This book is the result of over ten (10) years of research and development in flexible robots and structures at Sandia National Laboratories. The authors de cided to collect this wealth of knowledge into a set of viewgraphs in order to teach a graduate class in Flexible Robot Dynamics and Controls within the Mechanical En gineering Department at the University of New Mexico (UNM). These viewgraphs, encouragement from several students, and many late nights have produced a book that should provide an upper-level undergraduate and graduate textbook and a reference for experienced professionals. The content of this book spans several disciplines including structural dynam ics, system identification, optimization, and linear, digital, and nonlinear control theory which are developed from several points of view including electrical, me chanical, and aerospace engineering as well as engineering mechanics. As a result, the authors believe that this book demonstrates the value of solid applied theory when developing hardware solutions to real world problems. The reader will find many real world applications in this book and will be shown the applicability of these techniques beyond flexible structures which, in turn, shows the value of mul tidisciplinary education and teaming.

Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized. Applied Dynamic Programming for Optimization of Dynamical Systems presents applications of DP algorithms that are easily adapted to the reader's own interests and problems. The book is organized in such a way that it is possible for readers to use DP algorithms before thoroughly comprehending the full theoretical development. A general architecture is introduced for DP algorithms emphasizing the solution to nonlinear problems. DP algorithm development is introduced gradually with illustrative examples that surround linear systems applications. Many examples and explicit design steps applied to case studies illustrate the ideas and principles behind DP algorithms. DP algorithms potentially address a wide class of applications composed of many different physical systems described by dynamical equations of motion that require optimized trajectories for effective maneuverability. The DP algorithms determine control inputs and corresponding state histories of dynamic systems for a specified time while minimizing a performance index. Constraints may be applied to the final states of the dynamic system or to the states and control inputs during the transient portion of the manoeuvre.