  Computation of general state- and/or control-constrained Optimal Control
Problems (OCPs) is difficult for various constraints, especially the
intractable path constraint. For such problems, the theoretical convergence of
numerical algorithms is usually not guaranteed, and the right solution may not
be successfully obtained. With the recently proposed Variation Evolving Method
(VEM), the evolution equations, which guarantee the convergence towards the
optimal solution in theory even for the general constrained OCPs, are derived.
In particular, the costate-free optimality conditions are established. Besides
the analytic expressions of the costates and the Lagrange multipliers adjoining
the terminal constraint, the integral equation that determines the
Karush-Kuhn-Tucker (KKT) multiplier variable is also derived. Upon the work in
this paper, the general constrained OCPs may be transformed to the
Initial-value Problems (IVPs) to be solved, with common Ordinary Differential
Equation (ODE) numerical integration methods.
