A MATLAB GUI for a Legendre Pseudospectral algorithm for optimal control problems

Abstract

This implementation of a Legendre-Gauss-Lobatto Pseudospectral (LGLP) algorithm takes advantage of the MATLAB Graphical User Interface (GUI) and the Optimization Toolbox to allow an efficient implementation of a direct solution technique. Direct solutions techniques solve optimal control problems without solving for the optimality conditions. Using the LGLP method, an optimal control problem is discretized into a Nonlinear Program (NLP) and solved using an NLP solver, avoiding the problems of deriving the conditions of optimality and solving the resulting boundary value problem. The MATLAB GUI implementation solves optimal control problems without requiring knowledge of the specific implementation of the LGLP method. The GUI completes the discretization of the problem and solves the resulting NLP using a Sequential Quadratic Programming Algorithm. The GUI will convert any optimal control problem with fixed, free or optimal final time, a Mayer, Lagrange or Bolza cost function, constrained or unconstrained controls, with or without state inequalities, and point inequalities into a parameter optimization problem and returns a solution. The GUI creates a function file, output file, binary save file, and optimization script to allow full access to the strength of the LGLP method from the GUI or the command line. No prior knowledge of the LGLP algorithm is assumed or necessary