A new methodology for an adaptive state observer design for a class of nonlinear systems with unknown parameters in unmeasured state dynamics

Abstract

An adaptive state observer is an adaptive observer that does not require the persistent excitation condition to estimate the state. The usual structural requirement for designing this kind of observers is that the unknown parameters explicitly appear in the measured state dynamics. This paper deals with the problem of adaptive state observer synthesis for a class of nonlinear systems with unknown parameters in unmeasured state dynamics. The novelty of the proposed approach is that it requires neither a canonical form nor the approximation of some of the output’s time derivatives. Firstly, we establish a new matrix equality that characterizes the structure of almost all systems found in the very small literature dealing with this problem. Then, this equality is exploited in the construction of the adaptation law. This simplifies the design procedure and makes it very similar to the conventional adaptive state observer design procedure. The problem of finding the observer gains is expressed as a linear matrix inequalities optimization problem. Two examples are given to demonstrate the validity of the proposed scheme.

Estimation of Liquid Level in a Harsh Environment Using Chaotic Observer

“…So, the prediction of their variables for the long term is important due to the randomness present in the input and measurement [31]. Using unmeasured state dynamics, a novel approach for designing an adaptive state observer for a class of nonlinear systems with unknown parameters was presented in [32]. These were not descriptor systems, though.…”

An observer-based continuous adaptive sliding mode guidance against chattering for homing missiles

“…In particular, the ESO method has been applied in the field of engineering and has created economic benefits, the features of ESO are summarized as: (1) ability to deal with vast types of unmodelled uncertainties and external disturbances (Huang and Xue, 2014; Zhao and Guo, 2016); (2) less information demand for dynamic systems (Chen et al, 2016); (3) simplicity in engineering implement; (4) energy saving (Zhao and Guo, 2016). Compared with linear ESO (Li et al, 2012), nonlinear extended state observer (NESO) (Zhang et al, 2013) has several advantages: fast convergence capability, adaptability (Oucief et al, 2016) and high control precision. The first NESO was proposed in late 1980s by Han (1995).…”