GPOPS-II - Next-Generation Optimal Control Software

GPOPS-II: Next-Generation Optimal Control Software

GPOPS-II is the next-generation of general purpose optimal control software. GPOPS-II is a new MATLAB software intended to solve general nonlinear optimal control problems (that is, problems where it is desired to optimize systems defined by differential-algebraic equations). GPOPS-II implements the new class of variable-order Gaussian quadrature methods where a the continuous-time optimal control problem is approximated as a sparse nonlinear programming problem (NLP). This NLP is then solved using either the NLP solver IPOPT or the NLP solver SNOPT. GPOPS-II represents a major advancement in the numerical solution of optimal control problems. GPOPS-II is available at NO CHARGE TO MEMBERS OF THE UNIVERSITY OF FLORIDA OR ANY STATE OF FLORIDA INSTITUTION. All others are required to pay a licensing fee for using GPOPS-II. Licenses of GPOPS-II can be purchased by clicking here.

Features of GPOPS-II

The following are some the key features of GPOPS-II:

  • Allows for an extremely general formulation of the optimal control problem.
  • Allows for inclusion of integral constraints and highly general boundary conditions.
  • Complete first and second sparse finite-differencing of optimal control problem to compute all derivatives required by the NLP solver.
  • The latest advances in mesh refinement including hp-adaptive pseudospectral methods.
  • Gaussian quadrature integration methods for rapid convergence.
  • Highly accurate costate estimation.
  • Inclusion of the NLP solver IPOPT, so GPOPS-II can be used “out of the box”.
  • Interface to be able to call the NLP solver SNOPT (but SNOPT is not included with GPOPS-II. SNOPT must be purchased separately at
  • No third-party products other than MATLAB are required (with the stated exception of SNOPT which must be purchased separately at

It is important to note that all of the methods included in GPOPS-II have been published in the open literature. For more information about the details of the methods included in GPOPS-II, click here to download the recently published article on GPOPS-II that is published in the ACM Transactions on Mathematical Software. Please note that this article is open-access and is available for download worldwide and does not require a subscription to the ACM Transactions on Mathematical Software.

Fees for Obtaining and Using GPOPS-II

The fees for using GPOPS-II are as follows:

  • For K-12 or University Classroom Use: NO CHARGE
  • University of Florida Employees or Students and State of Florida Employees or Institutions: NO CHARGE
  • Academic Research, Not-for-Profit, U.S. Government, or Commercial Use: LICENSING FEES APPLY (CLICK HERE TO BE TAKEN TO THE LICENSE PAGE)
For users that must pay a licensing fee, the fees may be paid using PayPal with your PayPal account. One-time 30-day trial licenses are available for all users who register. Those who wish to obtain a trial license or an unlimited use license as either a University of Florida or State of Florida user can register by clicking here or by clicking on the link below.



Image Courtesy of NASA.