On resource-efficient algorithm for non-linear systems approximate reachability set construction

Abstract

The research considers the numerical solution method of the reachability set construction problem for non-linear dynamical system in n-dimensional Euclidean space. The study deals with the dynamical system on the finite time interval, which is described by differential equation satisfying a set of defined conditions. The existing step-by-step pixel methods are based on the time interval sampling and applying the step-by-step reachability set constructing procedure to every time moment in partition. These methods allow us to solve the approximate reachability set constructing problem for the complex non-linear systems, which do not have analytical solutions. However, applying these methods causes a sharp increase of number of points used for reachability set constructing on the next step of time partition. This results in increase of calculation time as well as lack of computing device memory. To reduce the calculation time and satisfy the existing constraints of used device memory, we developed the set filtration algorithm based on some way of picking the points, which are used on the next step of reachability set constructing algorithm. Moreover, the computations are moved from CPU to the CUDA based on GPU, which allows us to run computations with the hundreds of parallel threads. In this research, we provide the description of the algorithm and give some information about its efficiency.