The Continuous Reachability Analyzer (CORA) is a MATLAB-based toolbox designed for the formal verification of cyber-physical systems through reachability analysis. It offers a comprehensive suite of tools for modeling and analyzing various system dynamics, including linear, nonlinear, and hybrid systems. CORA supports both continuous and discrete-time systems, accommodating uncertainties in system inputs and parameters. These uncertainties are captured by a diverse range of set representations such as intervals, zonotopes, Taylor models, and polytopes. Additionally, CORA provides functionalities for the formal verification of neural networks as well as data-driven system identification with reachset conformance. Various converters are implemented to easily model a system in CORA such as the well-established SpaceEx format for dynamic systems and ONNX format for neural networks. CORA ensures the seamless integration of different reachability algorithms without code modifications and aims for a user-friendly experience through automatic parameter tuning, making it a versatile tool for researchers and engineers in the field of cyber-physical systems.
CORA computes reachable sets for linear systems, nonlinear systems as well as for systems with constraints. Continuous as well as discrete time models are supported. Uncertainty in the system inputs as well as uncertainty in the model parameters can be explicitly considered. In addition, CORA also provides capabilities for the simulation of dynamical models.
The toolbox is also capable of computing the reachable sets for hybrid systems. All implemented dynamic system classes can be used to describe the different continuous flows for the discrete system states. Further, multiple different methods for the computation of the intersections with guard sets are implemented in CORA.
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 implements vector set representation, e.g., intervals, zonotopes, Taylor models, and polytopes, as well as matrix set representations such as matrix zonotopes and interval matrices.
CORA enables the formal verification of neural networks, both in open-loop and in closed-loop scenarios. Open-loop verification refers to the task where properties of the output set of a neural network are verified, e.g., correctly classified images given noisy input. In closed-loop scenarios, the neural network is used as a controller of a dynamic system and is neatly integrated in the reachability algorithms above, e.g., controlling a car while keeping a safe distance. Additionally, one can train verifiably robust neural networks in CORA.
To install CORA, please follow the steps below:
Congratulations, you have successfully installed CORA!
CORA comes with plenty of examples to guide you through all components of CORA. Explore them on GitHub, or enjoy watching the playlist below showcasing the capabilities of CORA and check out the example script.
CORA would not be possible without its great team. Please view the contributors page for more details on the CORA team.