Optimal control of distributed processes using reduced order models

The open loop optimal control (dynamic optimization) of distributed parameter systems is considered here. These problems are usually solved by the Control Vector Parameterization (CVP) approach, which transforms the original dynamic optimization method into an outer nonlinear programming problem, which requires the solution of an inner initial value problem (IVP). The solution of this IVP (set of partial and ordinary differential equations) for each function evaluation is usually very demanding in terms of computation time, thus efficient numerical techniques are necessary in order to reduce the overall computational effort of the CVP optimizations. In this work, the use of low order models, obtained by Galërking projection on a set of proper orthogonal functions, is presented as a very efficient alternative for the rapid solution of this class of problems.