# Earthquake Hazard Mitigation for Uncertain Building Systems Based on Adaptive Synergetic Control
###### Abstract  
This study presents an adaptive control scheme based on synergetic control theory for suppressing the vibration of building structures due to earthquake. The control key for the proposed controller is based on a magneto-rheological (MR) damper, which supports the building. According to Lyapunov-based stability analysis, an adaptive synergetic control (ASC) strategy was established under variation of the stiffness and viscosity coefficients in the vibrated building. The control and adaptive laws of the ASC were developed to ensure the stability of the controlled structure. The proposed controller addresses the suppression problem of a single-degree-of-freedom (SDOF) building model, and an earthquake control scenario was conducted and simulated on the basis of earthquake acceleration data recorded from the El Centro Imperial Valley Earthquake. The effectiveness of the adaptive synergetic control was verified and assessed via numerical simulation, and a comparison study was conducted between the adaptive and classical versions of synergetic control (SC). The vibration suppression index was used to evaluate both controllers. The numerical simulation showed the capability of the proposed adaptive controller to stabilize and to suppress the vibration of a building subjected to earthquake. In addition, the adaptive controller successfully kept the estimated viscosity and stiffness coefficients bounded. s +
Footnote †: journal: Applied systems  
and efficiency with a tradeoff of high cost. The semi-active control systems are a class of active control systems that are supplied with limited external power sources to monitor the actual motions of building structures and to provide the necessary forces that ensure the stability of the controlled building structures. Due to their many benefits, magneto-rheological (MR) dampers have recently been studied, along with other semi-active devices, for the purpose of reducing earthquake risk. A magneto-rheological damper is a smart device that is supplied by synthetic fluids. The viscosity of the damper fluid can be adjusted from a liquid state to a semi-solid state in milliseconds by applying an electric current to embedded coils. Mechanical simplicity, strong dynamic range, low power requirements, low cost, and extremely quick and excellent control effort responses are some of the distinguishing features of these dampers [2]. To mitigate structural vibration, the control strategies that incorporate MR dampers in their actions can be classified into two categories. The first type is based on Lyapunov stability analysis, which, in turn, requires a mathematical model of the device [3], while the second type applies intelligent control techniques to develop the control signals, where a mathematical model of the device is not required [4]. The hybrid category is the third type of control technique, mixing both classes of control approaches [5]. Many previous studies have presented various control strategies to suppress the vibration of buildings subjected to earthquakes. The following is a brief review of various control approaches that have been applied for the vibration control of buildings under earthquakes. In [1], [PERSON] et al. proposed regulation control to suppress structural vibration during earthquakes based on a semi-active MR damper. The control design presented a robust feedback law based on a Linear Quadratic Regulator (LQR) to actuate the MR damper with the required control energy to reduce the effect of vibration for a three-story building structure supported by an MR damper on the building's first floor. In [2], [PERSON] et al. developed an adaptive control method to suppress the vibration of building structures against earthquake excitation and wind loading by utilizing a semi-active MR damper. Adaptive laws were developed to estimate the unknown parameters of the MR damper, while a nonlinear observer was applied to estimate the unmeasurable internal state variable.