Fourier-based optimal control approach for structural systems

This paper considers the optimal control of structural systems with quadratic performance indices. The proposed approach approximates each configuration variable of a structural model by the sum of a fifth-order polynomial and a finite-term Fourier-type series. In contrast to standard linear optimal control approaches, the method adopted here is a near optimal approach in which the necessary condition of optimality is derived as a system of linear algebraic equations. These equations can be solved directly by a method such as Gaussian elimination. The proposed approach is computationally efficient and can be applied to structural systems of high dimension and to systems with linear boundary constraints.