A set-based approach to model checking of nonlinear systems (invited tutorial)

Abstract

Summary form only given. The complete presentation was not made available for publication as part of the conference proceedings. In this tutorial, we address model checking of nonlinear dynamical systems, with specific focus on bounded safety. In particular, we consider a discrete time nonlinear system x <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> = f(x) initialized within a zonotopic set Xi, and aim at verifying if, along the time horizon [1,m], the state of the system evolves within a sequence of polyhedral sets described via intersection of specified half-spaces Spt. The proposed solution is based on the piecewise affine (PWA) approximation of the nonlinear dynamics, and on the reachability analysis of the obtained PWA model via propagation of zonotopic sets, which are closed under affine transformations and Minkowski sum and have a compact representation compared with polytopes without a central symmetry. If the PWA model is a conformant approximation of the original system, then, its reach sets over-approximate the actual reach sets. If they are contained within S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p_t</sub> , t = 1, ..., m, then, the original system is guaranteed to be safe. Otherwise, the PWA approximation needs to be progressively refined, possibly locally, through a procedure that guarantees that the new PWA reach sets are contained within those of the rougher PWA approximation (refinement inclusion). Possible extensions of the approach including the enforcement of the specification when the system evolution can be affected by some control input are also discussed.