Chapter Two - Differential inclusion solver

Abstract

Solving a differential inclusion (DI) is more difficult that solving an ordinary differential equation. First, we should define the term “solution to a DI.” As there is some confusion about this, we will avoid the word “solution” (commonly used for a single DI trajectory) and rather discuss reachable sets. The aim of the DI solver described below is to obtain and to show graphically the reachable sets of DIs. The algorithm is based on some concepts from optimal control theory. As mentioned before, information about the reachable set may be useful when dealing with uncertainty in model parameters and when analyzing functional sensitivity. A common error encountered in many algorithms to compute reachable sets is that the interior of the set is explored. The DI solver described here scans the boundary and not the interior of the set. The solver may also be used in the analysis of control systems.