We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and
control constraints. In contrast to the existing results, the optimal controller addressed in this paper is
allowed to be discontinuous. This generalization requires a substantial modification to the existing
convergence analysis in terms of both the framework as well as the notion of convergence around points of
discontinuity. Although the nonlinear system is assumed to be feedback linearizable, the optimal control
does not necessarily linearize the dynamics. Such problems frequently arise in astronautical applications
where stringent performance requirements demand optimality over feedback linearizing controls. We
prove that a sequence of solutions obtained using the Legendre pseudospectral method converges to
the optimal solution of the continuous-time problem under mild conditions
