Adaptive Control of a Class of Incommensurate Fractional Order Nonlinear Systems With Input Dead-Zone

Abstract

This paper develops a new adaptive control scheme for a class of incommensurate fractional order nonlinear systems with external disturbances and input dead-zone. Based on the backstepping algorithm, the radial basis function neural network (RBF NN) is used to approximate the unknown nonlinear uncertainties in each step of the backstepping, and the fractional order parameters update laws for RBF NN are proposed as well as the fractional order nonlinear disturbance estimator to estimate the external disturbances. The adaptive RBF NN controller is designed based on the frequency distributed model of fractional integrator for the fractional order systems, and the stability of the closed loop system is proved. Finally, three simulation examples are given to verify the effectiveness and robustness of the proposed method. INDEX TERMS Fractional order systems, adaptive backstepping control, nonlinear system, neural networks (NNs), input dead-zone.

Adaptive control realization for canonic Caputo fractional-order systems with actuator nonlinearity: application to mechatronic devices

“…It is well known that many real world systems, such as robot manipulators, mass-springdamper systems, structure dynamics, most of mechatronic and mechanical systems, and many of chaotic models belong to a special class of nonlinear systems called canonical (or normal) systems. Furthermore, a wide range of other classes of nonlinear systems can be transformed into the canonic forms using some mappings [27]. Therefore, in this paper a class of uncertain n-dimensional fractional-order systems in the canonic form is considered and is described as follows:…”

“…The research [26] provided some results on the stability region and the disturbance rejection properties of the linear fractional processes working with saturating actuators. Wang et al [27] proposed a backstepping-based neural network control algorithm for stabilization of a class of fractional-order plants in the presence of dead-zone input nonlinearity. However, most of the above-mentioned research works have been developed either for linear fractional systems where the outputs of the controlled systems involve steady state errors or for the systems with known structures and dynamics.…”

Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks With Time-Varying Delay via Hybrid Sliding Mode Control

“…where K 1 , K 2 and W are designed matrices with appropriate dimension, η is an invariable signal time delay, and sgn(t) is defined by | t |= t × sgn(t) for all t ∈ R. Remark 2: Compared with the controller designed in [30], [31], [32], [33], [34], [35], [36], [37], the designed HSMC not only has the properties of feedback SMC and sampleddata control, but also excludes f (•) and g(•) terms, keeping the property of the FNNTVD (3).…”

“…From the inequalities (27) and (32), the sliding mode surface s(t) and the system state trajectory e(t) converge exponentially to zero. Therefore, the system (3) is GMLS.…”

“…From recent results in [30], [31], [32], [33], [34], [35], [36], [37], [38], we may find that various controlling approaches are put forward, such as adaptive feedback control [30], [31], [32], active pinning control [33], [34], adaptive impulsive control [35], periodical intermittent control [36], adaptive fuzzy observer-based cooperative control [37] and sliding mode control (SMC) in [38]. Compared with the controllers in [30], [31], [32], [33], [34], [35], [36], [37], SMC can deal with uncertainties and external disturbances more effectively [39]. Thereby, many scholars adopt SMC to study the dynamic performance of linear and nonlinear system [40], [41], [42].…”