Gunther Reißig.

Abstraction based solution of complex attainability
problems for decomposable continuous plants.

Proc. 49th IEEE Conf. Decision and Control (CDC), Atlanta, Georgia, U.S.A.,
Dec. 15-17, 2010, pp. 5911-5917.

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**Erratum:**

Whenever results from [1] are mentioned in the text, this
refers to the first version of the report [1].

**Abstract:**

The focus of the present paper is systems of nonlinear continuous
sub-plants that share a common input but are otherwise coupled only
through the specification of a control problem, possibly including
state constraints. Examples include cart-pole systems and collision
avoidance problems involving multiple vehicles. We propose a method
that uses finite state models for solving highly complex continuous
attainability problems.
We first prove that finite state models, also called discrete
abstractions, of the overall plant may be obtained as products of
abstractions of sub-plants. The latter, which we call factors, may be
determined quickly and concurrently, e.g. by a method recently
proposed by this author.
We also modify a state-of-the-art algorithm for the discrete,
auxiliary attainability problems that arise, to work directly with the
set of factors and prove that the
asymptotic computational complexity of the modified algorithm matches
that of the original one. In practice, the latter will often be much
slower since the representation of the abstraction of the overall
plant on a computer is likely to require an excessive amount of
memory.
Practicability of our method is demonstrated by successfully designing
discrete controllers that globally stabilize decomposable
nonlinear continuous plants whose overall finite state models would
include millions of states and billions of transitions. Working with
the factors instead, problem data fit into main memory of a customary
personal computer, and computations take only minutes.

**BibTeX entry:**

@InProceedings{Reissig10a,
author = {Gunther Rei{\ss}ig},
title = {Abstraction based solution of complex attainability problems for decomposable continuous plants},
booktitle = {Proc. 49th IEEE Conf. Decision and Control (CDC), Atlanta, GA, U.S.A., 15-17 Dec. 2010},
PAGES = {5911-5917},
YEAR = 2010,
ADDRESS = {New York},
PUBLISHER = {IEEE},
doi = {10.1109/CDC.2010.5718125}
}

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