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Tuesday 07 Dec 2021Control-based Continuation A new paradigm for testing nonlinear systems

Ludovic Renson - Imperial University

Harrison 101 13:30-14:30

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) – a method originally proposed by Sieber & Krauskopf in 2008 – 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 a mechanical structure exhibiting modal interactions. I will then discuss the use of local surrogate models to improve the robustness of path following techniques in the presence of noise and perform more efficient data collection. I will then conclude by discussing our attempts to extend CBC to autonomous systems and systems with multiple time scales such as neurons

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