High gain observer for a class of nonlinear systems with coupled structure and sampled output measurements: application to a quadrotor

ABSTRACT

This paper proposes a new high gain observer for a class of non-uniformly observable nonlinear systems with coupled structure driven by sampled outputs. The considered class of systems is particularly constituted by several subsystems where each subsystem is associated to a subset of the output variables. The observer design is carried out through two steps. First, a high-gain observer is proposed in the continuous-time output case under the assumption that an adequate persistent excitation condition is satisfied by each subsystem. Then, the proposed observer is redesigned to handle the case of sampled outputs leading thereby to a continuous-discrete time observer. The latter property is achieved thanks to the approach pursued along the convergence analysis. The effectiveness of the proposed observer is emphasised in a realistic simulation framework involving a mathematical model of a quadrotor which is diffeomorphic to the proposed class of considered systems.

KEYWORDS:

• Non-uniformly observable nonlinear systems
• high gain observer design
• sampled output
• continuous-discrete time observer
• unmanned aerial vehicle

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Omar Hernández-González http://orcid.org/0000-0002-5870-556X

María-Eusebia Guerrero-Sánchez http://orcid.org/0000-0001-5256-6266

Additional information

Notes on contributors

Omar Hernández-González

Omar Hernández-González received his M.Sc. degree in electronic engineering from CENIDET, México, in 2008, and the Ph.D. degree in automatic control from the University of Caen Normandie, France, in 2017. Since 2008, he has held a position of Professor in the Technological Institute of México/Coatzacoalcos (ITESCO). His research interests include the nonlinear observers, nonlinear control, and UAV.

María-Eusebia Guerrero-Sánchez

María-Eusebia Guerrero-Sánchez María-Eusebia Guerrero-Sánchez received the Ph.D. degree in electronic engineering from the Centro Nacional de Investigación y Desarrollo Tecnológico (CENIDET), México, in 2017. She is currently a Professor at the Technological Institute of México/Coatzacoalcos (ITESCO). Her research interests are focused on passivity-based control, nonlinear control, and UAV.

Mondher Farza

Mondher Farza received his degrees of engineering and M.Sc. in computer sciences and applied mathematics from ENSEEIHT Toulouse in 1988. Then, he joined the Laboratoire d’Automatique de Grenoble from 1988 to 1994 and obtained his Ph.D. in control sciences in 1992. From 1994 to 1997, he occupied a postdoctoral position at Laboraoire d’Automatique et de Génie de Procédés in Lyon. He joined the University of Caen Normandie in 1997 where he occupies since 2007 the position of Professor. His research interests are in nonlinear control and systems and applications.

Tomas Ménard

Tomas Ménard received the B.S. and M.S. degrees in Mathematics from the University of Nantes, France, in 2005 and 2008, respectively. He joined the IRCCyN laboratory at Ecole Centrale de Nantes in 2008, where he received the Ph.D. degree in 2011. From 2011 to 2012, he held a postdoctoral position at the Research Center ‘E. Piaggio’ of the University of Pisa. In 2012, he joined the University of Caen, where he is currently assistant-professor. He received his Habilitation to direct research in 2017. In 2017–2018 he was teacher at Rajamangala University of Technology Thanyaburi, Thailand. His research interests include nonlinear observers, homogeneity theory and identification.

Mohammed M'Saad

Mohammed M'Saad was educated at the Ecole Mohammadia d’Ingénieurs where he held an assistant professor position in September 1978. He started his research activities at the LEESA where he prepared an engineering thesis of the Université de Mohammed V on the adaptive control of industrial processes. In November 1982, Mohammed M’SAAD joined the LAG to prepare a Ph.D. thesis of the Institut National Polytechnique de Grenoble on the fundamental features of the adaptive control and its applicability, which he obtained in April 1987. In April 1988, he held a research position at the CNRS with an affectation in the LAG. In September 1996, Mohammed M’Saad held a professor position at the ENSICAEN where he founded a control process laboratory in 1997 which became a control group at the GREYC UMR CNRS in January 2004 and a Control Laboratory of Caen since March 2017. His main research activities are mainly devoted to the fundamental, methodological and applied features of the identification, observation and adaptive control of dynamical systems.

Rogelio Lozano

Rogelio Lozano is CNRS Research Director at UTC, France. He obtained his Ph.D. degree in automatic control at Laboratoire d’Automatique de Grenoble, INPG in 1981. He was Professor at CINVESTAV, Mexico 1981–1989. He was a visiting professor at the University of Newcastle, Australia 1984–1985. He was Senior Researcher at NASA Langley Research Center, USA, 1987–1988. He was Head of the Heudiasyc Lab from 1995 to 2007. He was Associate Editor of Automatica from 1987 to 2000. He was member of the French National Committee from 2000 to 2006. He was Head of International Collaborations at CNRS STIC Department from 2006 to 2009. Since 2008 he is Head of the Joint Mexican-French UMI 3175 CNRS. He is currently associate Editor of the Journal of Intelligent and Robotics Systems since 2012 and Associate Editor in the International Journal of Adaptive Control and Signal Processing since 1988.