Heisenbergprofessur: Optimization Based Control
Mathematik und Naturwissenschaften
The term „Optimizafion Based Control" encompasses the development and analysis of optimization based methods for optimal and feedback control. This research area is located at the intersection of mathematical control theory, numerics, and optimization. An important subbranch and - so to speak - the prototype of „Optimization Based Control" is Model Predictive Control (MPC), which can be considered as a model and/or complexity reduction with respect to time.
We want to derive design guldelines, which balance the System dynamics and the optimization criteria while taking control and State constraints into account This is the mathematical foundation to ensure proper functioning of optimization based methods like MPC. Furthermore, our goal is to set up a systematic procedure to rigorously verify stability and suboptimality conditions and, thus, to quantify key Parameters like the length of the optimization horizon. To this end, the System dynamics are quantized to efficiently construct auxlliary trajectories. The results are also used during runtime of the optimization based methods to meet numerical requirements like real-time capability. In distributed Systems are, in addition, scalability w.r.t the number of Subsystems and plug-and-play-capability of utmost importance. In all steps, qualitative properties of the underlying System classes, e.g. differential-algebraic or partial differential equations, are directly taken into account.
Another aspect is the interplay between optimality and robustness. The relation is typically characterized via sensitivity Information, which is encoded in the adjoint variables like the Lagrange-multipliers in nonlinear optimization. The gained mathematical insight is used in optimization based control: On the one hand, critical time instances are identified to counteract an increased susceptibility to failure and, on the other hand, autonomously acting Subsystems are coordinated in distributed optimization and control.