  Level set method is a widely used tool for solving reachability, viability
and invariance problems. However, some shortcomings, such as the difficulties
of handling dissipation function and constructing terminal condition for
solving the Hamilton-Jacobi partial differential equation, limit the
application of level set method in some problems with non-affine nonlinear
systems and irregular target sets. In this paper, we propose a method which can
effectively avoid the above difficult issues thus has better generality. In the
proposed method, the reachable, viable and invariant sets are characterized by
some non-zero level sets of different value functions. Instead of solving
partial differential equations, the value functions are approximated by
recursion and interpolation. At the end of this paper, some examples are taken
to illustrate the accuracy and generality of the proposed method.
