Categories of Nonlinear Dynamic Models
Many industrially-promising model-based control strategies require nonlinear, discrete-time dynamic models of restricted complexity relative to that of detailed mechanistic descriptions. One possible route to these models is empirical, permitting explicit control of model complexity through the class C of approximating models considered. Conversely, if this choice is not made with sufficient care, the resulting model may fit available input/output data reasonably well but violate certain important behavioral requirements (e.g., stability, monotonicity of step responses, etc.). This paper proposes category theory as a general framework for simultaneously considering both the structural and behavioral aspects of empirical model identification. Two particular advantages of this use of category theory are first, that it forces the consideration of models and input sequences together and second, that it provides a simple framework for examining the behavioral differences between model classes.
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