79,345 research outputs found
Abstraction of Elementary Hybrid Systems by Variable Transformation
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing
elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in
practice, especially in safety-critical domains. Due to the non-polynomial
expressions which lead to undecidable arithmetic, verification of EHSs is very
hard. Existing approaches based on partition of state space or
over-approximation of reachable sets suffer from state explosion or inflation
of numerical errors. In this paper, we propose a symbolic abstraction approach
that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all
non-polynomial terms with newly introduced variables. Thus the verification of
EHSs is reduced to the one of PHSs, enabling us to apply all the
well-established verification techniques and tools for PHSs to EHSs. In this
way, it is possible to avoid the limitations of many existing methods. We
illustrate the abstraction approach and its application in safety verification
of EHSs by several real world examples
On Model Based Synthesis of Embedded Control Software
Many Embedded Systems are indeed Software Based Control Systems (SBCSs), that
is control systems whose controller consists of control software running on a
microcontroller device. This motivates investigation on Formal Model Based
Design approaches for control software. Given the formal model of a plant as a
Discrete Time Linear Hybrid System and the implementation specifications (that
is, number of bits in the Analog-to-Digital (AD) conversion)
correct-by-construction control software can be automatically generated from
System Level Formal Specifications of the closed loop system (that is, safety
and liveness requirements), by computing a suitable finite abstraction of the
plant.
With respect to given implementation specifications, the automatically
generated code implements a time optimal control strategy (in terms of set-up
time), has a Worst Case Execution Time linear in the number of AD bits , but
unfortunately, its size grows exponentially with respect to . In many
embedded systems, there are severe restrictions on the computational resources
(such as memory or computational power) available to microcontroller devices.
This paper addresses model based synthesis of control software by trading
system level non-functional requirements (such us optimal set-up time, ripple)
with software non-functional requirements (its footprint). Our experimental
results show the effectiveness of our approach: for the inverted pendulum
benchmark, by using a quantization schema with 12 bits, the size of the small
controller is less than 6% of the size of the time optimal one.Comment: Accepted for publication by EMSOFT 2012. arXiv admin note:
substantial text overlap with arXiv:1107.5638,arXiv:1207.409
Hybrid performance modelling of opportunistic networks
We demonstrate the modelling of opportunistic networks using the process
algebra stochastic HYPE. Network traffic is modelled as continuous flows,
contact between nodes in the network is modelled stochastically, and
instantaneous decisions are modelled as discrete events. Our model describes a
network of stationary video sensors with a mobile ferry which collects data
from the sensors and delivers it to the base station. We consider different
mobility models and different buffer sizes for the ferries. This case study
illustrates the flexibility and expressive power of stochastic HYPE. We also
discuss the software that enables us to describe stochastic HYPE models and
simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055
Towards a General Theory of Stochastic Hybrid Systems
In this paper we set up a mathematical structure,
called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a
mixing mechanism of stochastic processes, introduced
by Meyer. We prove that Markov strings are strong Markov processes with the cadlag property. We then show how a very general class of stochastic hybrid processes can be embedded
in the framework of Markov strings. This class, which
is referred to as the General Stochastic Hybrid Systems (GSHS), includes as special cases all the classes of stochastic hybrid processes, proposed in the literature
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