# Boundary Stabilization of a Bending and Twisting Wing by Linear Quadratic Gaussian Theory

## TL;DR

This paper develops a boundary stabilization method for a cantilever wing's bending and twisting using an infinite-dimensional LQR approach combined with a Kalman filter, incorporating aerodynamic forces based on Wagner's function.

## Contribution

It introduces a novel boundary control and estimation framework for wing stabilization using infinite-dimensional LQR and Kalman filtering with aerodynamic modeling.

## Key findings

- Effective boundary stabilization achieved for bending and twisting modes.
- Integration of aerodynamic forces into the control model.
- Demonstrated feasibility of the approach for high aspect ratio wings.

## Abstract

We first consider the stabilization of the bending and twisting of a rectangular cantilever beam of moderate to high aspect ratio using full state feedback boundary control. Our approach is an infinite dimesnional extension of Linear Quadratic Regulation (LQR). The we develop an infinite dimensional Kalman filter that processes two point measurements and returns an estimate of the full state. The Linear Quadartuc Gaussian approach is to use this estimate in the place of the full state in the LQR feedback Then we add aerodynamic forces to obtain a model of a wing. The aerodyamic model is based on a two dimensional state space approximate realiztion of Wagner's indicial function by R.~T.~Jones.