Enhancement of adaptive observer robustness applying sliding mode techniques

Abstract

The problem studied in this paper is one of improving the performance of a class of adaptive observer in the presence of exogenous disturbances. The H∞ gains of both, a conventional and the newly proposed sliding-mode adaptive observer, are evaluated to assess the effect of disturbances on the estimation errors. It is shown that if the disturbance is "matched" in the plant equations, then including an additional sliding-mode feedback injection term, dependent on the plant output, improves the accuracy of observation.

An adaptive sliding‐mode observer for a class of uncertain nonlinear systems

“…This paper contributes with a nonlinear adaptive sliding-mode observer based on a nonlinear parameter identification algorithm for uncertain nonlinear systems. The proposed nonlinear adaptive sliding-mode observer is a modified version of the one proposed by Efimov et al 24 Such a modification lies in the inclusion of a nonlinear parameter identification algorithm that provides a rate of convergence faster than exponential, ie, faster than classic linear algorithms. Then, the proposed parameter identification algorithm is included in the structure of a sliding-mode state observer, providing an ultimate bound for the state and parameter estimation error and attenuating the effects of the external disturbances.…”

“…Note that, if signal G(y, u) is persistently exciting, then, because of the filtering property of the variable Ω, the variable CΩ is also persistently exciting. The adaptive sliding-mode observer (10)-(12) represents a modified version of the one proposed by Efimov et al 24 Such a modification lies in the nonlinear parameter identification algorithm (11) (in the aforementioned work, 24 just the case when = 1 was studied, ie, the linear case). In this paper, it will be shown that the nonlinear algorithm (11) may improve the rate of convergence and the accuracy of the given estimation.…”

“…In this paper, it will be shown that the nonlinear algorithm (11) may improve the rate of convergence and the accuracy of the given estimation. However, from another side, the nonlinearity in (11) also complicates the proof drastically with respect to the work of Efimov et al 24 In the following, some properties of the nonlinear parameter estimation algorithm (11) are presented but, before that, let us introduce the following assumption.…”

“…Let us fix the parameter Γ = 100 and the gain k = 1. Then, the SeDuMi solver among YALMIP in MATLAB is used to find a solution for the LMIs (18), (24), and (21), respectively. The following feasible solution, with = I 2 , is found: For this matrix L and the given G (t, y, u), it is possible to show, after some simulations, that Assumption 2 is satisfied.…”

Adaptive relative velocity estimation algorithm for autonomous mobile robots using the measurements on acceleration and relative distance

“…Recalling the above limitations, an adaptive relative velocity estimation (ARVE) algorithm is presented in the current article. Adaptive techniques have been already developed as controller methods [19][20][21][22][23][24] as well as observer algorithms [25][26][27][28] in diverse applications. [29][30][31][32] Here, an adaptive technique is incorporated in a solution for problem of relative velocity estimation for aerial AMRs.…”