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.