# Earthquake Hazard Mitigation for Uncertain Building Systems Based on Adaptive Synergetic Control
###### Abstract
Stability analysis based on the Lyapunov functional was conducted to prove the finite-time stability of the controlled structure and to solve the problem of sufficient conditions arising from tolerated saturation. The study showed that the controlled system was finite-time stable, and the attenuation of vibration was successively achieved within a specified level of disturbance rejection. In [17], [PERSON] et al. proposed a control scheme, based on adaptive model reference sliding model control, to suppress the vibration of a multi-degree-of-freedom (MDOF) nonlinear building structure due to earthquake. The building was supported by an active mass damper (AMD), and the control design incorporated a modified unscented Kalman filter (UKF) to estimate the states and unknown parameters to synthesize the required control forces in an adaptive manner. In [18], [PERSON] et al. conducted adaptive control design using adaptive backstepping sliding mode control to mitigate the effect of vibrations in a building structure with uncertain building coefficients due to earthquake action. The study addressed a single-degree-of-freedom building, and the numerical simulation showed that better capability of suppression was obtained with the proposed adaptive scheme as compared to the conventional non-adaptive backstepping sliding mode controller. In [19], [PERSON] et al. presented a comparative study based on two passive control schemes to reduce the effect of resonant vibrations of a three-story building-like structure vibrated by an electromechanical shaker at its base. On the third floor of the structure, the first control scheme was established to actuate a Tuned Mass Damper, while an auto-parametric cantilever beam absorber was controlled by the second control scheme. A finite element model was developed to validate the frequency response, and the controlled building structure was verified via both numerical and experimental results. In [20], [PERSON] and [PERSON] reduced the effect of buffeting response in tall buildings by designing an LQR control scheme based on an Active Tuned Mass Damper (ATMD). As compared to other control schemes, the proposed control technique based on a flexible damper showed better control objectives. In [21], [PERSON] and [PERSON] presented a control design based on a fuzzy logic controller (FLC) and PID controllers to reject the vibration of an earthquakes building structure in the presence of nonlinear behavior in the soil structure. In representing the dynamic model of the structural system, the nonlinear behavior of the soil was characterized by nonlinear hysteresis and restoring forces. The variation in mass parameters at each story was addressed by the FL controller. In [22], [PERSON]. [PERSON] et al. presented an online algebraic identification technique for parameters of a flexible structure based on modal decomposition and frequency transform analysis. The proposed identification technique was used to support two control schemes for a perturbed building-like structure subjected to resonant operational conditions. A pendulum vibration absorber was applied to act as an auto-parametric system, and a tuned mass damper was used in order to mitigate resonance excitation. It has been shown that the control approach based on sliding mode control (SMC) is the most efficient, as compared to other control techniques, when suppression of building vibration is required. However, the chattering phenomenon accompanying this control approach design degrades its efficacy. As such, this study explored synergetic control (SC) to solve this problem. The concept of synergetic control is based on synergetic theory, which is inspired by state-space theory. This control approach has been applied in the control design of highly complex, nonlinear, coupled, and connected systems.