# DIDO (software)

(Redirected from DIDO (optimal control))

DIDO is a MATLAB optimal control tool for solving general-purpose hybrid optimal control problems.[1] Powered by the pseudospectral optimal control theory of Ross and Fahroo,[2] the general-purpose optimal control program is named after Dido, the legendary founder and first queen of Carthage who is famous in mathematics for her remarkable solution to a constrained optimal control problem even before the invention of calculus.

## Theory

Based on pseudospectral optimal control theory founded by Ross and his associates,[3] DIDO utilizes unique expressions and objects that facilitate one to formulate and solve optimal control problems in a manner that is similar to writing the problem on a piece of paper. The covector mapping principle of Ross and Fahroo eliminates traditional difficulties in solving for the costates in optimal control problems; thus, DIDO generates spectrally accurate solutions [4] whose extremality can be verified using Pontryagin's Minimum Principle.[5] Because no knowledge of pseudospectal methods is necessary to use DIDO, it is often used as a mathematical tool for solving optimal control problems. That is, a solution obtained from DIDO is treated as a candidate solution for the application of Pontryagin's minimum principle as a necessary condition.

## Applications

DIDO is used world wide in academia, industry and government laboratories.[6] Thanks to NASA, DIDO was flight-proven in 2006.[3] On November 5, 2006, NASA used DIDO to maneuver the International Space Station to perform the Zero Propellant Maneuver. The Zero Propellant Maneuver was discovered by Nazareth Bedrossian using DIDO. Watch a video of this historic maneuver.

## History

Invented by Ross, DIDO was first produced in 2001[7] and has many firsts to its credit:[2] [8] [9] [10] [11] [12] [13]

• First general-purpose object-oriented optimal control software
• First general-purpose pseudospectral optimal control software
• First flight-proven general-purpose optimal control software
• First embedded general-purpose optimal control solver

## Versions

DIDO is a professional optimal control solver; however, several different versions of DIDO are available:

In addition the complete source code for DIDO is also available so that an end user may customize it for any application.

## References

1. ^ Ross, I. M. and D’Souza, C. N., A Hybrid Optimal Control Framework for Mission Planning, Journal of Guidance, Control and Dynamics, Vol. 28, No. 4, July–August 2005, pp. 686–697.
2. ^ a b Ross, I. M. and Fahroo, F., Pseudospectral Knotting Methods for Solving Optimal Control Problems, Journal of Guidance, Control and Dynamics, Vol. 27, No. 3, pp. 397–405, 2004.
3. ^ a b I. M. Ross and M. Karpenko, "A Review of Pseudospectral Optimal Control: From Theory to Flight," Annual Reviews in Control, Vol. 36, pp. 182–197, 2012. http://www.sciencedirect.com/science/article/pii/S1367578812000375
4. ^ Gong, Q., Fahroo, F. and Ross, I. M., A Spectral Algorithm for Pseudospectral Methods in Optimal Control, Journal of Guidance, Control and Dynamics, Vol. 31, No. 3, pp. 460–471, 2008.
5. ^ Ross, I. M. A Primer on Pontryagin's Principle in Optimal Control, Collegiate Publishers, San Francisco, 2009.
6. ^ Q. Gong, W. Kang, N. Bedrossian, F. Fahroo, P. Sekhavat and K. Bollino, Pseudospectral Optimal Control for Military and Industrial Applications, 46th IEEE Conference on Decision and Control, New Orleans, LA, pp. 4128-4142, Dec. 2007.
7. ^ J. R. Rea, A Legendre Pseudospectral Method for Rapid Optimization of Launch Vehicle Trajectories, S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2001. http://dspace.mit.edu/handle/1721.1/8608
8. ^ F. Fahroo, D. B. Doman, and A. D. Ngo, "Modeling Issues in Footprint Generation of Resuable Launch Vehicles," Proceedings of the IEEE Aerospace Conference, Vol. 6, 2003, pp. 2791-2799.
9. ^ W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa \$1m in Under Three Hours," SIAM News, 40, 2007.
10. ^ B. Honegger, "NPS Professor's Software Breakthrough Allows Zero-Propellant Maneuvers in Space." Navy.mil. United States Navy. April 20, 2007. (Sept. 11, 2011) http://www.elissarglobal.com/wp-content/uploads/2011/07/Navy_News.pdf.
11. ^ S. Josselyn and I. M. Ross, "A Rapid Verification Method for the Trajectory Optimization of Reentry Vehicles," Journal of Guidance, Control and Dynamics, Vol. 26, No. 3, 2003, pp.505-508.
12. ^ National Aeronautics and Space Administration. "Fact Sheet: International Space Station Zero-Propellant Maneuver (ZPM) Demonstration." June 10, 2011. (Sept. 13, 2011) http://www.nasa.gov/mission_pages/station/research/experiments/ZPM.html
13. ^ L. Keesey, "TRACE Spacecraft's New Slewing Procedure." NASA's Goddard Space Flight Center. National Aeronautics and Space Administration. Dec. 20, 2010. (Sept. 11, 2011) http://www.nasa.gov/mission_pages/sunearth/news/trace-slew.html.