Control-Based Continuation – A New Paradigm for Testing Nonlinear Systems by Ludovic Renson, November 2021

Control-Based Continuation – A New Paradigm for Testing Nonlinear Systems

Ludovic Renson

Imperial College London, London, UK

November 16, 2021

Abstract:

Numerical continuation is a systematic and efficient computational tool to capture the established responses of nonlinear dynamic systems and detect boundaries between qualitatively and quantitatively distinct types of responses (bifurcations). Numerical continuation offers many advantages compared to direct, initial-value simulations and has therefore become one of the most popular methods for nonlinear dynamic analysis.

In this talk, I will argue that experimental testing methods commonly used to characterise the behaviour of nonlinear systems are analogue to direct simulations, and therefore new methods to test nonlinear systems more efficiently and systematically are required. Control-based continuation (CBC) is one of these methods. It uses feedback control to apply the principles of numerical continuation to a physical system, without the need for a mathematical model. I will introduce the principles of CBC and illustrate some of its capabilities on an academic structure with modal interaction. I will briefly compare the method with other similar approaches in the literature and present some recent work extending CBC to autonomous systems and systems with multiple time scales, including those with impact nonlinearity. I will briefly illustrate how responses measured with CBC can be used for parameter estimation and, to conclude, discuss some of the key challenges that need to be addressed to make CBC a widely applicable tool.

Biography:

Dr. Ludovic Renson is a Lecturer in the Department of Mechanical Engineering at Imperial College London where he leads a research group on nonlinear dynamics and control. Ludovic obtained his PhD at the University of Liege (Belgium) in 2014. Ludovic was a postdoctoral research fellow at the University of Bristol prior to his appointment at Imperial in 2019.