On solving optimal control problems with Julia

The numerical solution of optimal control of dynamical systems is a rich process that typically involves modelling, optimisation, differential equations (most notably Hamiltonian ones), nonlinear equations (e. g. for shooting), pathfollowing methods… and, at every step, automatic differentiation. We report on recent experiments with Julia on a variety of applied or more theoretical problems in optimal control and try to survey what the practitioner will find, and would like to find.

While tremendous efforts are being made in every one of the above-mentioned fields by the Julia community, there are still some missing parts to bridge the gap between them and have a fully satisfactory solving process - meaning: an abstract description, as close as possible to the mathematical problem formulation, and an efficient & reliable numerical computation. The Julia language has a lot to offer in this respect, and there already are excellent codes available [1, 2, 3, 4], while mostly oriented towards « direct solving » (that is direct transcription of the original optimal control problem into a mathematical program).

As a group of researchers with a 20+ year history in the numerical solution of optimal control problems, we are very interested by what Julia offers out of the box as a high-level and efficient language. We have been involved in the development of several libraries in Fortran, C/C++, Matlab, python [5, 6] and the associated use of automatic differentiation (with Adifor, Tapenade, CppAD…) and are eager to share our experience and get feedback from the Julia community. Several examples of the numerical solution of optimal control problems can be found in [7] and include applications in biology, aerospace engineering, marine navigation, turnpike computation and hybrid problems.

1. ControlSystems
2. InfiniteOpt
3. TrajectoryOptimization
4. Enzyme
5. Bocop
6. Hampath
7. ct: control toolbox gallery