31 research outputs found
Probabilistic bounded reachability for stochastic hybrid systems
PhD ThesisStochastic parametric hybrid systems provide a means of formalising automata
with continuous nonlinear dynamics, discrete interruptions, and
parametric uncertainty (e.g. randomness and/or nondeterminism). They
can be used for modelling a vast class of cyber-physical systems – machines
comprising physical components orchestrated by a digital control (e.g. medical
devices, self-driving cars, and aircraft autopilots). Assuring correct and
safe behaviour of such systems is crucial as human lives are often involved.
One of the main problems in system verification is reachability analysis.
It amounts to determining whether the studied model reaches an unsafe
state during its evolution. Introduction of parametric randomness allows
the formulation of a quantitative version of the problem – computing the
probability of reaching the undesired state.
Reachability analysis is a highly challenging problem due to its general undecidability
for hybrid systems and undecidability of nonlinear arithmetic
(e.g. involving trigonometric functions) over the real numbers. A common
approach in this case is to solve a simpler, yet useful, problem. In particular,
there are techniques for solving reachability rigorously up to a given
numerical precision.
The central problem of this research is probabilistic reachability analysis of
hybrid systems with random and nondeterministic parameters. In this thesis
I have developed two new distinct techniques: a formal approach, based
on formal reasoning which provides absolute numerical guarantees; and a
statistical one, utilising Monte Carlo sampling that gives statistical guarantees.
Namely, the former computes an interval which is guaranteed to
contain the exact reachability probability value, while the latter returns an
interval containing the probability value with some statistical confidence.
By providing weaker guarantees, the statistical approach is capable of handling
difficult cases more efficiently than the formal one, which in turn, can
be used for parameter set synthesis in the absence of random uncertainty.
The latter is one of the key problems in system modelling: identifying sets
of parameter values for which a given model satisfies the desired behaviour.
I have implemented the described techniques in the publicly available tool
ProbReach, which I have then applied to several realistic case studies such
as the synthesis of safe and robust controllers for artificial pancreas and the
design of UVB treatment for psoriasis.award N00014-13-1-0090 of the US
Office of Naval Research
Signal Convolution Logic
We introduce a new logic called Signal Convolution Logic (SCL) that combines temporal logic with convolutional filters from digital signal processing. SCL enables to reason about the percentage of time a formula is satisfied in a bounded interval. We demonstrate that this new logic is a suitable formalism to effectively express non-functional requirements in Cyber-Physical Systems displaying noisy and irregular behaviours. We define both a qualitative and quantitative semantics for it, providing an efficient monitoring procedure. Finally, we prove SCL at work to monitor the artificial pancreas controllers that are employed to automate the delivery of insulin for patients with type-1 diabetes
ARCH-COMP23 Category Report: Stochastic Models
This report is concerned with a friendly competition for formal verification and policy synthesis of stochastic models. The main goal of the report is to introduce new benchmarks and their properties within this category and recommend next steps toward next year’s edition of the competition. Given that the tools for stochastic models are at their early stages of development compared to those of non-probabilistic models, the main focus is to report on an initiative to collect a set of minimal benchmarks that all such tools can run, thus facilitating the comparison between the efficiency of the implemented techniques. This friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Summer 2023.</p
ProbReach: verified probabilistic delta-reachability for stochastic hybrid systems
We present ProbReach, a tool for verifying probabilistic reachability for
stochastic hybrid systems, i.e., computing the probability that the system
reaches an unsafe region of the state space. In particular, ProbReach will
compute an arbitrarily small interval which is guaranteed to contain the
required probability. Standard (non-probabilistic) reachability is undecidable
even for linear hybrid systems. In ProbReach we adopt the weaker notion of
delta-reachability, in which the unsafe region is overapproximated by a
user-defined parameter (delta). This choice leads to false alarms, but also
makes the reachability problem decidable for virtually any hybrid system. In
ProbReach we have implemented a probabilistic version of delta-reachability
that is suited for hybrid systems whose stochastic behaviour is given in terms
of random initial conditions. In this paper we introduce the capabilities of
ProbReach, give an overview of the parallel implementation, and present results
for several benchmarks involving highly non-linear hybrid systems.Comment: HSCC 201