Recent publications have presented successful implementations of adaptive control techniques in various applications whereas its application on vibration suppression of civil infrastructures under adverse conditions is not well developed. The advantage of a model-reference adaptive structural control (MRASC) algorithm is to adjust the control command signal and to force the controlled system follow the trajectory of designed reference model while estimating properties of the controlled structure in real time. An adaptive control application based on Lyapunov stability theory is presented in this paper. The Lyapunov equation used to define the adaptation law is designed based on a quadratic Lyapunov function candidate. This energy-like scalar function comprises weighted tracking-error states and parameterestimating error matrix. The adaptive feedback control force is calculated from both measured states and adjustable parameters estimated from the adaptation law. The tracking-error states illustrate the trajectory tracking performance between reference model and controlled system. The global asymptotical stability is guaranteed by choosing a pair of positive-definite weighting matrices for the time-invariant linear system. Systematic procedures based on fast convergence rate of the adjustable parameters are proposed to determine appropriate combination of coefficients embedded in the weighing matrices of Lyapunov function. A series of control performance investigation is performed on a single degree-of-freedom active tendon structure subjected to different earthquake excitations.
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