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

An approach is presented for optimization of Lyapunov stable control l aws for maneuvering of a flexible structure. The main idea is to estab lish a stabilizing control law using a Lyapunov approach and introduce some optimality condition for a particular control objective, and the n optimize over the stable region of the free parameters in the contro l law. Our approach for designing the optimal control law consists of two stages. The first stage is to find a stabilizing form for the cont rol law as a function of design parameters which are usually feedback gains. In the second stage, the control law is reshaped with the desig n parameters to satisfy an optimality criteria. Two kinds of control s chemes, constant gain feedback and tracking type control laws, are dis cussed to establish different perspectives on the optimization. The op timization scheme used in this work is a sequential nonlinear programm ing algorithm which uses a homotopy method to sweep through a sequence of minimum norm design parameter changes. Our results show how our co ntrolled performance is improved by optimizing the parameters appearin g in the reference trajectory as well as the associated tracking feedb ack control law.