## Dynamic Programming and Optimal Control: Volume I, Volume 1This is the leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. Among its special features, the book 1) provides a unifying framework for sequential decision making, 2) treats simultaneously deterministic and stochastic control problems popular in modern control theory and Markovian decision popular in operations research, 3) develops the theory of deterministic optimal control problems including the Pontryagin Minimum Principle, 4) introduces recent suboptimal control and simulation-based approximation techniques (neuro-dynamic programming), which allow the practical application of dynamic programming to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model, 5) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume The electronic version of the book includes 29 theoretical problems, with high-quality solutions, which enhance the range of coverage of the book. |

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### Contents

1 | |

Deterministic Systems and the Shortest Path Problem | 67 |

Problems with Perfect State Information | 109 |

Problems with Imperfect State Information | 183 |

Introduction to Infinite Horizon Problems | 231 |

Approximate Dynamic Programming | 291 |

Deterministic ContinuousTime Optimal Control | 425 |

Mathematical Review | 467 |

On Optimization Theory | 476 |

On Probability Theory | 480 |

On FiniteState Markov Chains | 485 |

Least Squares Estimation and Kalman Filtering | 489 |

Formulating Problems of Decision Under Uncertainty | 511 |

References | 533 |

551 | |

Selected Theoretical Problem Solutions | 1 |