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Estimation of bridge’s parameters is bound to give rise to a certain amount of inaccuracy. Given the size of cable-stayed bridge structures, any percentage of error can lead to estimated stiffness, mass, and damping that differ greatly from the actual structural parameters. During their service life, bridge structures experience cracking, temperature variations, localized damage, and deterioration, which result in parametric variation. Adaptive control strategies can be a good alternative to control bridges subjected to seismic excitation, as they present robustness when in face of parametric variation. In this study, a semi-active adaptive control approach is proposed for mitigation of seismic responses of cable-stayed bridges. The approach is based on the simple adaptive control, which is a direct model reference adaptive control strategy for multiple-input–multiple-output systems, proven to guarantee perfect tracking asymptotically, and successfully avoid the use of observers. The proposed adaptive scheme adopts the nominal bridge controlled by the linear–quadratic regulator with full-feedback as a model reference. The adaptive technique is implemented to control semi-active magnetorheological damper devices, considering realistic implementation and design. The scheme’s ability in reducing seismic response of a cable-stayed bridge subjected to three earthquake records with different angles of incidence is evaluated and its performance is compared to classical control solutions. In order to evaluate robustness of the control scheme proposed, two different parametric changes are introduced. The proposed adaptive scheme gives the least average variation in performance for all the different parametric variations considered. The control solution presents increased robustness when compared to passive and semi-active resettable controllers; it requires a small number of nodes to be monitored and avoids complicated reconstruction of states.

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Parametric variations occur throughout a bridge’s service life as a result of temperature variations, cracking, localized damage, and fatigue. Existing bridge’s parameters are difficult to estimate precisely and implemented control schemes may perform unsatisfactorily depending on how sensitive they are to parametric change. In this study, an adaptive control approach is developed utilizing the simple adaptive control algorithm and designed aiming to mitigate seismic responses of bridges considering realistic implementation. Adaptive control is a viable alternative to control bridge structures as it is able to calculate control gains that vary over time based on sensed responses, sustaining performance in face of parametric variations. The proposed approach allows the choice of a model reference of significantly low order and it does not require full-state feedback or the use of observers. The effectiveness and robustness of the control approach are investigated when controlling a seismically excited two-span highway bridge considering systematic parametric variations. Evaluation of relevant performance criteria indicates that the adaptive scheme is effective in reducing seismic responses and sustains well the overall performance when systematic parametric variations are introduced. The proposed approach requires a small and reasonable number of sensors to present effectiveness and performs satisfactorily even when in the presence of measurement noise.