Proper Orthogonal Decomposition technique for sub-optimal control of flexible aircraft wings using discrete actuators

Distributed parameter systems are, generally, described by a set of partial differential equations. Control design of these systems is a very complex task as compared to that of the lumped parameter systems that are defined by a set of ordinary differential equations. In this paper, we present a stabilizing state-feedback control design approach for a class of second order system, where the system can be controlled by discrete actuators in the spatial domain. The control methodology is developed by combining the technique of `Proper Orthogonal Decomposition´ and Approximate Dynamic Programming. The Proper Orthogonal Decomposition technique is utilized to obtain a low-order nonlinear lumped parameter model of the underlying infinite dimensional system. A sub-optimal state-feedback controller is, then, designed using the single-network adaptive-critic technique. A flexible aircraft wing model is used in this study to demonstrate the online implementation of the controller as designed from the presented methodology.