Generalized optimal control policy for stochastic optimal control of structures

A generalized formulation of optimal control policy for physical stochastic optimal control of structures is proposed in this paper, which extends the classic forms of optimal control policies of passively controlled modalities, actively controlled modalities, semi-actively controlled modalities, and hybridly controlled modalities. This unified scheme features the simultaneous consideration of optimal control force and optimal placement of control devices. A new controllability index associated with the exceedance probability is developed, which characterizes system safety, system serviceability, system comfort, control device workability, and their trade-off. A sequential procedure with a minimum storey controllability index gradient is defined to efficiently search for the optimal topology of control devices. Furthermore, a performance function for parameters optimization is proposed, which exhibits the same practical accounts as the controllability index. The resolution procedure of the generalized optimal control policy is detailed, and two randomly base-excited structural systems are investigated for illustrative purposes, which consist of a ten-storey shear frame equipped with viscoelastic dampers and an eight-storey shear frame controlled by active tendons. Numerical results reveal that the proposed generalized optimal control policy can gain the maximum control effectiveness with the minimum control cost. The controlled system response is significantly reduced and becomes smoother along the height of the structure, which results in a more desirable structural performance. Using the design criterion, meanwhile, of the minimum storey controllability index gradient, the structural stochastic optimal control achieves the objective performance more efficiently than that of the maximum storey controllability index currently in use. Copyright (c) 2011 John Wiley & Sons, Ltd.