Control Vector Parameterization Method with Time Nodes Parameters

Abstract

A time nodes optimization method is presented for the solution of optimal control problems (OCP) using control vector parameterization (CVP). The control variable in each time interval is approached by a function of time nodes parameters and other decision parameters. The infinite dimensional optimal control problems were approximated into nonlinear programming (NLP) problems, the gradient of which can be analytically obtained. The NLP problems were solved and resulted in non-uniform time grid. Two cases of optimal control problem were solved by the proposed methodology. One is OCP of an ODE system and the superior results are given comparing with the fixed time grid method. Another is optimal injection strategy determination of polymer flooding, which is a sort of OCP constrained to satisfy PDEs. The efficiency is illustrated for solving this kind of problem by the given method.