44 research outputs found
Multi-scale modeling of follicular ovulation as a reachability problem
During each ovarian cycle, only a definite number of follicles ovulate, while
the others undergo a degeneration process called atresia. We have designed a
multi-scale mathematical model where ovulation and atresia result from a
hormonal controlled selection process. A 2D-conservation law describes the age
and maturity structuration of the follicular cell population. In this paper, we
focus on the operating mode of the control, through the study of the
characteristics of the conservation law. We describe in particular the set of
microscopic initial conditions leading to the macroscopic phenomenon of either
ovulation or atresia, in the framework of backwards reachable sets theory
Numerical Verification of Affine Systems with up to a Billion Dimensions
Affine systems reachability is the basis of many verification methods. With
further computation, methods exist to reason about richer models with inputs,
nonlinear differential equations, and hybrid dynamics. As such, the scalability
of affine systems verification is a prerequisite to scalable analysis for more
complex systems. In this paper, we improve the scalability of affine systems
verification, in terms of the number of dimensions (variables) in the system.
The reachable states of affine systems can be written in terms of the matrix
exponential, and safety checking can be performed at specific time steps with
linear programming. Unfortunately, for large systems with many state variables,
this direct approach requires an intractable amount of memory while using an
intractable amount of computation time. We overcome these challenges by
combining several methods that leverage common problem structure. Memory is
reduced by exploiting initial states that are not full-dimensional and safety
properties (outputs) over a few linear projections of the state variables.
Computation time is saved by using numerical simulations to compute only
projections of the matrix exponential relevant for the verification problem.
Since large systems often have sparse dynamics, we use Krylov-subspace
simulation approaches based on the Arnoldi or Lanczos iterations. Our method
produces accurate counter-examples when properties are violated and, in the
extreme case with sufficient problem structure, can analyze a system with one
billion real-valued state variables
A Map-Reduce Parallel Approach to Automatic Synthesis of Control Software
Many Control Systems are indeed Software Based Control Systems, i.e. control
systems whose controller consists of control software running on a
microcontroller device. This motivates investigation on Formal Model Based
Design approaches for automatic synthesis of control software.
Available algorithms and tools (e.g., QKS) may require weeks or even months
of computation to synthesize control software for large-size systems. This
motivates search for parallel algorithms for control software synthesis.
In this paper, we present a Map-Reduce style parallel algorithm for control
software synthesis when the controlled system (plant) is modeled as discrete
time linear hybrid system. Furthermore we present an MPI-based implementation
PQKS of our algorithm. To the best of our knowledge, this is the first parallel
approach for control software synthesis.
We experimentally show effectiveness of PQKS on two classical control
synthesis problems: the inverted pendulum and the multi-input buck DC/DC
converter. Experiments show that PQKS efficiency is above 65%. As an example,
PQKS requires about 16 hours to complete the synthesis of control software for
the pendulum on a cluster with 60 processors, instead of the 25 days needed by
the sequential algorithm in QKS.Comment: To be submitted to TACAS 2013. arXiv admin note: substantial text
overlap with arXiv:1207.4474, arXiv:1207.409
Gross solids from combined sewers in dry weather and storms, elucidating production, storage and social factors
Variation in rates of sanitary hygiene products, toilet tissue and faeces occurring in sewers are presented for dry and wet weather from three steep upstream urban catchments with different economic, age and ethnic profiles. Results show, for example, that total daily solids per capita from the low income and ageing populations are almost twice that from high income or ethnic populations. Relative differences are verified through independent questionnaires. The relationship between solids stored in sewers prior to storms, antecedent dry weather period and the proportion of roof to total catchment area is quantified. A full solids' flush occurs when storm flows exceed three times the peak dry weather flow. The data presented will assist urban drainage designers in managing pollution caused by the discharge of sewage solids
Towards Efficient Exact Synthesis for Linear Hybrid Systems
We study the problem of automatically computing the controllable region of a
Linear Hybrid Automaton, with respect to a safety objective. We describe the
techniques that are needed to effectively and efficiently implement a
recently-proposed solution procedure, based on polyhedral abstractions of the
state space. Supporting experimental results are presented, based on an
implementation of the proposed techniques on top of the tool PHAVer.Comment: In Proceedings GandALF 2011, arXiv:1106.081
A Game-Theoretic approach to Fault Diagnosis of Hybrid Systems
Physical systems can fail. For this reason the problem of identifying and
reacting to faults has received a large attention in the control and computer
science communities. In this paper we study the fault diagnosis problem for
hybrid systems from a game-theoretical point of view. A hybrid system is a
system mixing continuous and discrete behaviours that cannot be faithfully
modeled neither by using a formalism with continuous dynamics only nor by a
formalism including only discrete dynamics. We use the well known framework of
hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis
Game on them, using two players: the environment and the diagnoser. The
environment controls the evolution of the system and chooses whether and when a
fault occurs. The diagnoser observes the external behaviour of the system and
announces whether a fault has occurred or not. Existence of a winning strategy
for the diagnoser implies that faults can be detected correctly, while
computing such a winning strategy corresponds to implement a diagnoser for the
system. We will show how to determine the existence of a winning strategy, and
how to compute it, for some decidable classes of hybrid automata like o-minimal
hybrid automata.Comment: In Proceedings GandALF 2011, arXiv:1106.081