner: • Static Optimization: The problem of optimizing a function that depends on static variables (i.e., parameters) is considered. Problems with equality and inequality constraints are addressed. • Numerical Methods: Static Optimization: Numerical algorithms for the solution of static optimization problems are presented here. The methods presented can accommodate both the unconstrained and constrained static optimization problems. • Calculus of Variation: The necessary and sufficient conditions for the ex­ tremum of functionals are presented. Both the fixed final time and free final time problems are considered.

This book provides the fundamentals of dynamic optimization which can be used to improve the performance of engineering systems. Most results are derived using the theory of calculus of variations. The methods are illustrated by a number of examples. Numerical implementation of the theory by direct and indirect methods is also described. Computer programs are provided that can be used to work out engineering problems. The book also introduces some new results in dynamic optimization using higher-order approaches. The book is appropriate for undergraduate seniors or first-year graduate students. It should also be of interest to professionals in the areas of automotive, aerospace, or manufacturing engineering. Students and researchers in the areas of systems theory, control, and optimization will benefit from the relatively simple exposition in this book.

Front Matter....Pages i-xi Static Optimization....Pages 1-18 Numerical Methods: Static Optimization....Pages 19-39 Calculus of Variations....Pages 41-59 Dynamic Optimization: Basic Results....Pages 61-91 Dynamic Optimization: Direct Solution....Pages 93-111 Dynamic Optimization: Indirect Solution....Pages 113-147 Finite Time Linear Systems....Pages 149-166 Steady State Linear Systems....Pages 167-175 Multi-Degree-of-Freedom Systems....Pages 177-197 Back Matter....Pages 199-228