Variation Evolving for Optimal Control Computation, A Compact Way

A compact version of the Variation Evolving Method (VEM) is developed for the optimal control computation. It follows the idea that originates from the continuous-time dynamics stability theory in the control field. The optimal solution is analogized to the equilibrium point of a dynamic system and is anticipated to be obtained in an asymptotically evolving way. With the introduction of a virtual dimension——the variation time, the Evolution Partial Differential Equation (EPDE), which describes the variation motion towards the optimal solution, is deduced from the Optimal Control Problem (OCP), and the equivalent optimality conditions with no employment of costates are derived. Since the EPDE is suitable to be solved with the semi-discrete method in the field of PDE numerical calculation, the resulting Initial-value Problems (IVPs) may be solved with mature Ordinary Differential Equation (ODE) numerical integration methods.