Applied hybrid system optimization: An empirical investigation of complexity

Design techniques for controlled hybrid systems often have to account for the interaction of continuous and discrete degrees of freedom. The presence of the latter leads to a drastic increase of complexity with the problem size such that the applicability of many methods proposed recently was only demonstrated for relatively small systems. In this contribution, the limits of applicability for MILP-based techniques are investigated, and those parts of the problem that contribute most to complexity are isolated. The investigation is carried out exemplarily for a well-known approach to optimal control of hybrid systems where the control task is transformed into a mixed-integer programming problem. The influence of different indicators of the problem size on the computational effort is investigated theoretically and empirically for a scalable example. The results reveal which parameters are most critical for improving the practical solvability. (C) 2004 Elsevier Ltd. All rights reserved.