Controllability results for fractional semilinear delay control systems

Shukla, Anurag; Patel, Rohit

doi:10.1007/s12190-020-01418-4

Cited by 43 publications

(16 citation statements)

References 25 publications

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“…According to the ADRC strategy, an ESO is applied to estimate the state and lumped disturbance of the control system. Thus, a commonly used linear ESO is derived for system (11) [29],…”

Section: Eso-based Composite Control Schemementioning

confidence: 99%

“…In the last few decades, fractional calculus has been continuously developed in system modeling and control fields [8][9][10]. Fractional differential systems have been widely studied and applied to describe various real systems and processes [11][12][13][14]. Recently, various strategies based on fractional calculus have been developed and applied to different areas, such as feedback control, disturbance estimation and signal processing [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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A Look-Up Table Based Fractional Order Composite Controller Synthesis Method for the PMSM Speed Servo System

et al. 2022

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Considering the performance requirements in actual applications, a look-up table based fractional order composite control scheme for the permanent magnet synchronous motor speed servo system is proposed. Firstly, an extended state observer based compensation scheme was adopted to suppress the motor parametric uncertainties and convert the speed servo plant into a double-integrator model. Then, a fractional order proportional-derivative (PDμ) controller was adopted as the speed controller to provide the optimal step response performance for the servo system. A universal look-up table was established to estimate the derivative order of the PDμ controller, according to the optimal samples collected by an improved differential evolution algorithm. With the look-up table, the optimal PDμ controller can be tuned analytically. Simulation and experimental results show that the servo system using the composite control scheme can achieve optimal tracking performance and has robustness to the motor parametric uncertainties and disturbance torques.

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“…According to the ADRC strategy, an ESO is applied to estimate the state and lumped disturbance of the control system. Thus, a commonly used linear ESO is derived for system (11) [29],…”

Section: Eso-based Composite Control Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Look-Up Table Based Fractional Order Composite Controller Synthesis Method for the PMSM Speed Servo System

et al. 2022

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“…Scholars discovered that physical phenomena in nature can be depicted more accurately by fractional-order models in comparison with classical integer-order ones [ 8 ]. Recently, quite a few researchers introduced fractional calculus into the predator-prey model and constructed fractional predator-prey models, for example, design and control of various ecological models [ 9 – 11 ], secure communication [ 12 , 13 ], system control [ 14 , 15 ], and so on. Furthermore, modelling and control based on the theory of the fractional calculus of complex systems can greatly enhance the capability of discrimination, design, and control for dynamic models since fractional calculus possesses infinite memory and more degrees of freedom [ 16 ].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis of a Fractional‐Order Predator‐Prey Network with Feedback Control Strategy

Zhang

et al. 2021

Computational Intelligence and Neuroscience

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This paper examines the bifurcation control problem of a class of delayed fractional-order predator-prey models in accordance with an enhancing feedback controller. Firstly, the bifurcation points of the devised model are precisely figured out via theoretical derivation taking time delay as a bifurcation parameter. Secondly, a set comparative analysis on the influence of bifurcation control is numerically studied containing enhancing feedback, dislocated feedback, and eliminating feedback approaches. It can be seen that the stability performance of the proposed model can be immensely heightened by the enhancing feedback approach. At the end, a numerical example is given to illustrate the feasibility of the theoretical results.

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“…Up to now, many divergences and academic controversies on the mild solutions to fractional impulsive systems still exist due to the fact that fractional derivatives have heredity, nonlocal behavior and memory property. Fortunately, some relevant literatures [88] have corrected these issues and given their correct expressions.…”

mentioning

confidence: 99%

“…The main reason is that these definitions based on that in [67] do not consider its memory and heredity. In recent years, some mathematicians have pointed out this error in the comments of [88].…”

mentioning

confidence: 99%

Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

Deng-feng

Liu

2021

era

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<p style='text-indent:20px;'>This paper presents a survey for some recent research on the controllability of nonlinear fractional evolution systems (FESs) in Banach spaces. The prime focus is exact controllability and approximate controllability of several types of FESs, which include the basic systems with classical initial and nonlocal conditions, FESs with time delay or impulsive effect. In addition, controllability results via resolvent operator are reviewed in detail. At last, the conclusions of this work and the research prospect are presented, which provides a reference for further study.</p>

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Controllability results for fractional semilinear delay control systems

Cited by 43 publications

References 25 publications

A Look-Up Table Based Fractional Order Composite Controller Synthesis Method for the PMSM Speed Servo System

A Look-Up Table Based Fractional Order Composite Controller Synthesis Method for the PMSM Speed Servo System

Mathematical Analysis of a Fractional‐Order Predator‐Prey Network with Feedback Control Strategy

Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

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