DIDO ( ) is a MATLAB optimal control toolbox for solving general-purpose

optimal control Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and ...

problems.Ross, I. M. ''A Primer on Pontryagin's Principle in Optimal Control'', Second Edition, Collegiate Publishers, San Francisco, 2015.Eren, H., "Optimal Control and the Software," ''Measurements, Instrumentation, and Sensors Handbook'', Second Edition, CRC Press, 2014, pp.92-1-16. It is widely used in academia, industry, and NASA. Hailed as a breakthrough software, DIDO is based on the

pseudospectral optimal control Pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems. It combines pseudospectral (PS) theory with optimal control theory to produce PS optimal control theory. PS optimal control theory ...

theory of

Ross Ross or ROSS may refer to: People * Clan Ross, a Highland Scottish clan * Ross (name), including a list of people with the surname or given name Ross, as well as the meaning * Earl of Ross, a peerage of Scotland Places * RoSS, the Republic of Sou ...

and Fahroo. The latest enhancements to DIDO are described in Ross.

Usage

DIDO utilizes trademarked expressions and objects that facilitate a user to quickly formulate and solve

problems.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 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: * primal.states, * primal.controls, and * primal.time The entire problem is codified using the key words, cost, dynamics, events and path: * problem.cost * problem.dynamics * problem.events, and * problem.path A user runs DIDO using the one-line command: ost, 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. The output dual is computed by an application of the

covector mapping principle The covector mapping principle is a special case of Riesz' representation theorem, which is a fundamental theorem in functional analysis. The name was coined by Ross and co-workers,Ross, I. M., “A Historical Introduction to the Covector Mappin ...

Theory

DIDO implements a spectral algorithm based on

theory founded by

and his associates. The

and Fahroo eliminates the curse of sensitivity associated in solving for the costates in

problems.

DIDO Dido ( ; , ), also known as Elissa ( , ), was the legendary founder and first queen of the Phoenician city-state of Carthage (located in modern Tunisia), in 814 BC. In most accounts, she was the queen of the Phoenician city-state of Tyre (t ...

generates spectrally accurate solutions whose extremality can be verified using

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 states that it ...

. Because no knowledge of pseudospectral methods is necessary to use it, DIDO is often used as a fundamental mathematical tool for solving

problems. That is, a solution obtained from DIDO is treated as a candidate solution for the application of

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 states that it ...

as a

necessary condition In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ...

for optimality.

Applications

DIDO is used world wide in academia, industry and government laboratories.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. Thanks to

NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding t ...

, DIDO was flight-proven in 2006. On November 5, 2006,

used DIDO to maneuver the

International Space Station The International Space Station (ISS) is the largest modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA ...

to perform the

zero-propellant maneuver A zero-propellant maneuver (ZPM) is an optimal attitude trajectory used to perform spacecraft rotational control without the need to use thrusters. ZPMs are designed for spacecraft that use momentum storage actuators. Spacecraft ZPMs are used to pe ...

. Since this flight demonstration, DIDO was used for the International Space Station and other NASA spacecraft. 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. It is also used in other industries. Most recently, DIDO has been used to solve traveling salesman type problems in aerospace engineering.

MATLAB optimal control toolbox

DIDO is primarily available as a stand-alone

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...

optimal control toolbox. That is, it does not require any third-party software like

SNOPT SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Pyth ...

IPOPT IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in Fortran and C and is released under the EPL (formerly CPL). IPOPT implement ...

or other

nonlinear programming In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or sta ...

solvers. 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. The MATLAB optimal control toolbox has been used to solve problems in aerospace,

robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrat ...

and

search theory In microeconomics, search theory studies buyers or sellers who cannot instantly find a trading partner, and must therefore search for a partner prior to transacting. Search theory clarifies how buyers and sellers choose when to acknowledge a coo ...

History

The optimal control toolbox is named after

Dido Dido ( ; , ), also known as Elissa ( , ), was the legendary founder and first queen of the Phoenician city-state of Carthage (located in modern Tunisia), in 814 BC. In most accounts, she was the queen of the Phoenician city-state of Tyre (t ...

, the legendary founder and first queen of

Carthage Carthage was the capital city of Ancient Carthage, on the eastern side of the Lake of Tunis in what is now Tunisia. Carthage was one of the most important trading hubs of the Ancient Mediterranean and one of the most affluent cities of the classi ...

who is famous in mathematics for her remarkable solution to a constrained

problem even before the invention of

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

. Invented by

, DIDO was first produced in 2001.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 The software is widely citedD. 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 205-247S. 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. and has many firsts to its credit: National Aeronautics and Space Administration. "Fact Sheet: International Space Station Zero-Propellant Maneuver (ZPM) Demonstration." June 10, 2011. (Sept. 13, 2011

/ref> W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa $1m in Under Three Hours," SIAM News, 40, 2007. 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. * 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, have undergone significant changes since 2007. The latest version of DIDO, available fro
Elissar Global
does not require a "guess" to start the problem and eliminates much of the minutia of coding by simplifying the input-output structure.
Low-cost student versions
and discounted academic versions are also available fro
Elissar Global

References

External links

How DIDO Works at How Stuff Works

Pseudospectral optimal control: Part 1

Pseudospectral optimal control: Part 2
Numerical software Mathematical optimization software Optimal control