A family of optimal control schemes for enhancing seismic performance of randomly base-driven structures is developed in this paper.Its principles are derived from the novel theoretical framework of physical stochastic systems

towards breaking through the barriers inherent in the classical stochastic optimal controls described by Ito[DD(-*3/5]^ stochastic differential equations.Having this knowledge

we proposed three classes of probabilistic criteria associated with parameters of control devices

including the probabilistic criterion in conjunction with system statistics assessment

the probabilistic criterion in conjunction with the exceedance probability of single objective and the probabilistic criterion in conjunction with the energy trade-off of multiple objective.These criteria are logically integrated into the generalized optimal control policy with probabilistic criterion for optimal allocation of control devices based on probabilistic controllability index.Two cases of randomly base-driven structural systems

controlled by active tendons

are investigated for illustrative purposes.The numerical results reveal that the proposed methodology can implement the accurate control of seismic performance of base-driven structures.