| In this thesis we propose a new mathematical formulation for learning properties of dynamical systems from experimental data. The main idea is the concept of falsification of hypotheses, which has its origins in Popper's “criteria of falsifiability” for determining the scientific status of a theory. Hypotheses about the dynamical system are tested against experimental data. This formulation is a generalization of the unfalsified control theory (Safonov et al.) to learning about dynamical systems, and it is developed in the behavioral approach to mathematical system theory (Willems). This new formulation is applied to control and system identification problems and it offers a unifying view to both disciplines.; This formulation has being specialized to truncated spaces, which are of interest in practical applications since experimental data is usually collected via an observation process. This process defines a truncated space through an observations operator. It offers simpler falsification conditions, which in turn lead to faster algorithms.; A missile autopilot design case study illustrates these ideas and provides practical insights for implementing data driven learning systems. In particular, we proposed a candidate controller parameterization and a performance specification, which led to a falsification condition for which the performance for any candidate controller is given by the product of two terms, one that consists of a nonlinear function of the candidate controller parameters, and the other one which is a state that summarizes the dynamics of all the controllers and the performance criteria at a given point in time. This structure provided substantial savings in the number of computations. |
