Mari_etal2013
ArticleInAPeriodical
IARIA
2013
International Journal on Advances in Software
vol. 6, nr 1&2
155-169
MariFederico
MelattiIgor
SalvoIvano
TronciEnrico
Luigi Lavazza
Linear Constraints and Guarded Predicates as a Modeling Language for Discrete Time Hybrid Systems
Intern. Journal on Advances in SW
Model based design is particularly appealing insoftware based control systems (e.g., embeddedsoftware) design, since in such a case systemlevel specifications are much easier to definethan the control software behavior itself. Inturn, model based design of embedded systemsrequires modeling both continuous subsystems(typically, the plant) as well as discretesubsystems (the controller). This is typicallydone using hybrid systems. Mixed Integer LinearProgramming (MILP) based abstraction techniqueshave been successfully applied to automatically synthesize correct-by-construction controlsoftware for discrete time linear hybrid systems,where plant dynamics is modeled as a linearpredicate over state, input, and next statevariables. Unfortunately, MILP solvers requiresuch linear predicates to be conjunctions oflinear constraints, which is not a natural way ofmodeling hybrid systems. In this paper we showthat, under the hypothesis that each variableranges over a bounded interval, any linearpredicate built upon conjunction and disjunction of linear constraints can be automaticallytranslated into an equivalent conjunctivepredicate. Since variable bounds play a key rolein this translation, our algorithm includes aprocedure to compute all implicit variable boundsof the given linear predicate. Furthermore, weshow that a particular form of linear predicates,namely guarded predicates, are a natural andpowerful language to succinctly model discretetime linear hybrid systems dynamics. Finally, weexperimentally show the feasibility of ourapproach on an important and challenging casestudy taken from the literature, namely themulti-input Buck DC-DC Converter. As an example,the guarded predicate that models (with 57constraints) a 6-inputs Buck DC-DC Converter istranslated in a conjunctive predicate (with 102linear constraints) in about 40 minutes.