Biegler's Dynamic Optimization Using Orthogonal Collocation Method (Simultaneous Approach)

This document presents MATLAB code implementing Biegler's dynamic optimization method using orthogonal collocation, also known as the simultaneous approach. The codebase was originally developed by researchers M. Cizniar, M. Fikar, and their team. The core algorithmic concept employs orthogonal design methodology to optimize computational models for enhanced performance. To better understand this implementation, let's examine its key characteristics: The algorithm utilizes dynamic optimization techniques to achieve superior computational results through direct transcription methods that convert differential equations into algebraic constraints. The orthogonal collocation component ensures balanced variable selection by strategically placing collocation points at roots of orthogonal polynomials (typically Legendre or Radau polynomials), which provides excellent numerical stability and convergence properties. The MATLAB implementation likely features several key functions including: - Collocation point generation using orthogonal polynomial roots - Simultaneous discretization of differential-algebraic equations (DAEs) - Sparse matrix handling for efficient large-scale optimization - NLP solver integration (possibly with fmincon or IPOPT) This approach offers significant practical advantages, including improved computational efficiency through parallelizable structure and enhanced solution accuracy via high-order polynomial approximations. Therefore, this MATLAB code serves not only as a robust computational tool but also as an excellent educational resource for understanding advanced optimization algorithms and their implementation in scientific computing environments.