4 research outputs found
Hybrid Reachability Analysis for Kuramoto-Lanchester Model
Cyber-physical systems are ubiquitous nowadays and play a significant role in people's daily life. These systems include, e.g., autonomous vehicles and aerospace systems. Since human lives rely on the performance of these systems, it is of utmost importance to ensure their reliability. However, their complexity makes analysis particularly challenging and computationally expensive. Thus, it is crucial to develop tools to efficiently analyze cyber-physical systems and their safety properties. Cyber-physical systems are often modeled by hybrid automata, i.e. finite-state machines augmented with ordinary differential equations. In the thesis, we investigate reachability analysis methods for hybrid automata. In particular, we extend JuliaReach, a framework for fast prototyping set-based reachability analysis algorithms, to support verification of hybrid automata. For this purpose, we add to JuliaReach concrete and lazy discrete post operators. Lazy operations are particularly efficient in flowpipe based reachability analysis with long sequences of computations. The implemented algorithms are interchangeable and support all three reachability scenarios available in JuliaReach for the purely continuous setting: techniques to analyze linear systems using support functions and zonotopes as well as Taylor model based analysis for nonlinear systems. In order to evaluate our methods, we apply them to the Kuramoto-Lanchester model. This model exhibits highly nonlinear dynamics and can be easily scaled, and thus is well-suited to assess performance of reachability analysis methods for hybrid automata
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
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
JuliaReach: a toolbox for set-based reachability
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