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:
primal.states,
primal.controls, and
primal.time
The entireproblem 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: = dido, 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.
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 it, DIDO 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.
DIDO is also available as a MATLAB "toolbox" product. It does not require the MATLAB Optimization Toolbox or any other third-party software like SNOPT or IPOPT or other nonlinear programming solvers. 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 and search theory.
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:
