Convergence of a pseudospectral method for optimal control of complex dynamical systems

Pseudospectral approximation techniques have been shown to provide effective and flexible methods for solving optimal control problems in a variety of applications. In this paper, we provide the conditions for the convergence of the pseudospectral method for general nonlinear optimal control problems. Further, we show that this proof is directly extendible to the multidimensional pseudospectral method for optimal ensemble control of a class of parameterized dynamical systems. Examples from quantum control and neuroscience are included to demonstrate the method.