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A Sweeping Gradient Method for Ordinary Differential Equations with Events

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  • Benjamin W. L. Margolis

    (NASA Ames Research Center)

Abstract

In this paper, we use the calculus of variations to derive a sensitivity analysis for ordinary differential equations with events. This sweeping gradient method (SGM) requires a forward sweep to evaluate the original model and a backwards sweep of the adjoint to compute the sensitivity. The method is applied to canonical optimal control problems with numerical examples, including the sampled linear quadratic regulator and the optimal time-switching and state-switching for minimum-time transfer of the double integrator. We show that the application of the SGM for these examples matches the gradient determined analytically. Numerical examples are produced using gradient-based optimization algorithms. The emphasis of this work is on modeling considerations for the effective application of this method.

Suggested Citation

  • Benjamin W. L. Margolis, 2023. "A Sweeping Gradient Method for Ordinary Differential Equations with Events," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 600-638, November.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:2:d:10.1007_s10957-023-02303-3
    DOI: 10.1007/s10957-023-02303-3
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    References listed on IDEAS

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    1. 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.
    2. Gregory Lantoine & Ryan P. Russell, 2012. "A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 2: Application," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 418-442, August.
    3. R. Griesse & A. Walther, 2004. "Evaluating Gradients in Optimal Control: Continuous Adjoints Versus Automatic Differentiation," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 63-86, July.
    Full references (including those not matched with items on IDEAS)

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