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

Abstract

Summary In this article, a joint adaptive observer design method is proposed for a class of affine nonlinear systems subject to sampled output data measurements. The considered class of system contains nonlinear terms which depend on unknown parameters. The considered unknown parameters enter the system in both the output and the system states equations which render the design of the sampled data observer for the affine nonlinear system more difficult to conceive. To solve this problem, and based on a new method of decoupling parameter estimation and state observation, a new online output sampling joint adaptive observer is proposed in this article, which can simultaneously guarantees the exponential convergence of the estimation of unknown state and parameter. The structure of the proposed observer has been extended to the case of sampled and delayed data measurements. To illustrate the performance of the proposed observer, a comparison is made with another observer with an output predictor on a satellite navigation system. And the observer proposed in this article is applied to the model‐free control of ultra‐local models.

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

“…Remark Equations (19)–(26) are the decoupling of system state and unknown parameters, which was first proposed by Zhang for linear systems 19 and was generalized to the case of sampling with a zero‐order hold in our previous work 26,27 . This article considers nonlinear systems and uses a new output predictor to deal with sampled output, which is different from previous results.…”

“…The first half of Step I is the same as (16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35). Following (36) and (38), one gets…”

“…One of them is the so‐called zero‐order holder (ZOH) approach. Based on this idea, Ahmed‐Ali et al 25 and Ahmed‐Ali 26 designed continuous‐discrete adaptive observers for a class of state affine systems with unknown parameters in the output equation, which is extended to the case where the state equation also has unknown parameters by Zhuang et al 27 Using the principle of iterative learning, an observer is designed by Ran et al 18 for the linear time‐invariant (LTI) system with unknown parameters in the state equation.…”

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

“…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

“…The observer stability was investigated by means of Lyapunov‐Krasowski functional. Zhuang et al 12 extended also the structure of the designed observer in Ahmed‐Ali et al 10 and Ahmed‐Ali 11 to a more general class of systems where the unknown parameter enters the system via the system states and the output equation. Farza et al, 13 introduced an exponential decay term in the corrective gain of the observer.…”