LYAPUNOV OPTIMAL-CONTROL LAWS FOR FLEXIBLE STRUCTURE MANEUVER AND VIBRATION CONTROL

Abstract

An approach is presented for optimization of Lyapunov stable control laws for maneuvering of a flexible structure. The main idea is to establish a stabilizing control law using a Lyapunov approach and introduce some optimality condition for a particular control objective, and then optimize over the stable region of the free parameters in the control law. Our approach for designing the optimal control law consists of two stages. The first stage is to find a stabilizing form for the control law as a function of design parameters which are usually feedback gains. In the second stage, the control law is reshaped with the design parameters to satisfy an optimality criteria. Two kinds of control schemes, constant gain feedback and tracking type control laws, are discussed to establish different perspectives on the optimization. The optimization scheme used in this work is a sequential nonlinear programming algorithm which uses a homotopy method to sweep through a sequence of minimum norm design parameter changes. Our results show how our controlled performance is improved by optimizing the parameters appearing in the reference trajectory as well as the associated tracking feedback control law.