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

该项目的目的是研究微分代数方程（DAE）的最优控制问题离散化的收敛性。该项目建立在前一个项目的结果，旨在将这些结果大大扩展到新的问题设置和离散化方案。到目前为止，收敛性的隐式欧拉离散指数二DAE最优控制问题的混合控制状态约束已建立。为了证明收敛性，有必要在离散化水平上巧妙地重新表述代数约束。应研究此技术是否可以扩展到指数大于2的DAE的问题。为此，尚不清楚是否一个简单的隐式欧拉格式是足够的，或者是否需要更高阶的格式。这将通过研究高阶Runge-Kutta方法及其收敛特性来澄清。最后收敛结果寻求纯状态约束和线性出现的控制（Bang-Bang控制）的问题。

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).