An Introduction to CORA 2015 ( Tool Presentation ) Matthias Althoff

The philosophy, architecture, and capabilities of the COntinuous Reachability Analyzer (CORA) are presented. CORA is a toolbox that integrates various vector and matrix set representations and operations on them as well as reachability algorithms of various dynamic system classes. The software is designed such that set representations can be exchanged without having to modify the code for reachability analysis. CORA has a modular design, making it possible to use the capabilities of the various set representations for other purposes besides reachability analysis. The toolbox is designed using the object oriented paradigm, such that users can safely use methods without concerning themselves with detailed information hidden inside the object. Since the toolbox is written in MATLAB, the installation and use is platform independent. 1 Philosophy and Architecture The COntinuous Reachability Analyzer (CORA)1 is a MATLAB toolbox for prototype design of algorithms for reachability analysis. The toolbox is designed for various kinds of systems with purely continuous dynamics (linear systems, nonlinear systems, differential-algebraic systems, parameter-varying systems, etc.) and hybrid dynamics combining the aforementioned continuous dynamics with discrete dynamics. Let us denote the continuous part of the solution of a hybrid system for a given initial discrete state by χ(t;x0, u(·), p), where t ∈ R is the time, x0 ∈ R is the continuous initial state, u(t) ∈ R is the system input at t, u(·) is the input trajectory, and p ∈ R is a parameter vector. The continuous reachable set at time t = r can be defined for a set of initial states X0, a set of input values U(t), and a set of parameter values P, as R(r) = { χ(r;x0, u(·), p) ∈ R n ∣ x0 ∈ X0,∀t : u(t) ∈ U(t), p ∈ P } . CORA solely supports over-approximative computation of reachable sets since (a) exact reachable sets cannot be computed for most system classes [1] and (b) over-approximative computations qualify for formal verification. Thus, CORA computes over-approximations for particular points in time R(t) ⊇ R(t) and for time intervals: R([t0, tf ]) = ⋃ t∈[t0,tf ] R(t). CORA is built with the aim to construct one’s own reachable set computation in a short amount of time. This is achieved by the following design choices: • CORA is built for MATLAB, which is a script-based programming environment. Since the code does not have to be compiled, one can stop the program at any time and directly see the current values of variables. This makes it especially easy to understand the workings of the code and to debug new code. https://www6.in.tum.de/Main/SoftwareCORA