14 research outputs found
Reachability analysis of linear hybrid systems via block decomposition
Reachability analysis aims at identifying states reachable by a system within
a given time horizon. This task is known to be computationally expensive for
linear hybrid systems. Reachability analysis works by iteratively applying
continuous and discrete post operators to compute states reachable according to
continuous and discrete dynamics, respectively. In this paper, we enhance both
of these operators and make sure that most of the involved computations are
performed in low-dimensional state space. In particular, we improve the
continuous-post operator by performing computations in high-dimensional state
space only for time intervals relevant for the subsequent application of the
discrete-post operator. Furthermore, the new discrete-post operator performs
low-dimensional computations by leveraging the structure of the guard and
assignment of a considered transition. We illustrate the potential of our
approach on a number of challenging benchmarks.Comment: Accepted at EMSOFT 202
Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions
Efficiently handling time-triggered and possibly nondeterministic switches
for hybrid systems reachability is a challenging task. In this paper we present
an approach based on conservative set-based enclosure of the dynamics that can
handle systems with uncertain parameters and inputs, where the uncertainties
are bound to given intervals. The method is evaluated on the plant model of an
experimental electro-mechanical braking system with periodic controller. In
this model, the fast-switching controller dynamics requires simulation time
scales of the order of nanoseconds. Accurate set-based computations for
relatively large time horizons are known to be expensive. However, by
appropriately decoupling the time variable with respect to the spatial
variables, and enclosing the uncertain parameters using interval matrix maps
acting on zonotopes, we show that the computation time can be lowered to 5000
times faster with respect to previous works. This is a step forward in formal
verification of hybrid systems because reduced run-times allow engineers to
introduce more expressiveness in their models with a relatively inexpensive
computational cost.Comment: Submitte
On the Trade-off Between Efficiency and Precision of Neural Abstraction
Neural abstractions have been recently introduced as formal approximations of
complex, nonlinear dynamical models. They comprise a neural ODE and a certified
upper bound on the error between the abstract neural network and the concrete
dynamical model. So far neural abstractions have exclusively been obtained as
neural networks consisting entirely of activation functions, resulting
in neural ODE models that have piecewise affine dynamics, and which can be
equivalently interpreted as linear hybrid automata. In this work, we observe
that the utility of an abstraction depends on its use: some scenarios might
require coarse abstractions that are easier to analyse, whereas others might
require more complex, refined abstractions. We therefore consider neural
abstractions of alternative shapes, namely either piecewise constant or
nonlinear non-polynomial (specifically, obtained via sigmoidal activations). We
employ formal inductive synthesis procedures to generate neural abstractions
that result in dynamical models with these semantics. Empirically, we
demonstrate the trade-off that these different neural abstraction templates
have vis-a-vis their precision and synthesis time, as well as the time required
for their safety verification (done via reachability computation). We improve
existing synthesis techniques to enable abstraction of higher-dimensional
models, and additionally discuss the abstraction of complex neural ODEs to
improve the efficiency of reachability analysis for these models.Comment: To appear at QEST 202
JuliaReach: a Toolbox for Set-Based Reachability
We present JuliaReach, a toolbox for set-based reachability analysis of
dynamical systems. JuliaReach consists of two main packages: Reachability,
containing implementations of reachability algorithms for continuous and hybrid
systems, and LazySets, a standalone library that implements state-of-the-art
algorithms for calculus with convex sets. The library offers both concrete and
lazy set representations, where the latter stands for the ability to delay set
computations until they are needed. The choice of the programming language
Julia and the accompanying documentation of our toolbox allow researchers to
easily translate set-based algorithms from mathematics to software in a
platform-independent way, while achieving runtime performance that is
comparable to statically compiled languages. Combining lazy operations in high
dimensions and explicit computations in low dimensions, JuliaReach can be
applied to solve complex, large-scale problems.Comment: Accepted in Proceedings of HSCC'19: 22nd ACM International Conference
on Hybrid Systems: Computation and Control (HSCC'19
Computer Aided Verification
This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications