Optimisation of Region of Attraction Estimates for the Exponential Stabilisation of the Intrinsic Geometrically Exact Beam Model

TL;DR

This paper introduces a systematic method to optimize the region of attraction estimates for stabilizing nonlinear beam models using boundary feedback, leveraging Lyapunov functionals and semi-definite programming.

Contribution

It presents a novel approach to maximize stability bounds for nonlinear beam models through polynomial Lyapunov functionals and iterative semi-definite programming.

Findings

Enhanced estimates of the region of attraction for beam stabilization.

Demonstrated effectiveness of the semi-definite programming approach.

Improved stability bounds compared to previous methods.

Abstract

A systematic approach to maximise estimates on the region of attraction in the exponential stabilisation of geometrically exact (nonlinear) beam models via boundary feedback is presented. Starting from recently established stability results based on Lyapunov arguments, the main contribution of the presented work is to maximise the analytically found bounds on the initial datum, for which local exponential stability is guaranteed, via search of (optimal) polynomial Lyapunov functionals using an iterative semi-definite programming approach.