A Special Class of Multiple-criterion LQ Control

Optimal control is one of the most important methodologies for studies of dynamic systems in many areas of sciences, engineering and economics. In some cases, a single criterion may be insufficient to assess the performance of a control policy and multiple criteria should be considered. To facilitate optimal control decisions with multiple-criterion optimal control, we have to simultaneously consider all criteria and aggregate into one single-criterion model. The objective of this study is to extend the previously developed multiple-criterion optimal controls to incorporate a special class of problems which decision-maker has a preference ranking on the criteria.In the multiple-criterion optimal control studies, there is a technical difficulty of parameter-coupling in the scalarization scheme. We propose a re-formulation to simplify the solution scheme. The proposed algorithm is based on comparison of partial averages of scalarized performance indices and is easy-to-implement. Moreover, the algorithm requires no iterative search and offers high computational efficiency.