DIDO (/ˈdaɪdoʊ/ DY-doh) is a software product for solving general-purpose optimal control problems. It is widely used in academia, industry, and NASA. Hailed as a breakthrough software, DIDO is based on the pseudospectral optimal control theory of Ross and Fahroo.
Contents
Usage
DIDO utilizes trademarked expressions and objects that facilitate a user to quickly formulate and solve optimal control problems. Rapidity in formulation is achieved through a set of DIDO expressions which are based on variables commonly used in optimal control theory. For example, the state, control and time variables are formatted as:
In like manner, the entire problem is codified using the key words, cost, dynamics, events and path:
A user runs DIDO using the one line command:
[cost, primal, dual] = dido(problem, algorithm)
where, the object defined by algorithm allows a user to chose 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. The output dual is computed by an application of the covector mapping principle.
Theory
DIDO implements a spectral algorithm based on pseudospectral optimal control theory founded by Ross and his associates. The covector mapping principle of Ross and Fahroo eliminates the curse of sensitivity associated in solving for the costates in optimal control problems. DIDO generates spectrally accurate solutions whose extremality can be verified using Pontryagin's Minimum Principle. Because no knowledge of pseudospectral methods is necessary to use DIDO, it is often used 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. 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 Nazareth Bedrossian using DIDO. Watch a video of this historic maneuver.
Since this historic flight demonstration, DIDO has been used in operate the International Space Station and other NASA spacecraft. It is also used in other industries to generate real-time optimal solutions.
The youtube videos DIDO: Part 1 and DIDO: Part 2 show more applications and explain some of the advanced mathematics.
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. The software is widely cited and has many firsts to its credit:
Versions
Several different versions of DIDO are available from a company called Elissar Global.