A pseudospectral method for the optimal control of constrained feedback linearizable systems

We consider the optimal control of feedback linearizable dynamical systems subject to mixed state and control constraints. In general, the optimal control does not linearize the dynamics. Such problems frequently arise in astronautical applications where stringent performance requirements demand optimality that cannot be achieved by feedback linearizing controls. We prove that a sequence of solutions to the discretized, constrained problem converge to the optimal solution of the continuous-time problem under mild and verifiable conditions. The spectral coefficients of the state trajectories provide a practical method to verify the convergence of the computed solution. The proposed ideas are illustrated by several numerical examples