Adaptive Neural Network Conformable Fractional-Order Nonsingular Terminal Sliding Mode Control for a Class of Second-Order Nonlinear Systems

On characterisations of the input to state stability properties for conformable fractional order bilinear systems

“…Combining the solutions (34) and (35) gives inequality (20) for all t > t 0 . Thus, system (13) is fe-ISS.…”

“…Several attempts have been also made to generalise the Barbalat‐type lemmas in order to analyse the stability of time‐varying fractional‐order nonlinear systems where it is very difficult to find Lyapunov functions with negative definite derivative [13, 43]. Furthermore, in other research works, several nonlinear control methods have been extended into the fractional dynamic systems such as sliding mode control [34, 47], back‐stepping control [38], fuzzy control [20], adaptive control [48].…”

“…[27], a framework in terms of behavioral system theory has been presented to develop a general modelling specification as well as stability conditions for conformable linear systems with a fractional differential order, and the sufficient conditions and tests for stability were provided based on linear matrix inequalities. Furthermore, several well‐behaved modelling and control methods have been newly developed under conformable derivative including conformable fractional‐order neural sliding‐mode control [34], conformable fractional optimal control [22], robust $$\mathcal {H}_{\infty }$$ control scheme for nonlinear conformable fractional‐order systems [26, 28] and conformable fractional modeling and control of complex biological system [4, 15], to mention a few.…”

Novel Speed Sensorless DTC Design for a Five-Phase Induction Motor with an Intelligent Fractional Order Controller Based-MRAS Estimator

“…A fractional-order proportionalintegral (FOPI) controller can guarantee accurate speed estimation (He et al, 2021). An FOPI controller is a structure based on the theory of fractional calculus (FC), which has the advantage of a supplementary degree of freedom compared with the classical PI controller (Das et al, 2013;Razzaghian et al, 2022;Zhang et al, 2020). This technique aims to improve the performance of the MRAS of DTC for the five-phase induction motor.…”

Generalised conformable sliding mode control

“…In Haghighatnia et al, 32 a conformable derivative‐based chaotic system is considered, and a smooth sliding mode approximation enforces a quasi‐sliding motion. In Razzaghian et al, 33 an adaptive neural network is proposed, which relies on a conformable terminal sliding mode variable definition for the case of uncertain second order dynamical systems. In Haghighatnia and Shandiz, 34 a conformable sliding variable is defined, but during the sliding mode, a conventional motion takes place, without any dependence on the conformable definition.…”