Flatness and higher order differential model representations in dynamic optimization

Abstract A novel class of methods for solving path and end point constrained dynamic optimization problems is proposed. These methods aim at improving the performance of dynamic optimization algorithms employed in on-line applications, where the required solution time is a major concern. The presented approaches are all based on the reformulation of the dynamic model constraints into a higher order differential model representation, in which state variable derivatives are eliminated. Based upon this representation, the complete state information can be accessed analytically through explicit equations, implying that numerical integration, as required by sequential optimization techniques, is thus avoided. Since these equations depend on only a relatively few variables containing the entire dynamic system behavior, advantages over simultaneous optimization strategies can be expected as well. Three different dynamic optimization problem formulations involving higher order differential model representations are discussed, of which the first requires the dynamic system to be differentially flat. The remaining two, however, do not depend on the flatness property. By means of a set of examples, the three problem formulations are illustrated and classified according to their potential to improve the efficiency in solving dynamic optimization problems.