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

Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Function