DIDO (software)

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.

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.

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]

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]

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

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 Archived 2021-04-21 at the Wayback Machine and discounted academic versions are also available from Elissar Global.

• 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

• Ross, I. Michael; Fahroo, Fariba (2003). "Legendre Pseudospectral Approximations of Optimal Control Problems" (PDF). Springer Verlag. {{cite journal}}: Cite journal requires |journal= (help)
• Bollino, K.; Lewis, L. R.; Sekhavat, P.; Ross, I. M. (2007). "Pseudospectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning" (PDF). AIAA. {{cite journal}}: Cite journal requires |journal= (help)
• 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. S2CID 124435259.
• Ross, I. M. (2009). A Primer on Pontryagin's Principle in Optimal Control. Collegiate Publishers. ISBN 978-0-9843571-0-9.

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