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Author Mari, Federico; Melatti, Igor; Salvo, Ivano; Tronci, Enrico
Title Linear Constraints and Guarded Predicates as a Modeling Language for Discrete Time Hybrid Systems Type Journal Article
Year 2013 Publication International Journal on Advances in Software Abbreviated Journal Intern. Journal on Advances in SW
Volume vol. 6, nr 1&2 Issue Pages 155-169
Keywords Model-based software design; Linear predicates; Hybrid systems
Abstract Model based design is particularly appealing in
software based control systems (e.g., embedded
software) design, since in such a case system
level specifications are much easier to define
than the control software behavior itself. In
turn, model based design of embedded systems
requires modeling both continuous subsystems
(typically, the plant) as well as discrete
subsystems (the controller). This is typically
done using hybrid systems. Mixed Integer Linear
Programming (MILP) based abstraction techniques
have been successfully applied to automatically
synthesize correct-by-construction control
software for discrete time linear hybrid systems,
where plant dynamics is modeled as a linear
predicate over state, input, and next state
variables. Unfortunately, MILP solvers require
such linear predicates to be conjunctions of
linear constraints, which is not a natural way of
modeling hybrid systems. In this paper we show
that, under the hypothesis that each variable
ranges over a bounded interval, any linear
predicate built upon conjunction and disjunction
of linear constraints can be automatically
translated into an equivalent conjunctive
predicate. Since variable bounds play a key role
in this translation, our algorithm includes a
procedure to compute all implicit variable bounds
of the given linear predicate. Furthermore, we
show that a particular form of linear predicates,
namely guarded predicates, are a natural and
powerful language to succinctly model discrete
time linear hybrid systems dynamics. Finally, we
experimentally show the feasibility of our
approach on an important and challenging case
study taken from the literature, namely the
multi-input Buck DC-DC Converter. As an example,
the guarded predicate that models (with 57
constraints) a 6-inputs Buck DC-DC Converter is
translated in a conjunctive predicate (with 102
linear constraints) in about 40 minutes.
Corporate Author Thesis (up)
Publisher IARIA Place of Publication Editor Luigi Lavazza
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1942-2628 ISBN Medium
Area Expedition Conference
Notes Approved yes
Call Number Sapienza @ melatti @ Serial 115
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