  A novel method for computing reachable sets is proposed in this paper. In the
proposed method, a Hamilton-Jacobi-Bellman equation with running cost
functionis numerically solved and the reachable sets of different time horizons
are characterized by a family of non-zero level sets of the solution of the
Hamilton-Jacobi-Bellman equation. In addition to the classical reachable set,
by setting different running cost functions and terminal conditionsof the
Hamilton-Jacobi-Bellman equation, the proposed method allows to compute more
generalized reachable sets, which are referred to as cost-limited reachable
sets. In order to overcome the difficulty of solving the
Hamilton-Jacobi-Bellman equation caused by the discontinuity of the solution, a
method based on recursion and grid interpolation is employed.
  At the end of this paper, some examples are taken to illustrate the validity
and generality of the proposed method.
