Singular perturbations and the sounding rocket problemIn this paper, Goddard's problem of maximizing the final altitude of a sounding rocket (a singular problem of optimal control) is analyzed using singular perturbation methods. The problem is first cast in singular perturbation form and then solved to zero order by adding boundary-layer corrections to the reduced solution. For a quadratic drag law, a closed-form solution is obtained, although consideration of a numerical example indicates that this solution is not useful for practical sounding rockets. However, use of state variable transformations allows a very accurate numerical approximation to be constructed. It is concluded that application of singular perturbation methods to the well-known sounding rocket problem indicates that these methods may have utility in dealing with singular problems of optimal control.
Document ID
19800040098
Acquisition Source
Legacy CDMS
Document Type
Conference Proceedings
Authors
Ardema, M. D. (NASA Ames Research Center Moffett Field, Calif., United States)