Level set methods for computing reachable sets of systems with differential algebraic equation dynamics

Most existing algorithms for approximating the reachable sets of continuous systems assume an ordinary differential equation model of system evolution. In this paper we adapt such an existing algorithm-one based on level set methods and the Hamilton-Jacobi partial differential equation-in two distinct ways to work with systems modeled by index one differential algebraic equations (DAEs). The first method works by analytic projection of the dynamics onto the DAE´s constraint manifold, while the second works in the full dimensional state space. The two schemes are demonstrated on a nonlinear power system voltage safety problem.