93-151
Neighboring Suboptimal Control For Vehicle Guidance
David G. Hull* and Michael J. Nowak**
Abstract
The neighboring optimal feedback control law is developed for sys-tems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control) This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path.
*M. J. Thompson Regents Professor, Department of Aerospace Engineering and Engineering Mechanics, The University of Texas, Austin, Texas 78712-1085.
**Graduate Student. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas Austin, Texas 78712-1085. Major, U.S. Air Force..