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GPOPS-II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming

Authors:

Michael A. Patterson,

Anil V. RaoAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 41, Issue 1

Article No.: 1, Pages 1 - 37

https://doi.org/10.1145/2558904

Published: 27 October 2014 Publication History

Abstract

A general-purpose MATLAB software program called GPOPS--II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods. The software employs a Legendre-Gauss-Radau quadrature orthogonal collocation method where the continuous-time optimal control problem is transcribed to a large sparse nonlinear programming problem (NLP). An adaptive mesh refinement method is implemented that determines the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy. The software can be interfaced with either quasi-Newton (first derivative) or Newton (second derivative) NLP solvers, and all derivatives required by the NLP solver are approximated using sparse finite-differencing of the optimal control problem functions. The key components of the software are described in detail and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a useful platform upon which to solve a wide variety of complex constrained optimal control problems.

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Index Terms

GPOPS-II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Numerical differentiation
    2. Quadrature

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 41, Issue 1

October 2014

157 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2684421

Editor:
Michael A. Heroux
Sandia National Laboratories, USA

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Copyright © 2014 ACM.

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Publication History

Published: 27 October 2014

Accepted: 01 December 2013

Revised: 01 September 2013

Received: 01 February 2013

Published in TOMS Volume 41, Issue 1

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https://doi.org/10.3390/app15062952
Xue XXie YZhou HGong QZhao D(2025)Ascent Trajectory Optimization Using Second-Order Birkhoff Pseudospectral MethodsAerospace10.3390/aerospace1202014112:2(141)Online publication date: 13-Feb-2025
https://doi.org/10.3390/aerospace12020141
Ma ZWang CXu ZTang SMa Y(2025)Damped Iterative Explicit Guidance for Multistage Rockets with Thrust Drop FaultsAerospace10.3390/aerospace1201006112:1(61)Online publication date: 16-Jan-2025
https://doi.org/10.3390/aerospace12010061
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