Simultaneous Optimal Design of Structural Layout, Shape and Control Systems for Truss Structure

Abstract

This paper addresses simultaneous optimal design of adaptive truss structures, in which we compromise structural and control systems while taking into account structural layout, shape and control systems. The problem becomes nonconvex discrete optimization problem in terms of continuous and discrete design variables. Noticing that the nonconvex problem can be approximated by a convex one by adding a semidefinite positive function, so-called a convexifying function, to make the constraint convex, first, we solve this nonconvex problem using successive LMI optimization in cross-sectional area of truss members and state feedback gains. Second, we solve this discrete problem using genetic algorithm for simultaneous optimization of layout of truss structures. In this way, a hybrid method combining successive LMI optimization and genetic algorithm is used in this study. A numerical example of a simple structure is provided to demonstrate the effectiveness of the proposed method.