DIDO (optimal control)
Encyclopedia
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, 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
.
, 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.
MATLAB
MATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
program for solving hybrid optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
problems. Powered by the pseudospectral knotting method
Pseudospectral knotting method
In the mathematical theory of knots, a pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control. According to Ross and Fahroo, a pseudospectral knot is a double Lobatto point; i.e. two boundary points on top of one another...
, the general-purpose program is named after Dido, the legendary founder and first queen of Carthage
Carthage
Carthage , implying it was a 'new Tyre') is a major urban centre that has existed for nearly 3,000 years on the Gulf of Tunis, developing from a Phoenician colony of the 1st millennium BC...
who is famous in mathematics for her remarkable solution to a constrained optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
problem even before the invention of calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
.
Theory
Based on pseudospectral optimal controlPseudospectral optimal control
Pseudospectral optimal control is a computational method for solving optimal control problems. Pseudospectral optimal control techniques have been extensively used to solve a wide range of problems such as those arising in UAV trajectory generation, missile guidance, control of robotic arms,...
theory, DIDO utilizes unique expressions that facilitates one to formulate and solve optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
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
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
problem; thus, DIDO generates spectrally accurate solutions whose extremality can be verified using Pontryagin's Minimum Principle
Pontryagin's minimum principle
Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It was formulated by the Russian mathematician Lev Semenovich...
. Because no knowledge of pseudospectal methods is necessary to use DIDO, it is often used as a mathematical tool for solving optimal control
Optimal control
Optimal control theory, an extension of the calculus of variations, is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin and his collaborators in the Soviet Union and Richard Bellman in the United States.-General method:Optimal...
problems. That is, a solution obtained from DIDO is treated as a candidate solution for the application of Pontryagin's minimum principle
Pontryagin's minimum principle
Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It was formulated by the Russian mathematician Lev Semenovich...
as a necessary condition
Necessary and sufficient conditions
In logic, the words necessity and sufficiency refer to the implicational relationships between statements. The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true.-Definitions:A necessary condition...
.
Applications
DIDO is used world wide in academia, industry and governtment laboratories. Thanks to NASANASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
, DIDO was flight-proven in 2006. On November 5, 2006, NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
used DIDO to maneuver the International Space Station
International Space Station
The International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...
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 :- First object-oriented optimal control software
- First pseudospectral optimal control software
- First flight-proven general-purpose optimal control software
External links
- SIAM News
- Downloadable SIAM article
- Navy News
- NASA News
- DIDO (for further information)
- DIDO Capabilities
- Elissar Global distributes the software.