Robust design of actively controlled structures using cooperative fuzzy games

The combined structural and control optimization problem for flexible space structures is formulated as a multiple objective optimization (MOO) problem. An improvement in robustness of active controlled structures through structural modifications is also addressed. The structural weight, controlled system energy, and robustness indices are considered as objective functions of the integrated structure/control design problem with cross-sectional areas of members treated as design variables. To model vague and imprecise information in the problem formulation, the tools of fuzzy set theory are employed. A new methodology for solving the resulting MOO problem, referred to herein as a cooperative fuzzy game theoretic approach is presented. It is shown that existing techniques for solving crisp and fuzzy optimization problems are special cases of the fuzzy game theoretic formulation. The computational procedure is demonstrated via an application to a twelve member ACOSS-FOUR space structure. The qualitative aspects of optimum solutions are discussed through transient response simulations. The concept of cooperative fuzzy games should be more generically useful in solving other design problems where deterministic and probabilistic techniques are difficult or impossible to use due to the inherent qualitative, imprecise or subjective nature of problem formulation.