DIDO

Short description: Software product for solving general-purpose optimal control problems

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]

## Contents

* 1 Usage
* 2 Theory
* 3 Applications
* 4 MATLAB optimal control toolbox
* 5 History
* 6 Versions
* 7 See also
* 8 References
* 9 Further reading
* 10 External links

## Usage

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

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

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

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

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

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] Low-cost student versions and discounted academic versions are also available from Elissar Global.

## See also

* Bellman pseudospectral method
* Chebyshev pseudospectral method
* Covector mapping principle
* Fariba Fahroo
* Flat pseudospectral methods
* I. Michael Ross
* Legendre pseudospectral method
* Ross–Fahroo lemma
* Ross' π lemma
* Ross–Fahroo pseudospectral methods

## References

1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 Ross, Isaac (2020). "Enhancements to the DIDO Optimal Control Toolbox". arXiv:2004.13112 [math.OC].
2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 Ross, I. M. A Primer on Pontryagin's Principle in Optimal Control, Second Edition, Collegiate Publishers, San Francisco, 2015.
3. ↑ 3.0 3.1 3.2 3.3 Ross, I. M.; Karpenko, M. (2012). "A Review of Pseudospectral Optimal Control: From Theory to Flight". Annual Reviews in Control 36 (2): 182–197. doi:10.1016/j.arcontrol.2012.09.002.
4. ↑ 4.0 4.1 Eren, H., "Optimal Control and the Software," Measurements, Instrumentation, and Sensors Handbook, Second Edition, CRC Press, 2014, pp.92-1-16.
5. ↑ Ross, I. M.; D'Souza, C. N. (2005). "A Hybrid Optimal Control Framework for Mission Planning". Journal of Guidance, Control and Dynamics 28 (4): 686–697. doi:10.2514/1.8285. Bibcode: 2005JGCD...28..686R.
6. ↑ 6.0 6.1 "MIT OpenCourseWare | Aeronautics and Astronautics | 16.323 Principles of Optimal Control, Spring 2006 | Lecture Notes". https://dspace.mit.edu/bitstream/handle/1721.1/45583/16-323Spring-2006/OcwWeb/Aeronautics-and-Astronautics/16-323Spring-2006/LectureNotes/index.htm.
7. ↑ 7.0 7.1 7.2 7.3 Conway, B. A. (2012). "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamical Systems". Journal of Optimization Theory and Applications 152 (2): 271–306. doi:10.1007/s10957-011-9918-z.
8. ↑ 8.0 8.1 8.2 8.3 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. ↑ 9.0 9.1 9.2 9.3 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. ↑ 10.0 10.1 National Aeronautics and Space Administration. "Fact Sheet: International Space Station Zero-Propellant Maneuver (ZPM) Demonstration." June 10, 2011. (Sept. 13, 2011) [1]
11. ↑ 11.0 11.1 11.2 W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa $1m in Under Three Hours," SIAM News, 40, 2007.
12. ↑ 12.0 12.1 12.2 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. ↑ Steigerwald, Bill (2021-02-10). "Teaching an Old Spacecraft New Tricks to Continue Exploring the Moon". http://www.nasa.gov/feature/goddard/2021/lro-new-tricks.
14. ↑ 14.0 14.1 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 .
15. ↑ 15.0 15.1 15.2 Kallrath, Josef (2004). Modeling Languages in Mathematical Optimization. Dordrecht, The Netherlands: Kluwer Academic Publishers. pp. 379–403.
16. ↑ 16.0 16.1 16.2 Ross, I. M.; Fahroo, F. (2004). "Pseudospectral Knotting Methods for Solving Optimal Control Problems". Journal of Guidance, Control and Dynamics 27 (3): 397–405. doi:10.2514/1.3426. https://zenodo.org/record/1235937.
17. ↑ 17.0 17.1 17.2 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. ↑ 18.0 18.1 Josselyn, S.; Ross, I. M. (2003). "A Rapid Verification Method for the Trajectory Optimization of Reentry Vehicles". Journal of Guidance, Control and Dynamics 26 (3): 505–508. doi:10.2514/2.5074. Bibcode: 2003JGCD...26..505J.
19. ↑ 19.0 19.1 Infeld, Samantha I. (2005). Optimization of Mission Design for Constrained Libration Point Space Missions (PDF) (PhD thesis). Stanford University. Bibcode:2006PhDT.........7I.
20. ↑ 20.0 20.1 Gong, Q.; Fahroo, F.; Ross, I. M. (2008). "A Spectral Algorithm for Pseudospectral Methods in Optimal Control". Journal of Guidance, Control and Dynamics 31 (3): 460–471. doi:10.2514/1.32908. Bibcode: 2008JGCD...31..460G.
21. ↑ 21.0 21.1 21.2 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. ↑ "NASA Technical Reports Server (NTRS)". 31 January 2019. https://ntrs.nasa.gov/citations/20190000640.
23. ↑ Karpenko, Mark; King, Jeffrey T.; Dennehy, Cornelius. J.; Michael Ross, I. (April 2019). "Agility Analysis of the James Webb Space Telescope". Journal of Guidance, Control, and Dynamics 42 (4): 810–821. doi:10.2514/1.g003816. ISSN 0731-5090. Bibcode: 2019JGCD...42..810K. http://dx.doi.org/10.2514/1.g003816.
24. ↑ Karpenko, M. et al. "Fast Attitude Maneuvers for the Lunar Reconnaissance Orbiter." (2019) AAS 19-053.
25. ↑ King, Jeffery T.; Karpenko, Mark (March 2016). "A simple approach for predicting time-optimal slew capability". Acta Astronautica 120: 159–170. doi:10.1016/j.actaastro.2015.12.009. ISSN 0094-5765. Bibcode: 2016AcAau.120..159K. http://dx.doi.org/10.1016/j.actaastro.2015.12.009.
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. ↑ 27.0 27.1 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. ↑ Ross, I. M.; Proulx, R. J.; Karpenko, M. (July 2019). "Autonomous UAV Sensor Planning, Scheduling and Maneuvering: An Obstacle Engagement Technique". 2019 American Control Conference (ACC). IEEE. pp. 65–70. doi:10.23919/acc.2019.8814474. ISBN 978-1-5386-7926-5. http://dx.doi.org/10.23919/acc.2019.8814474.
29. ↑ "DIDO: Optimal control software". Promotional web page. Mathworks. https://www.mathworks.com/products/connections/product_detail/product_61633.html.
30. ↑ 30.0 30.1 Rao, A. V. (2014). "Trajectory Optimization: A Survey". Optimization and Optimal Control in Automotive Systems. Lecture Notes in Control and Information Sciences. LNCIS 455. pp. 3–21. doi:10.1007/978-3-319-05371-4_1. ISBN 978-3-319-05370-7.
31. ↑ Fahroo, F.; Doman, D. B.; Ngo, A. D. (2003). "Modeling issues in footprint generation for reusable vehicles". 2003 IEEE Aerospace Conference Proceedings (Cat. No.03TH8652). 6. pp. 2791–2799. doi:10.1109/aero.2003.1235205. ISBN 978-0-7803-7651-9.
32. ↑ "Elissar Global". web site. http://www.ElissarGlobal.com/. distributes the software.
33. ↑ Ross, I. Michael; Gong, Qi (2008-06-15). "Guess-Free Trajectory Optimization". AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, Virginia: American Institute of Aeronautics and Astronautics. doi:10.2514/6.2008-6273. ISBN 978-1-62410-001-7. http://dx.doi.org/10.2514/6.2008-6273.

## Further reading

* Ross, I. Michael; Fahroo, Fariba (2003). Legendre Pseudospectral Approximations of Optimal Control Problems. Springer Verlag. http://www.elissarglobal.com/wp-content/uploads/2012/03/Legendre-Pseudospectral-Approximations-of-Optimal-Control-Problems.pdf.
* Bollino, K.; Lewis, L. R.; Sekhavat, P.; Ross, I. M. (2007). Pseudospectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning. AIAA. http://www.elissarglobal.com/wp-content/uploads/2012/04/Pseudospectral-Optimal-Control-A-Clear-Road-for-Autonomous-Intelligent-Path-Planning.pdf.
* Kang, W.; Ross, I. M.; Gong, Q. (2008). "Pseudospectral Optimal Control and Its Convergence Theorems". Analysis and Design of Nonlinear Control Systems. Springer Berlin Heidelberg. pp. 109–124. doi:10.1007/978-3-540-74358-3_8. ISBN 978-3-540-74357-6.
* Ross, I. M. (2009). A Primer on Pontryagin's Principle in Optimal Control. Collegiate Publishers. ISBN 978-0-9843571-0-9.

## External links

* How DIDO Works at How Stuff Works
* NASA News
* Pseudospectral optimal control: Part 1
* Pseudospectral optimal control: Part 2

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