Non-linear optimal control of a Duffing system (Q1187551)

The Duffing oscillator is a useful current model for the behavior of structural systems including columns, gyroscopes, plates, pendulums and certain types of bridges. This paper studies a class of nonlinear optimal controls for these oscillators, and determines the effects of higher- order feedback corrections based upon series expansions of the optimal cost function and the optimal control function in a Hamilton-Jacobi context. A novel representation of the solution is presented, in terms of the indicial formulation of tensor algebra. Numerical studies are provided, and an analysis of the effect of higher-order feedbacks upon the stability region of the controlled system is presented.