No abstract

Tool Presentation: Computing guaranteed bounds of function outputs when their input variables are bounded by intervals is an essential technique for many formal methods. Due to the importance of bounding function outputs, several techniques have been proposed for this problem, such as interval arithmetic, affine arithmetic, and Taylor models. While all methods provide guaranteed bounds, it is typically unknown to a formal verification tool which approach is best suitable for a given problem. For this reason, we present an implementation of the aforementioned techniques in our MATLAB tool CORA so that advantages and disadvantages of different techniques can be quickly explored without hav- ing to compile code. In this work we present the implementation of Taylor models and affine arithmetic; our interval arithmetic implementation has already been published. We evaluate the performance of our implementation using a set of benchmarks against Flow* and INTLAB. To the best of our knowledge, we have also evaluated for the first time how a combination of interval arithmetic and Taylor models performs: our results indicate that this combination is faster and more accurate than only using Taylor models.

We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2018. In this year, six tools CORA, CORA/SX, C2E2, Flow*, Isabelle/HOL, and SymReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmarks problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools.

The popularity of model predictive control (MPC) is mainly founded on its easy implementation and its ability to consider state and input constraints. For future applications in safety-critical systems, however, it is necessary to provide formal guarantees of safety despite disturbances and measurement noise. In this paper, we include reachability analysis in an MPC approach to obtain provably safe controllers which are easy to implement. We consider continuous-time, nonlinear systems affected by disturbances and measurement noise. In contrast to most existing techniques, we explicitly consider the computation time and guarantee the satisfaction of state and input constraints despite the previously-mentioned disturbances. We use a novel type of dual mode MPC, which does not require the computation of Lyapunov functions. We demonstrate the applicability of our approach with a numerical example of a chemical reactor, where we show the advantages of our approach compared to existing MPC.

We prove that each bounded polytope can be represented as a polynomial zonotope, which we refer to as the Z-representation of polytopes. Previous representations are the vertex representation (V-representation) and the halfspace representation (H-representation). Depending on the polytope, the Z-representation can be more compact than the V-representation and the H-representation. In addition, the Z-representation enables the computation of linear maps, Minkowski addition, and convex hull with a computational complexity that is polynomial in the representation size. The usefulness of the new representation is demonstrated by range bounding within polytopes.