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A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

Author

Listed:
  • Gregory Lantoine

    (Georgia Institute of Technology)

  • Ryan P. Russell

    (The University of Texas at Austin)

Abstract

A new algorithm is presented to solve constrained nonlinear optimal control problems, with an emphasis on highly nonlinear dynamical systems. The algorithm, called HDDP, is a hybrid variant of differential dynamic programming, a proven second-order technique that relies on Bellman’s Principle of Optimality and successive minimization of quadratic approximations. The new hybrid method incorporates nonlinear mathematical programming techniques to increase efficiency: quadratic programming subproblems are solved via trust region and range-space active set methods, an augmented Lagrangian cost function is utilized, and a multiphase structure is implemented. In addition, the algorithm decouples the optimization from the dynamics using first- and second-order state transition matrices. A comprehensive theoretical description of the algorithm is provided in this first part of the two paper series. Practical implementation and numerical evaluation of the algorithm is presented in Part 2.

Suggested Citation

  • Gregory Lantoine & Ryan P. Russell, 2012. "A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 382-417, August.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:2:d:10.1007_s10957-012-0039-0
    DOI: 10.1007/s10957-012-0039-0
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    Cited by:

    1. David Ottesen & Ryan P. Russell, 2021. "Unconstrained Direct Optimization of Spacecraft Trajectories Using Many Embedded Lambert Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 634-674, December.
    2. Joris T. Olympio, 2013. "A Continuous Implementation of a Second-Variation Optimal Control Method for Space Trajectory Problems," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 687-716, September.

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