The research interests address the development and analysis of discretization methods for the numerical solution of control and state constrained optimal control problems and parameter identification problems subject to ordinary differential equations (ODEs), differential-algebraic equations (DAEs), and partial differential equations (PDEs). We are interested in both, theoretical topics and implementational issues. Specific theoretical questions address the derivation of necessary and sufficient conditions for optimal control problems subject to mixed control-state constraints and pure state constraints. Closely connected with necessary and sufficient conditions are the postoptimal estimation of adjoints and the convergence of discretized optimal control problems. An extension towards optimal control problems subject to partial differential-algebraic equations (PDAEs) is subject of our current research and provides a huge field of research for the next years.

Optimal control and parameter identification with ODEs, DAEs and PDEs: Necessary conditions and numerical methods