An Approach Problem for Control Systems Based on Runge-Kutta Methods

This paper explores nonlinear control systems within a finite dimensional Euclidean space. To guide the system towards a compact set at a specific time instant, the approach presented in this paper relies on the construction of approximate solvability sets. The Runge-Kutta methods, coupled with distance clustering, is employed to construct these approximate solvability sets. Simultaneously, the corresponding controls are recorded. The effectiveness of our theoretical results is demonstrated through simulation results.