## M. Mönnigmann, W. Marquardt, C. H. Bischof, T. Beelitz, B. Lang, and
P. Willems.
A hybrid approach for efficient robust design of dynamic systems.
*SIAM Review*, 49(2):236-254, 2007.

We propose a novel approach for the parametrically
robust design of dynamic systems. The approach can be
applied to system models with parameters that are
uncertain in the sense that values for these parameters
are not known precisely, but only within certain bounds.
The novel approach is guaranteed to find an optimal
steady state that is stable for each parameter
combination within these bounds. Our approach combines
the use of a standard solver for constrained
optimization problems with the rigorous solution of
nonlinear systems. The constraints for the optimization
problems are based on the concept of parameter space
normal vectors that measure the distance of a tentative
optimum to the nearest *known* critical point,
i.e., a point where stability may be lost. Such normal
vectors are derived using methods from Nonlinear
Dynamics. After the optimization, the rigorous solver
is used to provide a *guarantee* that no critical
points exist in the vicinity of the optimum, or to
detect such points. In the latter case, the
optimization is resumed, taking the newly found critical
points into account. This optimize-and-verify
procedure is repeated until the rigorous nonlinear
solver can guarantee that the vicinity of the optimum is
free from critical points and therefore the optimum is
parametrically robust. In contrast to existing design
methodologies, our approach can be *automated* and
does not rely on the experience of the designing
engineer. A simple model of a fermenter is used to
illustrate the concepts and the order of activities
arising in a typical design process.

[ DOI ]