Design of a joint adaptive high‐gain observer for a class of nonlinear sampled‐output system with unknown states and parameters

Abstract

In this article, a joint adaptive high-gain observer design method is proposed for a class of nonlinear systems subject to sampled output data measurements. The considered class of system is characterized by a nonlinear term coupled with an unknown parameter that enters the system in both the outputs and the states equations. The fact that the considered system involves an output sampling process and an unknown parameter renders the design of the nonlinear adaptive observer more difficult. To overcome this difficulty, a novel closed-loop output predictor is proposed. Based on the well-known decoupling method between the state and unknown parameters, a joint adaptive high-gain observer which can simultaneously guarantee the exponential convergence of the estimation of the unknown state and the unknown parameter is proposed in this article. The structure of the designed observer has been extended to the case of sampled and delayed data measurements. The effectiveness of our proposed observer is demonstrated through numerical simulations and performance comparison with another observer structure proposed in the literature.

Predictor‐based continuous‐discrete nonlinear observer design subject to aperiodic sampled and delayed measurement

“…43 The NLNS (1) encompasses the modeling of integral chain systems commonly found in these applications. This feature greatly facilitates the design of high-gain observers, 23 widely used in nonlinear systems, as well as extended state observers to handle unknown dynamics. 41 Consequently, effective observer algorithms can be constructed, enabling accurate estimation.…”

“…Based on the principle of output predictor, 11 an output predictor-based observer was proposed, 20,21 whose required system output is compensated by a predicted output. This approach inspired some follow-up work, for example, the adaptive observer design, 22,23 the controller and observer joint design 24 and cascade observer design, 25 etc. The cascade observers are mainly used to deal with large delay, whose principle is exploiting a series of subobservers to estimate the states with different delays.…”

Continuous‐discrete high gain observer design with PI output predictor

“…In the case of output delay, compared with Lyapunov Krasovskii observer (LKO), 39 integral compensation-based observer (ICO) exhibits better scalability due to retaining the original observer structure, such as extending to situations where the system contains uncertainties. 22 In addition, in some cases, ICO has a faster convergence speed and smaller static error than LKO. 30 Compared with the previous observers' structures notably the ones designed in Wang et al 29,30 and Cuny et al, 40 the proposed observer structure ( 36)-( 37) is characterized by the following features:…”

“…Remark In the case of output delay, compared with Lyapunov Krasovskii observer (LKO), 39 integral compensation‐based observer (ICO) exhibits better scalability due to retaining the original observer structure, such as extending to situations where the system contains uncertainties 22 . In addition, in some cases, ICO has a faster convergence speed and smaller static error than LKO 30 .…”

“…This method is characterized by its simplicity since only one equation of the observer is initialized, in addition to the fact that the design does not change the original state observer structure. Scholars have extended this design to different cases, such as involving unknown parameters, 22,23 Multirate Sampled‐Data Observer 24 and so forth. In Reference 25, the authors introduced a closed‐loop correction term in the output predictor structure featuring larger sampling intervals in comparison with previous design approach 21 …”