Fuzzy optimal controller design with application to fuzzy modeled structures

Fuzzy analysis can be used to model the uncertainties present in structures. In particular, the fuzzy finite element method can be used to find the response of structures (isotropic or composite) involving uncertainties. For the integrated structural control of a system, the design of a fuzzy optimal controller is explored. In the past few years, some researchers have tried to design a fuzzy optimal controller based on the Takagi and Sugeno model. In this work, a different (new) approach is proposed for the design of a controller in the context of fuzzy optimal control theory. In most practical applications, the structural and material parameters vary considerably and are subject to uncertainties, mainly due to the uncontrollable aspects associated with the manufacturing and assembly of composite materials. These uncertainties, in many cases, cannot be modeled probabilistically because the probability distributions of the uncertain parameters are not usually known. Also, in some situations, the parameters are known only in linguistic form. A fuzzy finite element approach has been developed for the analysis of structures with fuzzy parameters. Using the deterministic optimal control theory as a basis, a fuzzy optimal control theory is developed so that the controller can be used to act as either a regulator or a tracking system. The control of a planar truss is presented to demonstrate the feasibility and applicability of the methodology presented.