Application of Optimal Control Theory to Civil Engineering Structures

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Abstract
Modern control theory has been successfully applied to control the motions of aerospace vehicles. An exploratory study is made herein to investigate the feasibility of applying such a theory to control the vibration of civil engineering structures under random loadings. It is assumed that random excitations to structures, such as wind loads and earthquakes, can be modeled by passing either a stationary Gaussian white noise or a nonstationary Gaussian shot noise through a filter. The performance index to be minimized consists of the covariances of both the structural responses and the control forces. Under these conditions, the optimal control law is a linear feedback control. The optimal control forces are obtained by solving a matrix Riccati equation. Applications of the optimal control to a multi-degree-of-freedom structure, under stationary wind loads and nonstationary earthquakes, are demonstrated. It is shown that significant reduction in covariances of the structural responses can be achieved by the use of an active control system.

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