Systems theory of partial differential-algebraic equations

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Numerous dynamical systems of practical relevance with input, state, and output variables are modelled as systems of partial differential equations and/or systems of differential-algebraic equations, e.g. electrical circuits or classical mechanical systems. Within the proposed project, differential-algebraic systems with an infinite dimensional state space are used in order to describe this class of systems.While systems theory is already quite mature for finite and infinite dimensional systems of ordinary differential equations, there are still challenging open problems for differential-algebraic systems both for finite and infinite dimensional systems. For example, structural properties of differential-algebraic equations are ignored in model predictive control where the algebraic equations are considered as another constraint in the optimal control problem.Our goal in the proposed project is to contribute to the development of the theory of (partial) differential-algebraic equations. In particular, we aim at gaining fundamental insight with respect to structural properties like zero dynamics and so called outer transfer functions. Then, we want to make use of our findings in optimal and model predictive control of finite and infinite dimensional differential-algebraic systems. To this end, functional analytic methods as well as the theory of time-varying systems are expected to serve as key ingredients in our approach.