Input-constrained closed-loop systems with grazing bifurcations in optimal robust design

In this work, the normal vector method for robust design is considered to account for actuator saturation effects when unknown time-varying disturbances are present, and desired dynamic properties have to be guaranteed. The normal vector method ensures that desired dynamic properties hold despite uncertain parameters by maintaining a minimal distance between the operating point and so-called critical manifolds where the process behavior changes qualitatively. In this paper input saturation is considered for the first time in the normal vector framework. In order to solve the resulting optimization problem, first and second order derivatives of the flow of a dynamical system has to be computed efficiently. For this purpose, a new platform for source-level manipulation of mathematical models, currently under development at RWTH Aachen University, is proposed to solve the technical difficulties arising when the event of actuator saturation takes place.