## A Combined Newton-Raphson and Gradient Parameter Correction Technique for Solution of Optimal-control Problems |

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a,tf a,tfj algorithm angular velocity APPENDIX arbitrary assumed axis system circular orbit class of two-point computed continuous function convergence convergence problems defined in equation differential equations dynamical system equa equation A2 Equation continued equations 15 equations Bll Euclidean space exists figure B-3 final time tf fuel-optimal given by equation Given x(a,t gradient influence matrices Integral equations iteration Langley Research Center lemma m-dimensional matrices that describe maximum principle ref method monotonic decreasing sequence moon necessary conditions negative definite Newton-Raphson nonsingular obtained optimal control Optimal-Control Theory optimization theory orbital plane p(tf piecewise continuous Pontryagin maximum principle positive definite Pq(t procedure rendezvous respect Rs(t satellite satisfies equation set of switching signum function singular control subroutines switching function switching points terminal conditions terminal errors theorem thrust vector tion two-point boundary-value problem unknown parameters v(tf variables vector with elements xyz-axis system yields