Observer‐based control approach for fractional‐order delay systems of neutral type with saturating actuator

Aghayan, Zahra Sadat; Alfi, Alireza; Machado, J. A. Tenreiro

doi:10.1002/mma.7282

Cited by 12 publications

(7 citation statements)

References 40 publications

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“…Observers have been applied in many FO system studies to address the issue of unavailability of state measurements. In some studies, the observer for FO linear systems with different constraints had been considered [22][23][24][25][26]. Other studies have employed nonlinear observers to estimate unmeasured states for nonlinear FO systems [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Rahmani Nooshabadi,

Shahrokhi,

Malek

2024

Math Methods in App Sciences

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This work addresses design of an adaptive controller for nonlinear fractional‐order (FO) systems in the strict‐feedback form. The system is subject to unknown dynamics, unavailable state variables, quantized input and output, and input nonlinearity. The fuzzy logic system (FLS) is used to estimate the unknown dynamics, and instead of updating all the regressor weights, only the maximum of their norms is updated, which significantly reduces the computational load. Limitations imposed by data transmission bandwidth have been addressed by incorporating sector‐bounded quantizers, which include both logarithmic and hysteresis quantizers at the system input and output, and their errors have been considered in the controller design. It is assumed that system states are not measured. To estimate the system states, a linear observer has been used. Because of output quantization, the continuous output signal is not available, and therefore the observer has been designed based on the quantized output signal. In addition, the constraints of input nonlinearities, including symmetric and asymmetric saturation, backlash, hysteresis, and dead‐zone, have been considered in the controller design. Input nonlinearity and input quantization have been investigated simultaneously, which makes the analysis more challenging. Moreover, it is assumed that the type of input nonlinearity and its characteristics are not known, which makes the controller design more difficult. These problems have been resolved by using two novel adaptive laws. The adaptive backstepping method and the direct Lyapunov stability analysis have been used to construct the controller, and a nonlinear modified FO filter is used to avoid the explosion of complexity occurring in the traditional backstepping technique. Stability of the closed loop system has been established, and it has been shown that the tracking and state estimation errors converge to a small neighborhood of the origin. Finally, the proposed controller performance has been demonstrated via three simulation examples.

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Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Rahmani Nooshabadi,

Shahrokhi,

Malek

2024

Math Methods in App Sciences

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“…Although a well consolidated area, there are, however, still numerous open problems and paths to be unraveled [14][15][16][17]. A research path that some mathematicians have recently been interested consists to investigate fractional calculus on time scales [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness, and controllability for Hilfer differential equations on times scales

Sousa

Oliveira

Frederico

et al. 2023

Math Methods in App Sciences

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We introduce a new version of ψ$$ \psi $$‐Hilfer fractional derivative, on an arbitrary time scale. The fundamental properties of the new operator are investigated, and in particular, we prove an integration by parts formula. Using the Laplace transform and the obtained integration by parts formula, we then propose a ψ$$ \psi $$‐Riemann–Liouville fractional integral on times scales. The applicability of the new operators is illustrated by considering a fractional initial value problem on an arbitrary time scale, for which we prove existence, uniqueness, and controllability of solutions in a suitable Banach space. The obtained results are interesting and nontrivial even for the following particular choices: (i) of the time scale, (ii) of the order of differentiation, and/or (iii) function ψ$$ \psi $$, opening new directions of investigation. Finally, we end the article with comments and future work.

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“…FO neutral-type delay systems are more general than other types of delayed systems [ 27 ]. Thus, the stabilization of such systems for both integer- [ 28 , 29 ] and fractional-order [ 30 , 31 , 32 , 33 , 34 ] systems is a challenging topic. In the real world, mechanical and electrical components can cause a time delay in actuators.…”

Section: Introductionmentioning

confidence: 99%

“…A great deal of works reporting on the stability of neutral systems adopted a state-feedback controller [ 31 , 32 , 33 , 34 , 51 , 52 ]. However, it is possible that not all the system’s states are accessible.…”

Section: Introductionmentioning

confidence: 99%

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

Aghayan

Alfi

Lopes

2022

Entropy

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In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov’s theory. Two application examples verify the analytic findings.

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Observer‐based control approach for fractional‐order delay systems of neutral type with saturating actuator

Cited by 12 publications

References 40 publications

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

Existence, uniqueness, and controllability for Hilfer differential equations on times scales

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

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