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F. B. Hanson, Techniques in Computational Stochastic Dynamic Programming in Digital and Control System Techniques and Applications, within series Advances in Control and Dynamical Systems, vol. 76, (C. T. Leondes, Editor), Academic Press, New York, NY, 60 pages in Mats, to appear April 1996.

Table of Contents:

(in lieu of abstract)

    I. INTRODUCTION

    II. COMPUTATIONAL STOCHASTIC DYNAMIC PROGRAMMING IN CONTINUOUS TIME

      A. FORMULATION OF PDE FOR STOCHASTIC DYNAMIC PROGRAMMING

        1. Boundary Conditions

        2. Nearly Quadratic Costs

        3. Forward Computations for Optimal, Expected Trajectory

      B. COMPUTATIONAL APPROACH

        1. Computational Difficulties

        2. Crank-Nicolson, Predictor-Corrector Finite Difference Algorithm

        3. Finite Element Version of Solution Algorithm for SDP

        4. Bellman's Curse of Dimensionality

      C. ALGORITHMIC CONVERGENCE

      D. OTHER COMPUTATIONAL METHODS

    III. PARALLEL COMPUTATIONAL DYNAMIC PROGRAMMING

      A. HARDWARE ADVANCES

      B. SOFTWARE ADVANCES: FASTER AND MORE EFFICIENT NUMERICAL ALGORITHMS

        1. Other Advanced Techniques: Loop Optimizations, Decompositions, Broadcasting

        2. Vector versus Hypercube Data Structures

      C. Graphical Visualization of Multidimensional Results

      D. Numeric and Symbolic Interface

    IV. SOME RELATED METHODS

      A. DIFFERENTIAL DYNAMIC PROGRAMMING

        1. Dynamic Programming in Discrete Time

        2. Final Time DDP Backward Sweep

        3. General DDP Backward Sweep in Time

        4. DDP Forward Sweep

        5. Similarities and Differences between DDP and SDP

        6. DDP Variations and Applications

      B. MARKOV CHAIN APPROXIMATION

        1. MCA Dynamic Programming Model Formulation

        2. MCA Local Consistency Conditions

        3. MCA Dynamic Programming Equation and Transition Probabilities Construction from Finite Differences

        4. MCA Dynamic Programming Equation Solution

        5. Similarities and Differences between MCA and SDP

    V. RESEARCH DIRECTIONS

    ACKNOWLEDGEMENT

    VI. REFERENCES

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