Abstract
In this article we describe the three most common approaches for numerically solving nonlinear optimal control problems governed by ordinary differential equations. For computing approximations to optimal value functions and optimal feedback laws, we present the Hamilton-Jacobi-Bellman approach. For computing approximately optimal open-loop control functions and trajectories for a single initial value, we outline the indirect approach based on Pontryagin’s maximum principle and the approach via direct discretization.
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Grüne, L. (2015). Numerical Methods for Nonlinear Optimal Control Problems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_208
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DOI: https://doi.org/10.1007/978-1-4471-5058-9_208
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Online ISBN: 978-1-4471-5058-9
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