  A new method for the optimal solutions is proposed. Originating from the
continuous-time dynamics stability theory in the control field, the optimal
solution is anticipated to be obtained in an asymptotically evolving way. By
introducing a virtual dimension, the variation time, a dynamic system that
describes the variation motion is deduced from the Optimal Control Problem
(OCP), and the optimal solution is its equilibrium point. Through this method,
the intractable OCP is transformed to the Initial-value Problem (IVP) and it
may be solved with mature Ordinary Differential Equation (ODE) numerical
integration methods. Especially, the deduced dynamic system is globally stable,
so any initial value will evolve to the extremal solution ultimately.
