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frequency distributed model of Caputo derivatives and robust stability of a class of multi-variable fractional-order neural networks with uncertainties

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NEUROCOMPUTING 2016年 202卷 91-97页

作者： Gai, Mingjiu Cui, Shiwei Liang, Shu Liu, Xiaolei Naval Aeronaut & Astronaut Univ Inst Syst Sci & Math Yantai 264001 Japan Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China

This paper addresses the problems of the robust stability of a class of multi-variable fractional order neural networks with linear fractional uncertainties. Firstly, a continuous frequency distributed model of Caputo derivatives which extend the continuous frequency distributed model of the fractional integrator to Caputo derivatives is given. Then, a sufficient condition of robust stability for a class of multi-variable fractional order neural networks with linear fractional uncertainties is presented via the Lyapunov direct method and linear matrix inequality approach. Finally, two numerical examples are provided to demonstrate the effectiveness of the result. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Caputo derivatives frequency distributed model Neural networks Robust stability Linear matrix inequality (LMI)

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Robust finite-time control of fractional-order nonlinear systems via frequency distributed model

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NONLINEAR DYNAMICS 2016年第4期85卷 2133-2142页

作者： Wang, Bin Ding, Junling Wu, Fengjiao Zhu, Delan Northwest A&F Univ Dept Elect Engn Yangling 712100 Shaanxi Peoples R China

This paper studies the application of frequency distributed model for finite-time control of a class of fractional-order nonlinear systems. Firstly, a class of fractional-order nonlinear systems with model uncertainties and external disturbances are introduced, and a new frequency distributed model with theoretical inference is presented. Secondly, a novel fast terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite-time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional-order nonlinear systems. Finally, two typical examples of three-dimensional nonlinear fractional-order Lorenz system and four-dimensional nonlinear fractional-order Chen system are employed to demonstrate the validity of the proposed method.

关键词： Fractional-order nonlinear systems frequency distributed model Robust finite-time control Terminal sliding mode Uncertainty

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Disturbance observer-based Takagi-Sugeno fuzzy control of a delay fractional-order hydraulic turbine governing system with elastic water hammer via frequency distributed model

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INFORMATION SCIENCES 2021年 569卷 766-785页

作者： Ma, Teng Wang, Bin Northwest A&F Univ Coll Water Resources & Architectural Engn Dept Elect Engn Yangling 712100 Shaanxi Peoples R China Northwest A&F Univ Key Lab Agr Soil & Water Engn Arid & Semiarid Are Minist Educ Yangling 712100 Shaanxi Peoples R China

The hydraulic turbine governing system (HTGS) is a core part of a hydropower station, and the dynamic characteristics of its transition process and stability under disturbances have been strong concerns for the stable operations of units. In this paper, a disturbance observer-based Takagi-Sugeno (T-S) fuzzy control (DOBFC) method using the frequency distributed model (FDM) is proposed to improve the anti-interference control performance of a delay fractional-order HTGS. First, a more practical mathematical model of a fractional order HTGS considering both the mechanical time delay and an elastic water hammer is established, and then its fuzzy model is presented on the basis of the generalized T-S fuzzy rules. Second, the disturbance observer is constructed by utilizing the system state and disturbance information, and the output estimated value of the observer is input into the designed fuzzy state feedback controller to compensate for the effect of external disturbances on the system and achieve disturbance suppression. Third, by means of a new FDM transformation and the construction of a novel Lyapunov function, the stability condition and the parameter solving method of the controller are derived using the linear matrix inequality (LMI) technique. Finally, simulation results are given to verify the effectiveness of the proposed algorithm. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Takagi-Sugeno fuzzy control Time delay frequency distributed model Disturbance observer Linear matrix inequality Fractional-order hydraulic turbine governing system

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A novel algorithm on adaptive backstepping control of fractional order systems

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NEUROCOMPUTING 2015年 165卷 395-402页

作者： Wei, Yiheng Chen, Yuquan Liang, Shu Wang, Yong Univ Sci & Technol China Dept Automat Hefei 230026 Peoples R China Univ N Carolina Coll Engn Charlotte NC 28223 USA

This article presents a new method of designing the adaptive backstepping controller for triangular fractional order systems with non-commensurate orders. The fractional order indirect Lyapunov method is available for the 0 < alpha < 1 case, by introducing the appropriate transformations of frequency distributed model. Meanwhile, based on the semigroup property of fractional order derivative and the fractional order tracking differentiator, we extend the result to the 1 < alpha < 2 case. The case of controlling fractional order systems with unknown control input coefficient is also investigated. Simulation examples are given to demonstrate the effectiveness of the proposed controllers. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Fractional order systems Adaptive backstepping control frequency distributed model Lyapunov function

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Stabilization of Fractional-Order T-S Fuzzy Systems with Time Delays via an H∞Performance model

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2024年第4期26卷 1300-1312页

作者： Liu, Yiyu Zhang, Xiulan Guangxi Minzu Univ Sch Math & Phys Nanning 530006 Peoples R China Nanjing Univ Aeronaut & Astronaut Sch Aerosp Engn Nanjing 210016 Peoples R China

Takagi-Sugeno (T-S) fuzzy model is an effective technology for describing complex nonlinear industrial processes and dynamic systems with un measurable parameters. However, to stabilize this type of system, feedback linearization techniques and complex adaptive schemes usually need to be adopted. This paper focuses on the stabilization of uncertain fractional-order (FO) systems with unmeasurable states, external disturbances, and time delays, where certain ''IF-THEN'' rules based on an FO T-S model are proposed to describe FO systems. A new FOH(infinity)performance model is established to provide stabilization sufficient conditions. A fuzzy observer is implemented to reconstruct system states, and a feedback controller is established to stabilize the integrated system. Benefiting from a continuous frequency distribution model,the stabilization can be discussed through integer-orderstabilization theories, and several stabilization conditionsare obtained. Moreover, the proposed control approachavoids the usage of feedback linearization techniques,which effectively reduces the computational *** from theoretical analysis, through a numericalexperiment, the feasibility of derived results is verified.

关键词： Fractional-order system Takagi-Sugeno fuzzy model frequency distributed model Time delay Fuzzy observer

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Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems

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NONLINEAR DYNAMICS 2016年第1期85卷 633-643页

作者： Chen, Yuquan Wei, Yiheng Zhong, Hua Wang, Yong Univ Sci & Technol China Dept Automat Hefei 230026 Peoples R China China Acad Engn Phys Inst Elect Engn Mianyang 621999 Peoples R China

This article investigates a novel sliding model control approach for a class of nonlinear fractional order systems. In particular, the sliding surface with additional nonlinear part is designed by a Lyapunov-like function and one can achieve much more satisfying system performances by selecting suitable parameters. Moreover, a second-order switching law is generated from the commonly used adaptive switching law. Its properties are carefully discussed, and it is proven that the reaching time of the sliding surface can be guaranteed nonsensitive to the initial conditions with the second-order switching law, while the adaptive switching law cannot even guarantee the finite-time convergence. Then the stability of the closed-loop control system is rigorously analyzed via indirect Lyapunov method. Finally, simulation examples are presented to illustrate the effectiveness of the proposed control method.

关键词： Fractional order systems Sliding mode control Second-order switching law Indirect Lyapunov method frequency distributed model

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Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2024年第3期238卷 410-424页

作者： Wang, Hong Wei, Jianming Wang, Zhe Naval Aviat Univ Yantai Peoples R China Naval Univ Engn Wuhan Peoples R China Naval Univ Engn Wuhan 430033 Peoples R China

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

关键词： Adaptive iterative learning control parameterized fractional-order systems backlash-like hysteresis Mittag-Leffler function boundary layer function frequency distributed model

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Adaptive backstepping output feedback control for a class of nonlinear fractional order systems

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NONLINEAR DYNAMICS 2016年第2期86卷 1047-1056页

作者： Wei, Yiheng Tse, Peter W. Yao, Zhao Wang, Yong Univ Sci & Technol China Dept Automat Hefei 230026 Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Tat Chee Ave Hong Kong Hong Kong Peoples R China Changchun Univ Sci & Technol Mech & Elect Engn Coll Changchun 130022 Peoples R China

This article presents a novel fractional order adaptive backstepping output feedback control scheme for nonlinear fractional order systems. The needed feedback information is constructed via a state estimation filter. To improve the control performance, tracking differentiators, nonlinear elements and fractional order update laws were introduced and applied to the control systems. With the aids of this frequency distribute model and the indirect Lyapunov method, the stability and the tracking convergence of the resulting closed-loop system were established. A careful simulation study was provided to illustrate the effectiveness of this novel scheme.

关键词： Fractional order systems Adaptive backstepping control frequency distributed model Indirect Lyapunov method Tracking differentiator

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Stability for nonlinear fractional order systems: an indirect approach

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NONLINEAR DYNAMICS 2017年第2期89卷 1011-1018页

作者： Chen, Yuquan Wei, Yiheng Zhou, Xi Wang, Yong Univ Sci & Technol China Dept Automat Hefei 230026 Peoples R China

In this paper, we first verify that fractional order systems using Caputo's or Riemann-Liouville's derivative can be represented by the continuous frequency distributed model with initial value carefully allocated. Then, the relation of the stability between the fractional order system and its corresponding integer order system is discussed and it is proven that stability of integer order system implies the stability of its corresponding fractional order system under some mild conditions. Moreover, we extend the stability theorems to the finite-dimensional case since fractional order systems are always implemented by approximation. Some illustrative examples are finally provided to show the usage and effectiveness of the proposed stability theorems.

关键词： Stability analysis Nonlinear fractional order system frequency distributed model

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Neural adaptive quantized output-feedback control-based synchronization of uncertain time-delay incommensurate fractional-order chaotic systems with input nonlinearities

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NEUROCOMPUTING 2017年 237卷 200-225页

作者： Zouari, Farouk Boulkroune, Abdesselem Ibeas, Asier Univ Tunis El Manar ENIT Lab Rech Automat LARA BP 37 Tunis 1002 Tunisia Univ Jijel LAJ BP 98 Ouled Aissa 18000 Jijel Algeria Univ Autonoma Barcelona Dept Telecommun & Syst Engn E-08193 Barcelona Spain Univ Bogota Jorge Tadeo Lozano Fac Ciencias Nat & Ingn Dept Ingn 22 St4-96Mod 7A Bogota 110311 Colombia

This research is concerned with the problem of generalized function projective synchronization of nonlinear uncertain time-delay incommensurate fractional-order chaotic systems with input nonlinearities. The considered problem is challenging owing to the presence of unmeasured master-slave system states, external dynamical disturbances, unknown nonlinear system functions, unknown time-varying delays, quantized outputs, unknown control directions unknown actuator nonlinearities (backlash-like hysteresis, dead-zone and asymmetric saturation actuators) and distinct fractional-orders. Under some mild assumptions and using Caputo's definitions for fractional-order integrals and derivatives, the design procedure of the proposed neural adaptive controller consists of a number of steps to solve the generalised function projective synchronization problem. First, sinooth functions and the mean value theorem are utilized to overcome the difficulties from actuator nonlinearities and distributed time-varying delays, respectively. Then, a simple linear observer is established to estimate the unknown synchronization error variables. In addition, a Nussbaum function is incorporated to cope with the unknown control direction and a neural network is adopted to tackle the unknown nonlinear functions. The combination of the frequency distributed model, the Razumikhin Lemma, the neural network parameterization, the Lyapunov method and the Barbalat's lemma is employed to perform the stability proof of the closed-loop system and to derive the adoption laws. The major advantages of this research are that: (1) the Strictly Positive Real (SPR) condition on the estimation error dynamics is not required, (2) the considered class of master-slave systems is relatively large, (3) all signals in the resulting closed-loop systems are semi-globally uniformly ultimately bounded and the synchronization errors semi-globally converge to zero. Finally, numerical examples are presented to illustrate the p

关键词： Generalized function projective synchronization Uncertain time-delay chaotic systems Incommensurate fractional-order systems Input nonlinearities Nussbaum function Razumikhin Lemma frequency distributed model Adaptive quantized output-feedback control

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