Hybrid System Identification

Hybrid systems are mathematical models that are used to describe continuous processes that occasionally exhibit discontinuous behaviors due to sudden changes of dynamics. For instance, the continuous trajectory of a bouncing ball results from alternating between free fall and elastic contact with the ground. However, hybrid systems can also be used to describe a complex process or time series that does not itself exhibit discontinuous behaviors, by approximating the process or series with a simpler class of dynamical models. For example, a nonlinear dynamical system can be approximated by switching among a set of linear systems, each approximating the nonlinear system in a subset of its state space. As another example, a video sequence can be segmented to different scenes by fitting a piecewise linear dynamical model to the entire sequence.

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