Investigation of convergence properties of discretized optimal control problems subject to differential-algebraic equations

• Applicant: Professor Dr. Matthias Gerdts
• Subject Area: Mathematics
• Term: from 2015 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 280870320

The purpose of the project is to investigate convergence properties of discretizations of optimal control problems subject to differential-algebraic equations (DAEs). The project builds upon the outcome of the preceding project and aims to extend these results substantially to new problem settings and discretization schemes. So far the convergence of an implicit Euler discretization for index-two DAE optimal control problems with mixed control-state constraints has been established. In order to show the convergence, it was necessary to use a clever reformulation of the algebraic constraints on discretization level. It shall be investigated whether this technique can be extended to problems with DAEs of index greater than two. To this end it is not clear whether a simple implicit Euler scheme is sufficient or whether higher order schemes are required. This shall be clarified by investigating higher order Runge-Kutta methods and their convergence properties. Finally convergence results are sought for problems with pure state constraints and linearly appearing controls (bang-bang controls).

• DFG Programme: Research Grants