Abstract
This paper treats the following design problem: find the set of design parameters which minimizes the cost of an idealized multi-story framed structure, subject to constraints that the relative displacements between adjacent story levels do not exceed preassigned limits when the structure is subjected to ground motion of a design earthquake. The design problem has the format of a state-constrained optimal control problem, which is solved by an algorithm based on a recent paper of Polak and Mayne. Because of hysteresis in the operator equation describing system dynamics, directional derivatives of the constraints cannot be calculated by standard techniques. Formulae for calculating the required derivatives appearing in the basic algorithm are presented and discussed.
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