Modeling and Robust Optimization for System of Systems Problems under Uncertainty

The paper proposes a novel idea for how to model and optimize uncertain problems of system of systems (SoS). Firstly, the background and necessity on researching SoS and its robust optimization under uncertainty are introduced. Secondly, preparatory models are constructed to model the aggregations and cooperation among SoS and are regarded as the main body of further studies. Subsequently, a scenario-based model to formulate uncertainties and a Markov-based model to simulate uncertainty evolutions of SoS are introduced. Then, a novel idea for how to solving robust optimization under uncertainties in single-stage and multi-stage is proposed. The methods of the researches can be applied to solve SoS problems under uncertainty in real world, such as transportation systems planning, power grid systems operation and competition considered financial cooperation etc.