TRAJECTORY OPTIMIZATION-BASED ON DIFFERENTIAL INCLUSION

A method for generating finite-dimensional approximations to the solut ions of optimal control problems is introduced. By employing a descrip tion of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminate d from the system model. Besides reducing the dimensionality of the di scretized problem compared to state-of-the-art collocation methods, th is approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics o f the new method are illustrated on a simple double integrator problem . The performance of the new algorithm is demonstrated on a one-dimens ional rocket ascent problem (Goddard Problem) in presence of a dynamic pressure constraint.