GPOPS-II
Top Cited Papers
Open Access
- 27 October 2014
- journal article
- research article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 41 (1), 1-37
- https://doi.org/10.1145/2558904
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.Keywords
Funding Information
- Office of Naval Research (N00014-11-1-0068)
- Defense Advanced Research Projects Agency (HR0011-12-C-0011)
This publication has 36 references indexed in Scilit:
- Costate Estimation using Multiple-Interval Pseudospectral MethodsJournal of Spacecraft and Rockets, 2011
- ACADO toolkit—An open‐source framework for automatic control and dynamic optimizationOptimal Control Applications and Methods, 2011
- Direct Trajectory Optimization Using a Variable Low-Order Adaptive Pseudospectral MethodJournal of Spacecraft and Rockets, 2011
- Pseudospectral methods for solving infinite-horizon optimal control problemsAutomatica, 2011
- Convergence rates for direct transcription of optimal control problems using collocation at Radau pointsComputational Optimization and Applications, 2007
- Connections between the covector mapping theorem and convergence of pseudospectral methods for optimal controlComputational Optimization and Applications, 2007
- On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programmingMathematical Programming, 2005
- Survey of Numerical Methods for Trajectory OptimizationJournal of Guidance, Control, and Dynamics, 1998
- Sparse Jacobian updates in the collocation method for optimal control problemsJournal of Guidance, Control, and Dynamics, 1990
- Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)Journal of Applied Mechanics, 1965