Section: New Results

Nonlinear Observer Design via LMIs

Participants : Ali Zemouche, Rajesh Rajamani [University of Minneapolis, USA] , Hieu Trinh [Deakin University, Australia] , Yan Wang [University of Minneapolis, USA] , Michel Zasadzinski [CRAN] , Hugues Rafaralahy [CRAN] , Boulaid Boulkroune [Flanders Make, Lommel, Belgium] , Gridsada Phanomchoeng [Chulalongkorn University,Thailand] , Khadidja Chaib-Draa [University of Luxembourg] , Mohamed Darouach [CRAN] , Marouane Alma [CRAN] , Holger Voos [University of Luxembourg] .

• Observer Design for Lipschitz and Monotonic nonlinear systems using LMIs:

  New LMI (Linear Matrix Inequality) design techniques have been developed to address the problem of designing performant observers for a class of nonlinear systems. The developed techniques apply to both locally Lipschitz as well as monotonic nonlinear systems, and allows for nonlinear functions in both the process dynamics and output equations [59], [34]. The LMI design conditions obtained are less conservative than all previous results proposed in literature for these classes of nonlinear systems. By judicious use of Young's relation, additional degrees of freedom are included in the observer design. These additional decision variables enable improvements in the feasibility of the obtained LMI. Several recent results in literature are shown to be particular cases of the more general observer design methodology developed in this paper. Illustrative examples are used to show the effectiveness of the proposed methodology. The application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented. Although this application was the main motivation of this work, the proposed techniques have been applied to an anaerobic digestion model for different contexts [43], [44], [45].

• HG/LMI Observer:

  A new high-gain observer design method with lower gain compared to the standard high-gain observer was proposed [62]. This new observer, called "HG/LMI" observer is obtained by combining the standard high-gain methodology with the LPVLMI-based technique. Through analytical developments, it is shown how the new observer provides a lower gain. A numerical example was used to illustrate the performance of the new "HG/LMI" observer that we can call "smart high-gain observer". The aim of this research is the application of this new observer design to estimate some variables in vehicle applications and other real-world applications.

• Dual Spatially Separated Sensors for Enhanced Estimation:

  Inspired by the function of spatially separated sensory organs found in nature, we explored the use of dual spatially separated sensors for enhanced estimation in modern engineering applications [26]. To illustrate the interest of dual spatially separated sensors, some real applications have been considered: 1) Adaptive parameter and state estimation in magnetic sensors; 2) Estimation of an unknown disturbance input in an automotive suspension; 3) Separation of inputs based on their direction of action in a digital stethoscope. Both analytical observer design developments and experimental evaluation of the results have been provided.