Convergence of Pseudospectral Methods for a Class of Discontinuous Optimal Control

We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized using pseudospectral (PS) methods. We prove that the discretized problem is always feasible and that the optimal solution to the discretized, constrained problem converges to the possibly discontinuous optimal control of the continuous-time problem.