Filtered High-Gain Observer Design For a Class of Nonlinear Systems subject to Delayed Measurements: Application to a Quadrotor UAV

In this paper, a novel structure of a Filtered high-gain Observer is proposed for a class of nonlinear systems subject to delayed measurements, bounded disturbances and noise measurements effects. The structure of the proposed observer is able to obtain a larger bound of the Maximum Allowable Value of Time Delay (MAVTD) that ensures the convergence of the observer in comparison with the one obtained by standard High Gain methodology. The convergence of the proposed observer is provided by means of Lyapunov-Krasovskii functional. The efficiency of the proposed observer has been validated experimentally on real UAV systems.

I. INTRODUCTION

High Gain observers appeared as one of the most popular techniques for state estimation of nonlinear systems. The success of such an estimation tool is coming from their easy implementation and the fact that the accuracy and the convergence rate can be adjusted by one single parameter namely the" high-gain parameter" [8]. Besides these features the High Observers suffer from 3 major drawbacks: 1) The high dimension of the system and the high values of the High gain parameter. 2) The peaking phenomenon. 3) The sensitivity to the output disturbances such as the delay, as well as the measurements noise. In this paper we will focus only on the design of a new high-gain like observers subject to time delayed and measurements noise. To cope with the problem of delay data measurements, several observers based on the high-gain methodologies has been proposed [7], [10], [14], [15]. The problem is becoming more complex when it comes to the matter of providing a Maximum Allowable Value of the Time- Delay (MAVTD) that ensures the convergence of the high gain observer. Although, sufficient conditions on the delay and the high-gain parameter that ensure convergence were derived by the authors in these works. The value of the MAVTD remains small due to high value of the tuning parameter which is traditionally required to be high in standard high gain observer design framework. In [1], the authors tackled this problem by proposing a new method which combines the high gain observer design framework, the LPV approach and the LMI techniques. This new method called the HG/LMI observer exhibits good performance in terms of enlarging the MAVTD value in comparison with standard high gain methodologies, however the condition on the MAVTD still remains small since that it is inversely proportional to the tuning parameter.