  An optimal control problem driven by an ordinary differential equation under
continuous state constraints is considered in this study. From an operational
point of view, we introduce a discrete state constraints optimal control
problem and prove that this discrete state constraints optimal control problem
is a near-optimal control problem of the original problem. Furthermore, we show
that the optimal solution of the near-optimal control problem converges to the
optimal solution of the original one. Finally, we use a linear quadratic
optimal problem to verify the main results of this study.
