Towards a System Theory for Model Set: Chain-Scattering Approach

Recent progress of robust control has shifted the target of control theory from a single model to a set of models. In robust control, model is no longer a precise description of the plant to be controlled. It is rather a crude description of the mechanism that explains behaviors of the plant subject to various kinds of uncertainties [14]. The uncertainty precludes the unique representation of the plant. Thus, the plant is actually characterized by a set of models that incorporates all possible perturbations to the nominal model. Robust control is expected to control this set of models, rather than the nominal model itself [13]. There, the set of models in naturally introduced to represent the uncertainty in the nominal model. The uncertainty is ascribable to various reasons. First, it is ascribed to the lack of sufficient knowledge and/or information for constructing a precise model. Second, it is ascribed to the need for simplifying the model. Third, it is ascribed to the complexity of the real system that generates intrinsic indeterminability. Discussions about the source of uncertainties in models and modeling would require a number of pages and are omitted here. We only note that the uncertainty is not an accidental feature of models. It is rather an intrinsic characteristic feature of model that tries to describe the real system by an abstract framework with a finite number of words [7].