MINES ParisTech CAS - Centre automatique et systèmes

CONTROL ACROSS SCALES, BY POSITIVE AND NEGATIVE FEEDBACK

Séance du mercredi 22 mai 2019, Salle L224, 16h00-17h00.

Rodolphe SEPULCHRE, Cambridge University, UK

Abstract: Feedback is a key element of regulation, as it shapes the sensitivity of a process to its environment. Positive feedback up-regulates, negative feedback down-regulates. Many regulatory processes involve a mixture of both, whether in nature or in engineering. This talk revisits the mixed feedback paradigm, with the aim of investigating control across scales. We propose that mixed feedback regulates excitability and that excitability plays a central role in multi-scale signalling. We analyse this role in a multi-scale network architecture inspired from neurophysiology. The nodal behavior defines a meso-scale that connects actuation at the micro-scale to measurements at the macro-scale. We show that mixed-feedback control at the nodal scale provides regulatory principles at the network scale, with a nodal resolution. In this sense, the mixed feedback paradigm is a control principle across scales.

Biography: Rodolphe Sepulchre is Professor of Engineering at Cambridge University and a fellow of Sidney Sussex College. His research interests are in dynamics, control and optimization. He is currently deputy Editor-in-Chief of the IEEE Control Systems Magazine and Associate Editor of Annual Review of Control, Robotics, and Autonomous Systems. He bas been EiC of Systems and Control Letters from 2009 to 2018 and an Associate Editor for SIAM Journal of Control and Optimization, the Journal of Nonlinear Science, and Mathematics for Control, Signals, and Systems. In 2008, he was awarded the IEEE Control Systems Society Antonio Ruberti Young Researcher Prize. He is a fellow of IEEE and SIAM. He has been IEEE CSS distinguished lecturer between 2010 and 2015. A focus of his current research is the ERC advanced grant "Switchlets", motivated by neurophysiological questions and aiming at a multiresolution control theory of excitable systems. He co-authored the monographs "Constructive Nonlinear Control" (Springer-Verlag, 1997) and "Optimization on Matrix Manifolds" (Princeton University Press, 2008).this talk, I discuss the null controllability for the heat equations with variable coefficients in space in one dimension using the backstepping approach. To achieve the null controllability, the idea is to use a sequence of kernels where the damping constants go to infinity. The analysis is then based on a new proof of the well-posedness and the optimal bound with respect to damping constants for the solutions of the kernel equations.