Bang-bang Control Design by Combing Pseudospectral Method with a novel Homotopy Algorithm

The bang-bang type of control problem for spacecraft trajectory optimization is solved by using a hybrid approach. First, a pseudospectral method is utilized to generate approximate switching times, control structures, and initial co-states. Second, a homotopy method is used to solve the two-point boundary value problems derived from the Euler-Lagrangian equations. The unknown variables in the homotopy method include both switching times and the unknown initial states and co-states. The homotopy algorithm is made robust to the nonlinearity of the problems by enforcing the constraint satisfaction along the homotopy path. The optimization variables are treated as continuous variables and the final solutions have the same accuracy as the ordinary differential equation solvers. An orbit transfer problem is presented to show the advantages of this hybrid methodology. ∗Current Affiliation:Graduate Research Assistant, Department of Aerospace Engineering, TAMU-3141; [email protected]; phone: 979-862-3394; fax: 979-845-6051. Student Member AIAA. †Research Professor, Department of Aerospace Engineering, TAMU-3141; Associate Fellow AIAA ‡Regents Professor, Distinguished Professor of Aerospace Engineering, Holder of the Royce E. Wisenbaker ’39 Chair in Engineering, Department of Aerospace Engineering, TAMU-3141. Fellow AIAA.