307 research outputs found
Control software model checking using bisimulation functions for nonlinear systems
Abstract — This paper extends a method for integrating source-code model checking with dynamic system analysis to verify properties of controllers for nonlinear dynamic systems. Source-code model checking verifies the correctness of control systems including features that are introduced by the software implementation, such as concurrency and task interleaving. Sets of reachable continuous states are computed using numerical simulation and bisimulation functions. The technique as origi-nally proposed handles stable dynamic systems with affine state equations for which quadratic bisimulation functions can be computed easily. The extension in this paper handles nonlinear systems with polynomial state equations for which bisimulation functions can be computed in some cases using sum-of-squares (SoS) techniques. The paper presents the convex optimizations required to perform control system verification using a source-code model checker, and the method is illustrated for an example of a supervisory control system. I
Algebra, coalgebra, and minimization in polynomial differential equations
We consider reasoning and minimization in systems of polynomial ordinary
differential equations (ode's). The ring of multivariate polynomials is
employed as a syntax for denoting system behaviours. We endow this set with a
transition system structure based on the concept of Lie-derivative, thus
inducing a notion of L-bisimulation. We prove that two states (variables) are
L-bisimilar if and only if they correspond to the same solution in the ode's
system. We then characterize L-bisimilarity algebraically, in terms of certain
ideals in the polynomial ring that are invariant under Lie-derivation. This
characterization allows us to develop a complete algorithm, based on building
an ascending chain of ideals, for computing the largest L-bisimulation
containing all valid identities that are instances of a user-specified
template. A specific largest L-bisimulation can be used to build a reduced
system of ode's, equivalent to the original one, but minimal among all those
obtainable by linear aggregation of the original equations. A computationally
less demanding approximate reduction and linearization technique is also
proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
Challenges in Quantitative Abstractions for Collective Adaptive Systems
Like with most large-scale systems, the evaluation of quantitative properties
of collective adaptive systems is an important issue that crosscuts all its
development stages, from design (in the case of engineered systems) to runtime
monitoring and control. Unfortunately it is a difficult problem to tackle in
general, due to the typically high computational cost involved in the analysis.
This calls for the development of appropriate quantitative abstraction
techniques that preserve most of the system's dynamical behaviour using a more
compact representation. This paper focuses on models based on ordinary
differential equations and reviews recent results where abstraction is achieved
by aggregation of variables, reflecting on the shortcomings in the state of the
art and setting out challenges for future research.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
Synthesizing SystemC Code from Delay Hybrid CSP
Delay is omnipresent in modern control systems, which can prompt oscillations
and may cause deterioration of control performance, invalidate both stability
and safety properties. This implies that safety or stability certificates
obtained on idealized, delay-free models of systems prone to delayed coupling
may be erratic, and further the incorrectness of the executable code generated
from these models. However, automated methods for system verification and code
generation that ought to address models of system dynamics reflecting delays
have not been paid enough attention yet in the computer science community. In
our previous work, on one hand, we investigated the verification of delay
dynamical and hybrid systems; on the other hand, we also addressed how to
synthesize SystemC code from a verified hybrid system modelled by Hybrid CSP
(HCSP) without delay. In this paper, we give a first attempt to synthesize
SystemC code from a verified delay hybrid system modelled by Delay HCSP
(dHCSP), which is an extension of HCSP by replacing ordinary differential
equations (ODEs) with delay differential equations (DDEs). We implement a tool
to support the automatic translation from dHCSP to SystemC
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