The problem of model building is of fundamental importance to science and engineering. Although modeling, especially linear modeling, has been extensively investigated and applied, most of the existing frameworks are based on stochastic approximation of the modeling error, an assumption that cannot be justified on physical ground in many applications. A general, deterministic, modeling framework for linear systems has recently been put forward by Willems. Parallel to this, Antoulas developed a detailed and explicit recursive realization theory, i.e. a theory of recursiveness of exact modeling based on impulse response time series. Preliminary results have shown that the above two research projects overlap and complement each other in significant ways. This motivates investigations into the recursiveness structure of exact and approximate modeling. These investigations, and in particular the recursiveness results, complemented with the necessary software in the form of a hard disc, will be used at a later stage to develop a new framework for deterministic adaptive control. We propose to develop a whole class of alternative (deterministic) ways of approaching linear recursive modeling. It has the potential of significant impact in areas where model building is needed for predictive purposes, as well as in areas where modeling is needed for control applications, especially so, for the control of plants in dynamically changing environments.
