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Author |
Mari, Federico; Melatti, Igor; Salvo, Ivano; Tronci, Enrico |
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Title |
Linear Constraints and Guarded Predicates as a Modeling Language for Discrete Time Hybrid Systems |
Type |
Journal Article |
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Year |
2013 |
Publication |
International Journal on Advances in Software |
Abbreviated Journal |
Intern. Journal on Advances in SW |
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Volume |
vol. 6, nr 1&2 |
Issue |
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Pages |
155-169 |
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Keywords |
Model-based software design; Linear predicates; Hybrid systems |
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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. |
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Publisher |
IARIA |
Place of Publication |
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Editor |
Luigi Lavazza |
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ISSN |
1942-2628 |
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Approved |
yes |
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Call Number |
Sapienza @ melatti @ |
Serial |
115 |
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Author |
Alimguzhin, V.; Mari, F.; Melatti, I.; Salvo, I.; Tronci, E. |
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Title |
Linearising Discrete Time Hybrid Systems |
Type |
Journal Article |
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Year |
2017 |
Publication |
IEEE Transactions on Automatic Control |
Abbreviated Journal |
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Volume |
62 |
Issue |
10 |
Pages |
5357-5364 |
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Keywords |
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Abstract |
Model Based Design approaches for embedded systems aim at generating correct-by-construction control software, guaranteeing that the closed loop system (controller and plant) meets given system level formal specifications. This technical note addresses control synthesis for safety and reachability properties of possibly non-linear discrete time hybrid systems. By means of syntactical transformations that require non-linear terms to be Lipschitz continuous functions, we over-approximate non-linear dynamics with a linear system whose controllers are guaranteed to be controllers of the original system. We evaluate performance of our approach on meaningful control synthesis benchmarks, also comparing it to a state-of-the-art tool. |
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0018-9286 |
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no |
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Call Number |
Sapienza @ mari @ ref7902199 |
Serial |
164 |
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Author |
Mari, Federico; Melatti, Igor; Salvo, Ivano; Tronci, Enrico |
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Title |
From Boolean Relations to Control Software |
Type |
Conference Article |
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Year |
2011 |
Publication |
Proceedings of ICSEA 2011, The Sixth International Conference on Software Engineering Advances |
Abbreviated Journal |
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Issue |
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Pages |
528-533 |
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Abstract |
Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware) synthesis process is finding effective solutions to the functional equation defined by K. This entails finding a (set of) boolean function(s) F (typically represented using OBDDs, Ordered Binary Decision Diagrams) such that: 1) for all x for which K is satisfiable, K(x, F(x)) = 1 holds; 2) the implementation of F is efficient with respect to given implementation parameters such as code size or execution time. While this problem has been widely studied in digital hardware synthesis, little has been done in a software synthesis context. Unfortunately the approaches developed for hardware synthesis cannot be directly used in a software context. This motivates investigation of effective methods to solve the above problem when F has to be implemented with software. In this paper we present an algorithm that, from an OBDD representation for K, generates a C code implementation for F that has the same size as the OBDD for F and a WCET (Worst Case Execution Time) linear in nr, being n = |x| the number of input arguments for functions in F and r the number of functions in F. |
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ThinkMind |
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ISSN |
978-1-61208-165-6 |
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Notes |
Best Paper Award |
Approved |
yes |
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Call Number |
Sapienza @ mari @ icsea11 |
Serial |
14 |
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Author |
Mari, Federico; Melatti, Igor; Salvo, Ivano; Tronci, Enrico |
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Title |
From Boolean Functional Equations to Control Software |
Type |
Report |
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Year |
2011 |
Publication |
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Abbreviated Journal |
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Volume |
abs/1106.0468 |
Issue |
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Pages |
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Keywords |
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Abstract |
Many software as well digital hardware automatic synthesis methods define the set of implementations meeting the given system specifications with a boolean relation K. In such a context a fundamental step in the software (hardware) synthesis process is finding effective solutions to the functional equation defined by K. This entails finding a (set of) boolean function(s) F (typically represented using OBDDs, Ordered Binary Decision Diagrams) such that: 1) for all x for which K is satisfiable, K(x, F(x)) = 1 holds; 2) the implementation of F is efficient with respect to given implementation parameters such as code size or execution time. While this problem has been widely studied in digital hardware synthesis, little has been done in a software synthesis context. Unfortunately the approaches developed for hardware synthesis cannot be directly used in a software context. This motivates investigation of effective methods to solve the above problem when F has to be implemented with software. In this paper we present an algorithm that, from an OBDD representation for K, generates a C code implementation for F that has the same size as the OBDD for F and a WCET (Worst Case Execution Time) at most O(nr), being n = |x| the number of arguments of functions in F and r the number of functions in F. |
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CoRR, Technical Report |
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Notes |
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Approved |
yes |
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Call Number |
Sapienza @ mari @ |
Serial |
105 |
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| Permanent link to this record |
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Author |
Mari, Federico; Melatti, Igor; Salvo, Ivano; Tronci, Enrico |
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Title |
Synthesizing Control Software from Boolean Relations |
Type |
Journal Article |
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Year |
2012 |
Publication |
International Journal on Advances in Software |
Abbreviated Journal |
Intern. Journal on Advances in SW |
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Volume |
vol. 5, nr 3&4 |
Issue |
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Pages |
212-223 |
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Keywords |
Control Software Synthesis; Embedded Systems; Model Checking |
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Abstract |
Many software as well digital hardware automatic
synthesis methods define the set of
implementations meeting the given system
specifications with a boolean relation K. In
such a context a fundamental step in the software
(hardware) synthesis process is finding effective
solutions to the functional equation defined by
K. This entails finding a (set of) boolean
function(s) F (typically represented using
OBDDs, Ordered Binary Decision Diagrams)
such that: 1) for all x for which K is
satisfiable, K(x, F(x)) = 1 holds; 2) the
implementation of F is efficient with respect
to given implementation parameters such as code
size or execution time. While this problem has
been widely studied in digital hardware synthesis,
little has been done in a software synthesis
context. Unfortunately, the approaches developed
for hardware synthesis cannot be directly used in
a software context. This motivates investigation
of effective methods to solve the above problem
when F has to be implemented with software. In
this paper, we present an algorithm that, from an
OBDD representation for K, generates a C code
implementation for F that has the same size as
the OBDD for F and a worst case execution time
linear in nr, being n = |x| the number of
input arguments for functions in F and r the
number of functions in F. Moreover, a formal
proof of the proposed algorithm correctness is
also shown. Finally, we present experimental
results showing effectiveness of the proposed
algorithm. |
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Corporate Author |
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Thesis |
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Publisher |
IARIA |
Place of Publication |
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Editor |
Luigi Lavazza |
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Language |
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Summary Language |
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Original Title |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1942-2628 |
ISBN |
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Notes |
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Approved |
yes |
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Call Number |
Sapienza @ melatti @ |
Serial |
108 |
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Author |
Tronci, Enrico |
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Title |
Automatic Synthesis of Controllers from Formal Specifications |
Type |
Conference Article |
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Year |
1998 |
Publication |
Proc of 2nd IEEE International Conference on Formal Engineering Methods (ICFEM) |
Abbreviated Journal |
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Issue |
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Pages |
134-143 |
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Keywords |
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Abstract |
Many safety critical reactive systems are indeed embedded control systems. Usually a control system can be partitioned into two main subsystems: a controller and a plant. Roughly speaking: the controller observes the state of the plant and sends commands (stimulus) to the plant to achieve predefined goals. We show that when the plant can be modeled as a deterministic finite state system (FSS) it is possible to effectively use formal methods to automatically synthesize the program implementing the controller from the plant model and the given formal specifications for the closed loop system (plant+controller). This guarantees that the controller program is correct by construction. To the best of our knowledge there is no previously published effective algorithm to extract executable code for the controller from closed loop formal specifications. We show practical usefulness of our techniques by giving experimental results on their use to synthesize C programs implementing optimal controllers (OCs) for plants with more than 109 states. |
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Place of Publication |
Brisbane, Queensland, Australia |
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Approved |
yes |
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Call Number |
Sapienza @ mari @ icfem98 |
Serial |
52 |
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Author |
Della Penna, Giuseppe; Intrigila, Benedetto; Melatti, Igor; Tronci, Enrico; Venturini Zilli, Marisa |
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Title |
Finite Horizon Analysis of Stochastic Systems with the Mur$\varphi$ Verifier |
Type |
Conference Article |
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Year |
2003 |
Publication |
Theoretical Computer Science, 8th Italian Conference, ICTCS 2003, Bertinoro, Italy, October 13-15, 2003, Proceedings |
Abbreviated Journal |
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Volume |
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Issue |
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Pages |
58-71 |
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Abstract |
Many reactive systems are actually Stochastic Processes. Automatic analysis of such systems is usually very difficult thus typically one simplifies the analysis task by using simulation or by working on a simplified model (e.g. a Markov Chain). We present a Finite Horizon Probabilistic Model Checking approach which essentially can handle the same class of stochastic processes of a typical simulator. This yields easy modeling of the system to be analyzed together with formal verification capabilities. Our approach is based on a suitable disk based extension of the Mur$\varphi$ verifier. Moreover we present experimental results showing effectiveness of our approach. |
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Springer |
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Editor |
Blundo, C.; Laneve, C. |
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Lecture Notes in Computer Science |
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Series Volume |
2841 |
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ISSN |
3-540-20216-1 |
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Approved |
yes |
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Call Number |
Sapienza @ mari @ DIMTZ03c |
Serial |
90 |
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Author |
Piperno, Adolfo; Tronci, Enrico |
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Title |
Regular Systems of Equations in λ-calculus |
Type |
Journal Article |
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Year |
1990 |
Publication |
Int. J. Found. Comput. Sci. |
Abbreviated Journal |
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Volume |
1 |
Issue |
3 |
Pages |
325-340 |
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Abstract |
Many problems arising in equational theories like Lambda-calculus and Combinatory Logic can be expressed by combinatory equations or systems of equations. However, the solvability problem for an arbitrarily given class of systems is in general undecidable. In this paper we shall focus our attention on a decidable class of systems, which will be called regular systems, and we shall analyse some classical problems and well-known properties of Lambda-calculus that can be described and solved by means of regular systems. The significance of such class will be emphasized showing that for slight extensions of it the solvability problem turns out to be undecidable. |
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yes |
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Call Number |
Sapienza @ mari @ ijfcs90 |
Serial |
60 |
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Author |
Piperno, Adolfo; Tronci, Enrico |
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Title |
Regular Systems of Equations in λ-calculus |
Type |
Conference Article |
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Year |
1989 |
Publication |
Ictcs |
Abbreviated Journal |
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Abstract |
Many problems arising in equational theories like Lambda-calculus and Combinatory Logic can be expressed by combinatory equations or systems of equations. However, the solvability problem for an arbitrarily given class of systems is in general undecidable. In this paper we shall focus our attention on a decidable class of systems, which will be called regular systems, and we shall analyse some classical problems and well-known properties of Lambda-calculus that can be described and solved by means of regular systems. The significance of such class will be emphasized showing that for slight extensions of it the solvability problem turns out to be undecidable. |
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Mantova - Italy |
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yes |
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Call Number |
Sapienza @ mari @ ictcs89 |
Serial |
61 |
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Author |
Mari, Federico; Tronci, Enrico |
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Title |
CEGAR Based Bounded Model Checking of Discrete Time Hybrid Systems |
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Conference Article |
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Year |
2007 |
Publication |
Hybrid Systems: Computation and Control (HSCC 2007) |
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399-412 |
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Keywords |
Model Checking, Abstraction, CEGAR, SAT, Hybrid Systems, DTHS |
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Abstract |
Many hybrid systems can be conveniently modeled as Piecewise Affine Discrete Time Hybrid Systems PA-DTHS. As well known Bounded Model Checking (BMC) for such systems comes down to solve a Mixed Integer Linear Programming (MILP) feasibility problem. We present a SAT based BMC algorithm for automatic verification of PA-DTHSs. Using Counterexample Guided Abstraction Refinement (CEGAR) our algorithm gradually transforms a PA-DTHS verification problem into larger and larger SAT problems. Our experimental results show that our approach can handle PA-DTHSs that are more then 50 times larger than those that can be handled using a MILP solver. |
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Springer |
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Bemporad, A.; Bicchi, A.; Buttazzo, G.C. |
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Lecture Notes in Computer Science |
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Series Volume |
4416 |
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yes |
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Call Number |
Sapienza @ mari @ MarTro07 |
Serial |
92 |
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