State estimation for nonlinear conformable fractional‐order systems: A healthy operating case and a faulty operating case

Abstract

The issue of estimating states for classical integer‐order nonlinear systems has been widely addressed in the literature. Yet, generalization of existing results to the fractional‐order framework represents a fertile area of research. Note that, recently, a new and advantageous type of fractional derivative, the conformable derivative, was defined. So far, the general query of designing observers for conformable fractional‐order systems has not been investigated. In addition, it has been proved in the literature that some important tools for stability analysis of fractional‐order systems are valid using the conformable derivative concept, but invalid using other fractional derivative concepts. Motivated by the cited facts, this paper presents a first‐state estimation scheme for fractional‐order systems under the conformable derivative concept. A healthy operating case and a faulty operating case are treated. In this paper, a version of Barbalat's lemma, which is invalid using the well‐known Caputo derivative, is exploited to prove the convergence of the estimation errors. In order to validate the theoretical results, a numerical example is studied in the simulation section.

On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems

“…e above theorem gives a fundamental result on the practical Mittag-Leffler stability of the closed-loop system (1). Note that the work introduced in [3] was among the first works which describes the concept of practical stability.…”

“…Stability and control problems of nonlinear systems have drawn a great deal of attention from multiple fields of science and engineering (see [1,2] and the references therein). On the other hand, fractional-order nonlinear systems (FONS) have become one of the most important subjects to be investigated on the control theory field.…”

“…On the other hand, fractional-order nonlinear systems (FONS) have become one of the most important subjects to be investigated on the control theory field. is includes fault estimation [1], observer design [3], stabilization [3,4], stability [5,6], finite-time stability (FTS) [7], neural networks [8], and stochastic systems [9].…”

Improved Quasiuniform Stability for Fractional Order Neural Nets with Mixed Delay

“…Note that the fractional-order calculus has been used in studying the systems' dynamics in many fields such as electrochemistry, physics, viscoelasticity, biology, and chaotic systems [1]. In a related context, the evolution of science and engineering systems has considerably stimulated the employment of the fractional calculus in many areas of the control theory, in the last decades, and this includes stability [3][4][5][6], finite-time stability (FTS) [7][8][9], stabilization [10], observer design [10,11], and fault estimation [12][13][14].…”

A Novel Finite Time Stability Analysis of Nonlinear Fractional-Order Time Delay Systems: A Fixed Point Approach

“…Note that, the Fractional Calculus (FC) has been involved in studying and analyzing the system dynamics in many fields like physics, electrochemistry, biology, viscoelasticity, economics, plasma turbulence models, heat conduction and chaotic systems [4,17,19,27]. In a same context, the evolution of engineering and sciences has notably refreshing the use of the FC in numerous areas of the control theory, and this includes FTS [6,18,23,25,31], asymptotic stability [3,20,21,28], stabilization [22], observer design [14,22] and fault estimation [13,15,16]. The demonstration of FTS of FOTDSs in the literature has been based on different methods and concepts such us the Gronwall inequalities [2,6,7,8,18,23,25,32,33] and the Lyapunov functions [29,30,31].…”