Gunther Reißig.

Computing abstractions of nonlinear systems.

IEEE Trans. Automat. Control, vol. 56, no. 11, Nov. 2011,
pp. 2583-2598.

Full text.
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Full text.
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**Abstract:**

Sufficiently accurate finite state models, also called symbolic models
or discrete abstractions, allow one to apply fully automated methods,
originally developed for purely discrete systems, to formally reason
about continuous and hybrid systems, and to design finite state
controllers that provably enforce predefined specifications.
We present a novel algorithm to compute such finite state models
for nonlinear discrete-time and sampled systems which depends on
quantizing the state space using polyhedral cells, embedding these
cells into suitable supersets whose attainable sets are convex, and
over-approximating attainable sets by intersections of supporting
half-spaces. We prove a novel recursive description of
these half-spaces and propose an iterative procedure to compute them
efficiently. We also provide new sufficient conditions for the convexity
of attainable sets which imply the existence of the aforementioned
embeddings of quantizer cells. Our method yields highly accurate
abstractions and applies to nonlinear systems under mild assumptions,
which reduce to sufficient smoothness in the case of sampled
systems. Its practicability in the design of discrete
controllers for nonlinear continuous plants under state and control
constraints is demonstrated by an example.

**BibTeX entry:**

@article{Reissig11a,
AUTHOR = {Rei{\ss}ig, Gunther},
TITLE = {Computing abstractions of nonlinear systems},
year = 2011,
journal = {IEEE Trans. Automat. Control},
volume = 56,
number = 11,
pages = {2583-2598},
month = nov,
doi = {10.1109/TAC.2011.2118950},
eprint = {0910.2187}
}

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