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        A self-stabilizing Pantoja-like indirect algorithm for optimal control

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        900584.pdf (PDF, 395Kb)
        Author
        Christianson, B.
        Attention
        2299/3374
        Abstract
        In 1983 Pantoja described a computationally efficient stagewise construction of the Newton direction for the discrete time optimal control problem. Automatic Differentiation can be used to implement Pantoja's algorithm and calculate the Newton direction, without truncation error, and without extensive manual re-writing of targetfunction code to form derivatives. Pantoja's algorithm is direct, in that the independent variables are the control vectors at each timestep. In this paper we formulate an indirect analogue of Pantoja's algorithm, in which the only independent variables are the components of a costate vector corresponding to the initial timestep. This reformulated algorithm gives exactly the Newton step for the initial costate with respect to a terminal transversality condition: at each timestep we solve implicit equations for the current controlsand successor costates. A remarkable feature of the indirect algorithm is that it is straiehtforward to comensate for the effect of non-zero residuals in the implicit costate equations. .The indirect reformulation of Pantoja's algorithm set out in this paper is a suitable basis for verified optimization using interval methods.
        Publication date
        2001
        Published in
        Optimization Methods and Software
        Published version
        https://doi.org/10.1080/10556780108805833
        Other links
        http://hdl.handle.net/2299/3374
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