Circular orbit transfer employing recursive nonlinear state transformations and nonlinear feedback

Abstract

A recursive application of approximate feedback linearization is applied to low-Earth circular orbit rendezvous utilizing continuous low thrust propulsion. A family of solutions is established up to the $\rho$-th degree utilizing the null space that appears at each step in the computations. A convergence analysis is presented to guarantee that the recursive process converges as $\rho \rightarrow \infty$. During the recursive computations, patterns were detected as part of the solution process that illuminated a family of exact nonlinear control solutions obtained by judiciously selecting the null space coefficients. Examples of various analytic solutions are presented. The relationship between the $\rho$-th degree exact solution obtained through the recursive approximations and a known exact solution is illustrated where it is shown that different exact solutions can have different performance in terms of fuel usage leading to the possibility of optimization considerations in selecting the desired exact solution.