## Dynamic Programming with Continuous Independent VariableDepartment of Electrical Engineering, Stanford University., 1964 - Programming (Mathematics) - 94 pages In this study a computational procedure for solving optimal control problems, called dynamic programming with continuous independent variable, has been developed. The new procedure, is based on iterative application of Bellman's principle of optimality. It differs from the conventional method in the choice of the time interval over which a given control is applied. Instead of using a fixed interval, the new procedure determines the time interval as the minimum time required for at least one of the state variables to change by one increment. Specialized computations near the boundaries of the block permit the optimal trajectories any desired degree of freedom in passing from block to block. This technique has been applied in a computer program which calculates minimum fuel trajectories for supersonic (Mach 3) aircraft under a variety of conditions and constraints. Computation of the optimal bounded control of linear plants has been studied in detail. (Author). |

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### Contents

INTRODUCTION | 1 |

Concept of Continuous Independent Variable | 7 |

Procedure without Complete Control | 18 |

7 other sections not shown

### Common terms and phrases

admissible controls altitude Bellman's boundary calculus of variations Calif Chapter chosen complete control computation of optimal constraints continuous independent variable control is applied control variables conventional dynamic programming conventional method coordinate Corp curse of dimensionality determined differential equations direction of motion dive EE Dept Electronics Engineering existing optimal points flow charts flow function given time interval high-speed memory requirement increment initial set initialization procedure integer interblock transitions interpolation l)AT l/s PLANT large number Librarian Library locations low-speed memory minimum fuel trajectories n-dimensional N.Y. 1 Attn North American Aviation optimal cost function optimal trajectory P.O. Box performance criterion point in Q Pontryagin's Maximum Principle possible preferred direction previously computed block principle of optimality processed programming with continuous quantized values Refs result set of admissible set of optimal space specified stored Supersonic Transport system equations Tech technique tion total number vector velocity Washington 25