Guaranteed master for interval-based cosimulation

Abstract

In this paper, we tackle the problem of guaranteed simulation of cyber-physical systems, an important model for current engineering systems. Their is always increasing complexity which leads to models of higher and higher dimensions, yet typically involving multiple subsystems or even multiple physics. Given this modularity, we more precisely explore cosimulation of such dynamical systems, with the aim of reaching higher dimensions of the simulated systems. In this paper, we present a guaranteed interval-based approach for cosimulation of continuous time systems. We propose an algorithm which first proves the existence and returns an enclosure of global solutions, using only local computations. This mitigates the curse of dimensionality faced by global (guaranteed) integration methods. Local computations are then realized with a safe estimate of the other sub-systems until the next macro-step. We increase the accuracy of the approach by using an interval extrapolation of the state of the other sub-systems. We finally propose some possible further improvements including adaptive macro-step size. Our method is fully guaranteed, taking into account all possible sources of error. It is implemented in a C++ prototype relying on the DynIbex library, and we illustrate our approach on multiple examples of the literature.