DIDO (software)

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DIDO (/ˈdaɪdoʊ/ DY-doh) is a MATLAB optimal control toolbox for solving general-purpose optimal control problems.[1][2][3][4][5] It is widely used in academia,[6][7][8] industry,[3][9] and NASA.[10][11][12][13] Hailed as a breakthrough software,[14][15] DIDO is based on the pseudospectral optimal control theory of Ross and Fahroo.[16] The latest enhancements to DIDO are described in Ross.[1]

Usage

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DIDO utilizes trademarked expressions and objects[1][2] that facilitate a user to quickly formulate and solve optimal control problems.[8][17][18][19] Rapidity in formulation is achieved through a set of DIDO expressions which are based on variables commonly used in optimal control theory.[2] For example, the state, control and time variables are formatted as:[1][2]

  • primal.states,
  • primal.controls, and
  • primal.time

The entire problem is codified using the key words, cost, dynamics, events and path:[1][2]

  • problem.cost
  • problem.dynamics
  • problem.events, and
  • problem.path

A user runs DIDO using the one-line command:[1]

[cost, primal, dual] = dido(problem, algorithm),

where the object defined by algorithm allows a user to choose various options. In addition to the cost value and the primal solution, DIDO automatically outputs all the dual variables that are necessary to verify and validate a computational solution.[2] The output dual is computed by an application of the covector mapping principle.

Theory

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DIDO implements a spectral algorithm[1][16][20] based on pseudospectral optimal control theory founded by Ross and his associates.[3] The covector mapping principle of Ross and Fahroo eliminates the curse of sensitivity[2] associated in solving for the costates in optimal control problems. DIDO generates spectrally accurate solutions [20] whose extremality can be verified using Pontryagin's Minimum Principle. Because no knowledge of pseudospectral methods is necessary to use it, DIDO is often used[7][8][9][21] as a fundamental 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 for optimality.

Applications

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DIDO is used world wide in academia, industry and government laboratories.[9] 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.

Since this flight demonstration, DIDO was used for the International Space Station and other NASA spacecraft.[12][22][23][24][25][26] It is also used in other industries.[2][9][21][27] Most recently, DIDO has been used to solve traveling salesman type problems in aerospace engineering.[28]

MATLAB optimal control toolbox

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DIDO is primarily available as a stand-alone MATLAB optimal control toolbox.[29] That is, it does not require any third-party software like SNOPT or IPOPT or other nonlinear programming solvers.[1] In fact, it does not even require the MATLAB Optimization Toolbox.

The MATLAB/DIDO toolbox does not require a "guess" to run the algorithm. This and other distinguishing features have made DIDO a popular tool to solve optimal control problems.[4][7][15]

The MATLAB optimal control toolbox has been used to solve problems in aerospace,[11] robotics[1] and search theory.[2]

History

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The optimal control toolbox 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. Invented by Ross, DIDO was first produced in 2001.[1][2][30][17] The software is widely cited[30][7][21][27] and has many firsts to its credit:[10] [11] [12] [14] [16] [18] [31]

  • 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
  • First guess-free general-purpose optimal control solver

Versions

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The early versions, widely adopted in academia,[8][15][17][19][6] have undergone significant changes since 2007.[1] The latest version of DIDO, available from Elissar Global,[32] does not require a "guess" to start the problem[33] and eliminates much of the minutia of coding by simplifying the input-output structure.[2]

See also

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References

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  1. ^ a b c d e f g h i j k Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  2. ^ a b c d e f g h i j k Ross, I. M. A Primer on Pontryagin's Principle in Optimal Control, Second Edition, Collegiate Publishers, San Francisco, 2015.
  3. ^ a b c d Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  4. ^ a b Eren, H., "Optimal Control and the Software," Measurements, Instrumentation, and Sensors Handbook, Second Edition, CRC Press, 2014, pp.92-1-16.
  5. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  6. ^ a b Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  7. ^ a b c d Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  8. ^ a b c d A. M. Hawkins, Constrained Trajectory Optimization of a Soft Lunar Landing From a Parking Orbit, S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2005. http://dspace.mit.edu/handle/1721.1/32431
  9. ^ a b c d 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.
  10. ^ a b National Aeronautics and Space Administration. "Fact Sheet: International Space Station Zero-Propellant Maneuver (ZPM) Demonstration." June 10, 2011. (Sept. 13, 2011) [1]
  11. ^ a b c W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa $1m in Under Three Hours," SIAM News, 40, 2007.
  12. ^ a b c 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.
  13. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  14. ^ a b 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 Archived 2016-03-04 at the Wayback Machine.
  15. ^ a b c Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  16. ^ a b c Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  17. ^ a b c 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
  18. ^ a b Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  19. ^ a b Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  20. ^ a b Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  21. ^ a b c D. Delahaye, S. Puechmorel, P. Tsiotras, and E. Feron, "Mathematical Models for Aircraft Trajectory Design : A Survey" Lecture notes in Electrical Engineering, 2014, Lecture Notes in Electrical Engineering, 290 (Part V), pp 205-247
  22. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  23. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  24. ^ Karpenko, M. et al. "Fast Attitude Maneuvers for the Lunar Reconnaissance Orbiter." (2019) AAS 19-053.
  25. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  26. ^ Karpenko, M., Ross, I. M., Stoneking, E. T., Lebsock, K. L., Dennehy, C., "A Micro-Slew Concept for Precision Pointing of the Kepler Spacecraft," AAS 15-628.
  27. ^ a b S. E. Li, K. Deng, X. Zang, and Q. Zhang, "Pseudospectral Optimal Control of Constrained Nonlinear Systems," Ch 8, in Automotive Air Conditioning: Optimization, Control and Diagnosis, edited by Q. Zhang, S. E. Li and K. Deng, Springer 2016, pp. 145-166.
  28. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  29. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  30. ^ a b Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  31. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  32. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). distributes the software.
  33. ^ Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).

Further reading

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  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
  • Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
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