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.
CITATION STYLE
Vidal, R., Ma, Y., & Sastry, S. S. (2016). Hybrid system identification. In Interdisciplinary Applied Mathematics (Vol. 40, pp. 431–451). Springer Nature. https://doi.org/10.1007/978-0-387-87811-9_12
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