Optimal design of uncertain complex dynamical systems

Recent advances in simulation and computation have greatly advanced model based design of complex industrial systems. However, these advances call for improved design methodolgies that can account for the complexities and uncertainties in the model descriptions in the design process. In this paper we consider the problem of optimal design of systems that are described by an uncertain discrete dynamical system. We consider a formulation of the design problem that accounts for complex behavior of the system and incorporates the system dynamics into the formulation of the cost functional. In particular, using some recently developed results from Random Dynamical Systems theory we incorporate both uncertainties from initial conditions and system parameters as well as system generated uncertainties into the cost functional.