Finite-Time Bounded Tracking Control for Fractional-Order Systems

Abstract

This paper solves the finite-time bounded tracking control problem for fractional-order systems. Firstly, by taking the fractional derivative on state equations and error signals, a fractional-order error system is constructed, and the error signal is taken as the output vector of the error system. Secondly, a state feedback controller is introduced into the error system, and the fractional derivative of disturbance signals and desired tracking signals are combined as the disturbance signal of the error system. Thus, the original problem is converted into the input-output finite time stability problem of the closed-loop error systems. Thirdly, based on the linear matrix inequalities (LMIs), the sufficient conditions which ensure the finite-time bounded tracking for the desired tracking signals are derived. Therefore, the finite-time bounded tracking controller of the original system is obtained. Finally, simulation results elucidate the effectiveness of the controller. INDEX TERMS Finite-time bounded tracking, fractional-order systems, error systems, linear matrix inequalities.

Fault detection of fractional‐order system based on finite frequency H−/H∞${{H}_{-}}/{{H}_{\infty }}$ unknown input observer

“…x ∈ ℝ n is the state estimate, r is the residual, and L, R, K , S are the parameter matrives to be designed. And there is a difference between the observer (11) and the observer (9), the observer (9) can only achieve a complete decoupling of the unknown input d 1 from estimation error, but cannot achieve the decoupling of d 2 .…”

“…Defining the state estimation error e(t ) = x(t ) − x(t ). According to formulas (10) and (11) can get:…”

“…Due to its particularity, fractional-order systems have received extensive attention. Compared with integer-order systems, which characterize instantaneous changes in object properties, fractionalorder systems represent changes in object properties [8][9][10][11][12]. Therefore, in a certain sense, modeling with fractional calculus theory can more truly reflect some special properties of the object, and the fractional derivative has memory and heritability.…”

Comparisons of Modeling Methods for Fractional-Order Cuk Converter

“…In recent years, with the development of fractional calculus, it has become the best mathematical theory to describe problems such as complex motion, irregular phenomenon, memory effect, and intermediate process. Also, it has been gradually applied to various modeling and control fields, such as random diffusion and wave propagation, transmission line theory, macromolecular chain and biomaterials, viscoelastic modeling, fractional filtering, and fractional-order PID controller [8][9][10][11][12].…”