Dynamic Programming and Optimal Control, Volume I, Third Edition by Dimitri P. Bertsekas provides a comprehensive treatment of dynamic programming and optimal control theory. The book is structured into two volumes, with Volume I focusing on finite horizon problems and Volume II on infinite horizon problems. The first volume introduces the fundamental concepts of dynamic programming, including the principle of optimality, the dynamic programming algorithm, and applications to deterministic and stochastic systems. It covers topics such as the shortest path problem, deterministic continuous-time optimal control, and problems with perfect and imperfect state information. The book also discusses control strategies, including certainty equivalent and adaptive control, limited lookahead policies, and model predictive control. It includes a detailed discussion of the mathematical foundations of dynamic programming, such as convex sets and functions, probability theory, and optimization theory. The book is written for a broad audience, including students and researchers in engineering, operations research, economics, and applied mathematics. It provides a unified treatment of dynamic programming and optimal control, with a focus on both theoretical and practical aspects. The book includes numerous examples and exercises, and it is accompanied by a series of appendices that provide additional background material on mathematical and probabilistic concepts. The book is an essential resource for anyone interested in dynamic programming and optimal control theory.Dynamic Programming and Optimal Control, Volume I, Third Edition by Dimitri P. Bertsekas provides a comprehensive treatment of dynamic programming and optimal control theory. The book is structured into two volumes, with Volume I focusing on finite horizon problems and Volume II on infinite horizon problems. The first volume introduces the fundamental concepts of dynamic programming, including the principle of optimality, the dynamic programming algorithm, and applications to deterministic and stochastic systems. It covers topics such as the shortest path problem, deterministic continuous-time optimal control, and problems with perfect and imperfect state information. The book also discusses control strategies, including certainty equivalent and adaptive control, limited lookahead policies, and model predictive control. It includes a detailed discussion of the mathematical foundations of dynamic programming, such as convex sets and functions, probability theory, and optimization theory. The book is written for a broad audience, including students and researchers in engineering, operations research, economics, and applied mathematics. It provides a unified treatment of dynamic programming and optimal control, with a focus on both theoretical and practical aspects. The book includes numerous examples and exercises, and it is accompanied by a series of appendices that provide additional background material on mathematical and probabilistic concepts. The book is an essential resource for anyone interested in dynamic programming and optimal control theory.