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In this study, the problem of vibration control of structures involving parameter uncertainties and actuator saturation using hedge-algebras-based fuzzy controller (HAC) is presented. When structural damping and stiffness cannot always be measured easily and precisely, their uncertainties are assumed to be norm-bounded. The proposed controller is designed based on hedge algebras theory, where inherent order relationships between linguistic values of each linguistic variable, determined by isomorphisms mapping called semantically quantifying mapping based on few fuzziness parameters of each linguistic variable instead of using any fuzzy sets, are always ensured. The performance of the proposed controller is investigated by numerical simulations on active control of a benchmark three-storey building structure with active bracing system subjected to excitation of typical earthquakes. A conventional fuzzy controller, designed based on parameters similar to those of HAC, is also considered for the purpose of comparing effectiveness between controllers in order to shown advantages of the proposed method.

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This study investigates a multi-objective optimal solution for active Hedge-algebras-based control of building structures subjected to earthquakes. The stability condition of the system is considered the constraint in the optimization process. Values in reference ranges of the state variables and the control variable of the Hedge-algebras-based controller are considered as design variables. The objective functions simultaneously minimize the system’s peak relative displacement and absolute acceleration. The simulation results show that the optimized Hedge-algebras-based controllers have a higher efficiency than the published studies for primary objectives: the structure’s peak relative displacement and absolute acceleration. In addition, the Pareto front, representing a trade-off level between the above primary objectives, allows selecting the appropriate configuration of the controller for the controlled models.