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| Describing the System and Evaluating Its Performance | |
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| Introduction | |
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| Problem Formulation | |
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| State Variable Representation of Systems | |
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| Concluding Remarks | |
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| References | |
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| Problems | |
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| The Performance Measure | |
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| Performance Measures for Optimal Control Problems | |
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| Selecting a Performance Measure | |
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| Selection of a Performance Measure: The Carrier Landing of a Jet Aircraft | |
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| References | |
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| Problems | |
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| Dynamic Programming | |
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| Dynamic Programming | |
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| The Optimal Control Law | |
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| The Principle of Optimality | |
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| Application of the Principle of Optimality to Decision-Making | |
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| Dynamic Programming Applied to a Routing Problem | |
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| An Optimal Control System | |
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| Interpolation | |
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| A Recurrence Relation of Dynamic Programming | |
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| Computational Procedure for Solving Control Problems | |
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| Characteristics of Dynamic Programming Solution | |
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| Analytical Results--Discrete Linear Regulator Problems | |
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| The Hamilton-Jacobi-Bellman Equation | |
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| Continuous Linear Regulator Problems | |
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| The Hamilton-Jacobi-Bellman Equation--Some Observations | |
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| Summary | |
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| References | |
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| Problems | |
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| The Calculus of Variations and Pontryagin's Minimum Principle | |
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| The Calculus of Variations | |
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| Fundamental Concepts | |
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| Functionals of a Single Function | |
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| Functionals Involving Several Independent Functions | |
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| Piecewise-Smooth Extremals | |
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| Constrained Extrema | |
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| Summary | |
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| References | |
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| Problems | |
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| The Variational Approach to Optimal Control Problems | |
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| Necessary Conditions for Optimal Control | |
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| Linear Regulator Problems | |
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| Pontryagin's Minimum Principle and State Inequality Constraints | |
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| Minimum-Time Problems | |
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| Minimum Control-Effort Problems | |
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| Singular Intervals in Optimal Control Problems | |
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| Summary and Conclusions | |
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| References | |
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| Problems | |
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| Iterative Numerical Techniques for Finding Optimal Controls and Trajectories | |
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| Numerical Determination of Optimal Trajectories | |
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| Two-Point Boundary-Value Problems | |
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| The Method of Steepest Descent | |
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| Variation of Extremals | |
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| Quasilinearization | |
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| Summary of Iterative Techniques for Solving Two-Point Boundary-Value Problems | |
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| Gradient Projection | |
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| References | |
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| Problems | |
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| Conclusion | |
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| Summation | |
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| The Relationship Between Dynamic Programming and the Minimum Principle | |
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| Summary | |
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| Controller Design | |
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| Conclusion | |
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| References | |
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| Appendices | |
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| Useful Matrix Properties and Definitions | |
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| Difference Equation Representation of Linear Sampled-Data Systems | |
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| Special Types of Euler Equations | |
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| Answers to Selected Problems | |
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| Index | |