  Enlightened from the inverse consideration of the stable continuous-time
dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal
solution to the equilibrium point of an infinite-dimensional dynamic system and
solves it in an asymptotically evolving way. In this paper, the compact version
of the VEM is further developed for the computation of Optimal Control Problems
(OCPs) with terminal constraint. The corresponding Evolution Partial
Differential Equation (EPDE), which describes the variation motion towards the
optimal solution, is derived, and the costate-free optimality conditions are
established. The explicit analytic expressions of the costates and the Lagrange
multipliers adjoining the terminal constraint, related to the states and the
control variables, are presented. With the semi-discrete method in the field of
PDE numerical calculation, the EPDE is discretized as finite-dimensional
Initial-value Problems (IVPs) to be solved, with common Ordinary Differential
Equation (ODE) numerical integration methods.
