DIDO (software)

DIDO is a MATLAB program for solving hybrid optimal control problems. Powered by the pseudospectral knotting method, the general-purpose 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, DIDO utilizes unique expressions that facilitates one to formulate and solve optimal control problems in a manner that is similar to writing the problem on a piece of paper. The pseudospectral optimal control method eliminates traditional difficulties in solving for the costates in the optimal control problem; thus, DIDO generates spectrally accurate solutions whose extremality can be verified using Pontryagin's Minimum Principle. 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 governtment laboratories. Thanks to NASA, DIDO was flight-proven in 2006. 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 Naz Bedrossian using DIDO. Watch a video of this historic maneuver.

History

DIDO was first produced in 2001 and has many firsts to its credit^{[citation needed]}:

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

References

• Infeld, S. I. (2005) (PDF). Optimization of Mission Design for Constrained Libration Point Space Missions. Stanford University. http://www.stanford.edu/group/SOL/dissertations/samantha-thesis.pdf. 

• Rea, J. R. (2001). A Legendre Pseudopectral Method for Rapid Optimization of Launch Vehicle Trajectories. MIT. http://www.draper.com/theses/theses2001.html#rea. 

• Ross, I. Michael; Fahroo, Fariba (2003) (PDF). Legendre Pseudospectral Approximations of Optimal Control Problems. Springer Verlag. http://www.didosolver.com/uploads/LSR-LectureNotes.pdf. 

• Gong, Qi.; Kang, W., Bedrossian, N., Fahroo, F., Sekhavat, P. and Bolino, K. (2007) (PDF). Pseudospectral Optimal Control for Military and Industrial Applications. IEEE. http://www.elissar.biz/uploads/LSR_APPS.pdf. 

• Bollino, K.; Lewis, L. R., Sekhavat, P. and Ross, I. M. (2007) (PDF). Pseudospectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning. AIAA. http://www.elissar.biz/uploads/LSR-InfoTech07.pdf. 

• Ross, I. M. (2005) (PDF). A Roadmap for Optimal Control: The Right Way to Commute. New York Academy of Sciences. http://www.didosolver.com/uploads/LSR-Roadmap.pdf. 

• Kang, W.; Ross, I. M., and Gong, Q. (2007). Pseudospectral Optimal Control and Its Convergence Theorems. Springer Berlin Heidelberg. http://www.springerlink.com/content/v1874282v4541275/. 

• Ross, I. M. (2009). A Primer on Pontryagin's Principle in Optimal Control. Collegiate Publishers. ISBN 978-0-9843571-0-9. 

External links

• SIAM News
• Downloadable SIAM article
• Navy News
• NASA News
• DIDO (for further information)
• DIDO Capabilities
• Elissar Global distributes the software.