The forward reachable set of a control system at a certain time is the set of states that can be reached at this time from the initial state. In order to solve the forward reachable set of a nonlinear control system

numerical methods for ordinary differential equations was used to discretize the continuous control system. Since the reachable set of a continuous system can be approximated by its discrete counterpart

a grid projection method based on optimization technology was proposed to approximate the reachable set. In this method

uniformly distributed grid points were placed and projected to the boundary of reachable set for a discrete control; each projection problem corresponded to an optimization problem; by solving these problems the approximated description of the reachable set was obtained. Theoretical analysis proves that the smaller the grid interval

the smaller the approximation error. Finally

numerical results verified the effectiveness of the proposed method

which were compared with those of the DFOG(distance fields on grids) method in literature. The research shows that the grid projection method can effectively handle control systems with non-convex reachable sets. Compared with the DFOG method

the method gets uniform distributed boundary points

solves less optimization problems and uses less computation time.