93-148
TRAJECTORY OPTIMIZATION BASED ON DIFFERENTIAL INCLUSION*
Hans Seywald**
Abstract
A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem ("Goddard Problem") in presence of a dynamic pressure constraint.
*Performed under NASA contract NAS1-18935.
**Senior Project Engineer, Analytical Mechanics Associates, Inc-, 17 Research Drive, Hampton, Virginia 23666, working under contract at the Spacecraft Controls Branch, NASA Langley Research Center. Member AIAA