Application of reachability analysis based on time-dependent Hamilton-Jacobi-Isaacs equations

An algorithm is presented for computing the reachable set of a dynamic system. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation (HJI PDE). We implement this approach to a more realistic aircraft dynamic model which the control input of this model can be given by pilot rather than general intermediate variables. According to desired trajectory states, we can compute the backward reachable set in certain time interval and use the simulate result to verify actual trajectory status.