## Convex Relaxations for Robust Identification of Hybrid Models
In order to extract useful information from a data set, it is necessary to understand the underlying model. This dissertation addresses two of the main challenges in identification of such models. First, the data is often generated by multiple, unknown number of sources; that is, the underlying model is usually a mixture model or hybrid model. This requires solving the identification and data association problems simultaneously. Second, the data is usually corrupted by noise necessitating robust identification schemes. Motivated by these challenges we consider the problem of robust identification of hybrid models that interpolate the data within a given noise bound. In particular, for static data we try to fit affine subspace arrangements or more generally a mixture of algebraic surfaces to the data; and for dynamic data we try to infer the underlying switched affine dynamical system. Clearly, as stated, these problems admit infinitely many solutions. For instance, one can always find a trivial hybrid model with as many submodels/subspaces as the number of data points (i.e. one submodel/subspace per data point). In order to regularize the problem, we define suitable a priori model sets and objective functions that seek “simple” models. Although this leads to generically NP-Hard problems, we develop computationally efficient algorithms based on convex relaxations. |