Abstract
Balakrishnan's epsilon technique is used to compute minimum time profiles for the F-104 airplane. This technique differs from the classical gradient method in that a quadratic penalty on the error in satisfying the equations of motion is included in the cost function to be minimized as a means of eliminating the requirement of satisfying the equations of motion. Although the number of unknown independent functions is increased to include the state variables, the evaluation of the gradient of the modified cost is simplified, resulting in considerable computational savings. The unknown control and state variables are approximated by a functional expansion with unspecified coefficients which are determined by means of Newton's method. Typically 8 to 10 iterations are required for convergence when using the epsilon technique. Comparisons are made of solutions obtained by using this technique and the energy method.
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References
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Taylor, L.W., Smith, H.J., Iliff, K.W. (1970). A comparison of minimum time profiles for the F-104 using Balakrishnan's epsilon technique and the energy method. In: Balakrishnan, A.V., Contensou, M., de Veubeke, B.F., Krée, P., Lions, J.L., Moiseev, N.N. (eds) Symposium on Optimization. Lecture Notes in Mathematics, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066691
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DOI: https://doi.org/10.1007/BFb0066691
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