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The compact Variation Evolving Method (VEM) that originates from thecontinuous-time dynamics stability theory seeks the optimal solutions withvariation evolution principle. It is further developed to be more flexible insolving the Optimal Control Problems (OCPs), by relaxing the definiteconditions from a feasible solution to an arbitrary one for the derivedEvolution Partial Differential Equation (EPDE). To guarantee the validity, anunconstrained Lyapunov functional that has the same minimum as the original OCPis constructed, and it ensures the evolution towards the optimal solution frominfeasible solutions. With the semi-discrete method, the EPDE is transformed tothe finite-dimensional Initial-value Problem (IVP), and then solved with commonOrdinary Differential Equation (ODE) numerical integration methods.Illustrative examples are presented to show the effectiveness of the proposedmethod.

Optimal Control Computation via Evolution Partial Differential Equation with Arbitrary Definite Conditions