Pseudospectral Optimal Control on Arbitrary Grids

Abstract

In advancing our prior work on a unified theory for pseudospectral (PS) optimal control, we present new results for PS methods over arbitrary grids. These results provide a way to compare performances among different PS methods and suggest guidelines to choose the proper grids and discretization approaches for solving optimal control problems. The new unified ideas reveal hidden properties of different types of PS methods and pave the way to construct more efficient algorithms for solving different types of optimal control problems. Our computational framework is not based on any particular choice of orthogonal polynomials; therefore, the approach unifies Legendre and Chebyshev PS methods under one framework.