Optimal Control Computation via Evolution Partial Differential Equation with Arbitrary Definite Conditions
For researchers in optimal control, this provides a more flexible method that can start from infeasible initial solutions, but the improvement is incremental.
The paper extends the Variation Evolving Method (VEM) to solve Optimal Control Problems (OCPs) by relaxing definite conditions from feasible to arbitrary solutions, constructing an unconstrained Lyapunov functional to guarantee convergence. Numerical examples demonstrate effectiveness.
The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the Optimal Control Problems (OCPs), by relaxing the definite conditions from a feasible solution to an arbitrary one for the derived Evolution Partial Differential Equation (EPDE). To guarantee the validity, an unconstrained Lyapunov functional that has the same minimum as the original OCP is constructed, and it ensures the evolution towards the optimal solution from infeasible solutions. With the semi-discrete method, the EPDE is transformed to the finite-dimensional Initial-value Problem (IVP), and then solved with common Ordinary Differential Equation (ODE) numerical integration methods. Illustrative examples are presented to show the effectiveness of the proposed method.