Funnel Observation and Funnel Control

Research Centre: Systems and Control Research Centre

Title: Funnel Observations and Funnel Control

Abstract:

We introduce the funnel observer as a novel and simple adaptive observer of "high-gain type". We show that this observer is feasible for a large class of nonlinear systems described by functional differential equations which have a known strict relative degree, the internal dynamics map bounded signals to bounded signals, and the operators involved are sufficiently smooth. Apart from that the funnel observer does not need specific knowledge of the system parameters, and we show that it guarantees prescribed transient behavior of the observation error. We compare the funnel observer to existing (adaptive) high-gain observers and illustrate it by a simulation of a bioreactor model. In the second part of the talk, we show how the funnel observer can be used to design a funnel control law for relative degree two systems such that the derivative of the output is not needed.

Short Bio:

Thomas Berger was born in Germany in 1986. He received his Bachelor of Science in Mathematics (2008) and his Master of Science in Mathematics and Business Mathematics (2010) from Technische Universität Ilmenau, Germany. From September 2011 to February 2012 he was at the City University London, UK, for a research visit and cooperation with Professor Nicos Karcanias. In 2013 he received his PhD in Mathematics from Technische Universität Ilmenau, under the supervision of Professor Achim Ilchmann. Since December 2013 Dr. Berger is a postdoctoral research assistant at the Universität Hamburg, Germany. His research interest includes differential-algebraic systems, systems and control theory, electrical circuits and mechanical systems. Dr. Berger received several awards for his dissertation including the "2015 European PhD Award on Control for Complex and Heterogeneous Systems" from the European Embedded Control Institute and the "Dr.-Körper-Preis 2015" from the International Association of Applied Mathematics and Mechanics.