Abstract
The Weierstrass condition, which requires the Hamiltonian to be minimized over the set of all admissible controls, is a powerful tool for solving a class of optimization problems that do not immediately yield to our familiar algorithm with the Euler-Lagrange equations and the transversality condition. However, the Weierstrass condition’s “set of all admissible controls” is limited to continuously differentiable, unbounded functions, which are by no means the only feasible controls in practice or in principle. For example, “bang-bang” or “on-off” control schemes are frequently employed in everyday engineering applications, but these controls do not fall within the Weierstrass condition’s set.
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Longuski, J.M., Guzmán, J.J., Prussing, J.E. (2014). The Minimum Principle. In: Optimal Control with Aerospace Applications. Space Technology Library, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8945-0_6
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DOI: https://doi.org/10.1007/978-1-4614-8945-0_6
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