DIDO is a user-friendly MATLAB program for solving hybrid optimal control problems. MATLAB is a numerical computing environment and Programming language. Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. 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. Dido was according to Greek and Roman sources the founder and first Queen of Carthage (in modern-day Tunisia) Carthage (Καρχηδών Karkhēdōn, Carthago from the Phoenician קרת חדשת phn-Latn Qart-ḥadašt meaning new town) refers Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. The isoperimetric inequality is a geometric Inequality involving the square of the Circumference of a Closed curve in the plane and the Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives
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Theory
Based on pseudospectral optimal control 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. Pseudospectral (PS optimal control is a computational method for solving Optimal control problems Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. 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. Costate equations are related to the state equations used in Optimal control. Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. Pontryagin's minimum principle is used in Optimal control theory to find the best possible control for taking a Dynamic system from one state to another especially Because no knowledge of pseudospectal methods is necessary to use DIDO, it is often used as a mathematical tool for solving optimal control problems. Optimal control theory, a modern extension of the Calculus of variations, is a mathematical optimization method for deriving control policies. 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. Pontryagin's minimum principle is used in Optimal control theory to find the best possible control for taking a Dynamic system from one state to another especially
Applications
DIDO is used world wide in academia, industry and governtment laboratories. Thanks to NASA, DIDO was flight-proven in 2006. The National Aeronautics and Space Administration ( NASA, ˈnæsə is an agency of the United States government, responsible for the nation's public space program On November 5, 2006, NASA used DIDO to maneuver the International Space Station to perform the Zero Propellant Maneuver. The National Aeronautics and Space Administration ( NASA, ˈnæsə is an agency of the United States government, responsible for the nation's public space program The zero propellant maneuver was discovered by Naz Bedrossian using DIDO. Watch a video of this historic maneuver.
References
- Infeld, S. I. (2005). "Optimization of Mission Design for Constrained Libration Point Space Missions" (PDF). . Stanford University
- Rea, J. R. (2001). "A Legendre Pseudopectral Method for Rapid Optimization of Launch Vehicle Trajectories". . MIT
- Ross, I. Michael; Fahroo, Fariba (2003). "Legendre Pseudospectral Approximations of Optimal Control Problems" (PDF). . Springer Verlag
- Gong, Qi. ; Kang, W. , Bedrossian, N. , Fahroo, F. , Sekhavat, P. and Bolino, K. (2007). "Pseudospectral Optimal Control for Military and Industrial Applications" (PDF). . IEEE
- Bollino, K. ; Lewis, L. R. , Sekhavat, P. and Ross, I. M. (2007). "Pseudospectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning" (PDF). . AIAA
- Ross, I. M. (2005). "A Roadmap for Optimal Control: The Right Way to Commute" (PDF). . New York Academy of Sciences
- Kang, W. ; Ross, I. M. , and Gong, Q. (2007). "Pseudospectral Optimal Control and Its Convergence Theorems". . Springer Berlin Heidelberg
External links
- SIAM News
- Downloadable SIAM article
- Navy News
- Downloadable Navy article
- NASA News
- DIDO (for further information)
- DIDO Capabilities
- Elissar distributes the software.
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