A Highly Efficient Numerical Algorithm Based on Pseudospectral Method and Maximum Principle

This document presents a sophisticated numerical algorithm suite based on pseudospectral methods integrated with maximum principle. The implementation employs Chebyshev or Legendre polynomial approximations for state and control variables, transforming continuous optimal control problems into nonlinear programming problems through collocation at Gaussian quadrature nodes. The algorithm demonstrates exceptional practicality for solving complex real-world optimization problems with high accuracy and convergence rates. However, users must note that this software requires separate installation of SNOPT optimization solver, as it relies on SNOPT's sequential quadratic programming algorithm to handle the large-scale nonlinear constraints generated by the pseudospectral discretization. Despite this additional dependency, the algorithm's advantages - including spectral accuracy, direct constraint handling, and efficient solution of path-constrained problems - significantly outweigh the minor installation requirement. We strongly recommend installing SNOPT to fully leverage this powerful computational framework for practical engineering applications. The core implementation features adaptive mesh refinement, costate estimation via Pontryagin's maximum principle, and automated differentiation for gradient computations.