Multi-objective optimization of actively controlled structures with topological considerations

This paper presents a novel approach for the optimum design of actively controlled structures using both cooperative and Stackelberg game theoretic formulations wherein the structural topology is also optimized. Most of the available literature for design of actively controlled structures deals with structures of a predetermined topology. It is recognized that the structural performance can be improved significantly by the optimization of topology. The optimum topology is created herein by minimizing the strain energy. Once the optimum topology is obtained, a simultaneous sizing and control system optimization of the optimum topology is performed which (i) maximizes the energy dissipated by the controller, (ii) minimizes the structural weight, and (iii) minimizes the controller performance index. The design variables include actuator locations, member cross-sectional areas and entries of state and control weighting matrices. The multi-objective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the levels. Two numerical examples illustrating the proposed approach are presented wherein topological, structural and control system aspects of the problem are addressed comprehensively.