An H_∞non‐fragile observer‐based adaptive sliding mode controller design for uncertain fractional‐order nonlinear systems with time delay and input nonlinearity

Abstract

In this paper the problem of non‐fragile adaptive sliding mode observer design is addressed for a class of nonlinear fractional‐order time‐delay systems with uncertainties, external disturbance, exogenous noise, and input nonlinearity. An H∞ observer‐based adaptive sliding mode control considering the non‐fragility of the observer is proposed for this system. The sufficient asymptotic stability conditions are derived in the form of linear matrix inequalities. It is proven that the sliding surface is reachable in finite time. An illustrative example is provided which corroborates the effectiveness of the theoretical results.

A non-fragile robust observer design for uncertain time-delay fractional Itô stochastic systems with input nonlinearity: An SMC approach

“…In Parvizian et al, 9 the problem of SMC design for fractional-order Markovian jump systems has been addressed, where the order of the systems is fractional and the systems are subject to random parameter changes. For such systems, Itô’s formula and the classical infinitesimal generator can be utilized to obtain the results.…”

“…1,2 A class of sliding mode observers, called non-fragile observers, have been introduced which are resilient against perturbations of the observer coefficients. 3–9 Stochastic systems have found applications in various fields of science and numerous stochastic models have been proposed to describe real-world randomly varying processes. 10–12 For such systems, several Sliding Mode Control (SMC) based observation strategies have been introduced in the literature.…”

A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

“…In addition to non-fragility of the observer, input nonlinearity such as dead zone, input saturation and hysteresis, is another practical issue that must be taken into account in the control design procedure. Several effective control approaches have been recently proposed to cope with such input limitations (Parvizian et al, 2020; Wang and Hu, 2018; Xiao et al, 2019). The problem of observer-based H ∞ control for a class of uncertain neutral-type systems has been solved in Liu et al (2017) by utilizing sliding mode technique.…”

Sliding mode control for electro‐hydraulic proportional directional valve‐controlled position tracking system based on an extended state observer

“…(ii) Its response speed is fast, and it is robust to external noise interference and parameter perturbation. SMC has been used to handle the model parameter uncertainties and nonlinearities in many complex dynamical systems, for example, [23][24][25][26][27] and the references therein. This is the other one of motivations for our research.…”