Model-Reference Adaptive Control of Distributed Lagrangian Infinite-Dimensional Systems Using Hamilton’s Principle
Nhan T. Nguyen, Kelley E. Hashemi, Ehsan Arabi, Tansel Yucelen
Abstract
This paper presents a Hamilton’s principle for distributed control of infinite-dimensional systems modeled by a distributed form of the Euler-Lagrange method. The distributed systems are governed by a system of linear partial differential equations in space and time. A generalized potential energy expression is developed that can capture most physical systems including those systems that have no spatial distribution. The Hamil- ton’s principle is applied to derive distributed feedback control methods without resorting to the standard weak-form discretization approach to convert an infinite-dimensional systems to a finite-dimensional systems. It can be shown by the principle of least action that the distributed control synthesized by the Hamilton’s prin- ciple is a minimum-norm control. A model-reference adaptive control framework is developed for distributed Lagrangian systems in the presence of uncertainty. The theory is demonstrated by an application of adaptive flutter suppression control of a flexible aircraft wing.