986 research outputs found
Guaranteed Error Bounds on Approximate Model Abstractions Through Reachability Analysis
It is well known that exact notions of model abstraction and reduction
for dynamical systems may not be robust enough in practice because they are
highly sensitive to the specific choice of parameters. In this paper we consider this
problem for nonlinear ordinary differential equations (ODEs) with polynomial
derivatives. We introduce approximate differential equivalence as a more permissive
variant of a recently developed exact counterpart, allowing ODE variables
to be related even when they are governed by nearby derivatives. We develop
algorithms to (i) compute the largest approximate differential equivalence; (ii)
construct an approximate quotient model from the original one via an appropriate
parameter perturbation; and (iii) provide a formal certificate on the quality of
the approximation as an error bound, computed as an over-approximation of the
reachable set of the perturbed model. Finally, we apply approximate differential
equivalences to study the effect of parametric tolerances in models of symmetric
electric circuits
Probabilistic Guarantees for Safe Deep Reinforcement Learning
Deep reinforcement learning has been successfully applied to many control
tasks, but the application of such agents in safety-critical scenarios has been
limited due to safety concerns. Rigorous testing of these controllers is
challenging, particularly when they operate in probabilistic environments due
to, for example, hardware faults or noisy sensors. We propose MOSAIC, an
algorithm for measuring the safety of deep reinforcement learning agents in
stochastic settings. Our approach is based on the iterative construction of a
formal abstraction of a controller's execution in an environment, and leverages
probabilistic model checking of Markov decision processes to produce
probabilistic guarantees on safe behaviour over a finite time horizon. It
produces bounds on the probability of safe operation of the controller for
different initial configurations and identifies regions where correct behaviour
can be guaranteed. We implement and evaluate our approach on agents trained for
several benchmark control problems
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
Proving Abstractions of Dynamical Systems through Numerical Simulations
A key question that arises in rigorous analysis of cyberphysical systems
under attack involves establishing whether or not the attacked system deviates
significantly from the ideal allowed behavior. This is the problem of deciding
whether or not the ideal system is an abstraction of the attacked system. A
quantitative variation of this question can capture how much the attacked
system deviates from the ideal. Thus, algorithms for deciding abstraction
relations can help measure the effect of attacks on cyberphysical systems and
to develop attack detection strategies. In this paper, we present a decision
procedure for proving that one nonlinear dynamical system is a quantitative
abstraction of another. Directly computing the reach sets of these nonlinear
systems are undecidable in general and reach set over-approximations do not
give a direct way for proving abstraction. Our procedure uses (possibly
inaccurate) numerical simulations and a model annotation to compute tight
approximations of the observable behaviors of the system and then uses these
approximations to decide on abstraction. We show that the procedure is sound
and that it is guaranteed to terminate under reasonable robustness assumptions
Abstracting the Traffic of Nonlinear Event-Triggered Control Systems
Scheduling communication traffic in networks of event-triggered control (ETC)
systems is challenging, as their sampling times are unknown, hindering
application of ETC in networks. In previous work, finite-state abstractions
were created, capturing the sampling behaviour of LTI ETC systems with
quadratic triggering functions. Offering an infinite-horizon look to all
sampling patterns of an ETC system, such abstractions can be used for
scheduling of ETC traffic. Here we significantly extend this framework, by
abstracting perturbed uncertain nonlinear ETC systems with general triggering
functions. To construct an ETC system's abstraction: a) the state space is
partitioned into regions, b) for each region an interval is determined,
containing all intersampling times of points in the region, and c) the
abstraction's transitions are determined through reachability analysis. To
determine intervals and transitions, we devise algorithms based on reachability
analysis. For partitioning, we propose an approach based on isochronous
manifolds, resulting into tighter intervals and providing control over them,
thus containing the abstraction's non-determinism. Simulations showcase our
developments
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