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function approximation technique Based Adaptive Control for Chaos Synchronization between Different Systems with Unknown Dynamics

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2021年第8期19卷 2611-2621页

作者： Wang, Yujie Bai, Yang Svinin, Mikhail Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Ritsumeikan Univ Informat Sci & Engn Dept 1-1-1 Noji Higashi Kusatsu Shiga 5258577 Japan

This paper presents a function approximation technique based immersion and invariance adaptive controller for chaos synchronization between nonidentical systems with unknown dynamics. In the proposed control scheme, the control system is reconstructed as the combination of a controllable linear system and a variation term from the original system. The variation term is treated as time-varying uncertainty and approximated by a group of weighted chosen basis functions. The immersion and invariance methodology is employed to design the adaptive control law such that both the synchronization error and uncertainty estimation error converge to zero. Two typical chaos synchronization problems are used in numerical simulations to verify the effectiveness and superiority of the proposed controller.

关键词： Chaotic system function approximation technique robust adaptive control synchronization

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function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator

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ROBOTICA 2014年第3期32卷 375-399页

作者： Al-Shuka, Hayder F. N. Corves, B. Zhu, Wen-Hong Rhein Westfal TH Aachen Dept Mech & Machine Dynam Aachen Germany

The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamics-based control problem of complex robots. However, the regressor-based adaptive control used by VDC to control every subsystem and to estimate the unknown parameters demands specific knowledge about the system physics. Therefore, in this paper, we focus on reorganizing the equation of the VDC for a serial chain manipulator using the adaptive function approximation technique (FAT) without needing specific system physics. The dynamic matrices of the dynamic equation of every subsystem (e. g. link and joint) are approximated by orthogonal functions due to the minimum approximation errors produced. The control, the virtual stability of every subsystem and the stability of the entire robotic system are proved in this work. Then the computational complexity of the FAT is compared with the regressor-based approach. Despite the apparent advantage of the FAT in avoiding the regressor matrix, its computational complexity can result in difficulties in the implementation because of the representation of the dynamic matrices of the link subsystem by two large sparse matrices. In effect, the FAT-based adaptive VDC requires further work for improving the representation of the dynamic matrices of the target subsystem. Two case studies are simulated by Matlab/Simulink: a 2-R manipulator and a 6-DOF planar biped robot for verification purposes.

关键词： Virtual decomposition control Adaptive control function approximation technique Computational complexity Biped robot Orthogonal functions

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function approximation technique Based Immersion and Invariance Control for Motor Servo System 40

Function Approximation Technique Based Immersion and Invaria...

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40th Chinese Control Conference (CCC)

作者： Chen, Wei Hu, Jian Nie, Weirong Nanjing Univ Sci & Technol Sch Mech Engn Nanjing 210094 Peoples R China

ISBN: (纸本)9789881563804

In the motor servo system, structured and unstructured uncertainties are the main reasons to limit motion accuracy. Most nonlinear controllers discuss structured and unstructured uncertainties separately, which increases the complexity of controller design. In this paper, a function approximation technique based immersion and invariance (IIFAT) adaptive controller is proposed for the motor servo system. In this method, both the structured and unstructured uncertainties of the system are regarded as unmodeled dynamics, and the unmodeled dynamics are fitted by weighted basis functions and a remainder term. The updated law of the weight of the basis function is designed by the immersion and invariant method. On the one hand, the function approximation technique simplifies the design of the controller, on the other hand, the immersion and invariance adaptive method enhances the robustness of the controller. In addition, the reliability of the controller theory is proved by Lyapunov stability analysis, and the good performance of the controller under different working conditions is verified by simulation experiments.

关键词： Adaptive control Immersion and invariance function approximation technique motor servo system

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function approximation technique based Sliding Mode Controller Adaptive Control of Robotic Arm with Time-Varying Uncertainties

Function Approximation Technique based Sliding Mode Controll...

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IEEE International Symposium on Robotics and Intelligent Sensors (IEEE IRIS)

作者： Shanta, Mst. Nafisa Tamanna Azlan, Norsinnira Zainul Int Islamic Univ Malaysia Dept Mechatron Engn Jalan Gombak Kuala Lumpur 53100 Malaysia

The controlling of robotic arm is really challenging due to the involvement of various uncertainties such as-time varying payload, friction and disturbances. These challenges attract many researchers to develop advanced control strategies for robot arm. However, most of the developed controllers focus on time invariant uncertainties. This paper presents the formulation of a new Sliding Mode Control-function approximation technique (SMC-FAT) based adaptive controller for a robot arm carrying unknown time-varying payload with the presence of time-varying disturbance and friction. The limitation of previous controllers to cope up with wide range time-varying uncertainty is solved using FAT expression. The stability of the controller can be proven by selecting a proper Lyapunov function and the update law can be derived easily. Three different time-varying uncertainties in sinusoidal, sawtooth and random functions have been considered as the payload and disturbance in the computer simulation to evaluate the controller's performance. The results with error less than 0.02 percentages proved the effectiveness of the proposed controller. (C) 2015 The Authors. Published by Elsevier B.V.

关键词： adaptive control sliding mode control function approximation technique robot arm uncertainties disturbance

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function approximation technique (FAT)-Based Adaptive Feedback Linearization Control for Nonlinear Aeroelastic Wing Models Considering Different Actuation Scenarios

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Mathematical Models and Computer Simulations 2023年第1期15卷 152-166页

作者： Al-Shuka, Hayder F. N. Corves, B. Department of Aeronautical Engineering University of Baghdad Baghdad Iraq Department of Mechanism Theory Machine Dynamics and Robotics (IGMR) RWTH Aachen University Aachen Germany

Abstract: This paper introduces a comprehensive study on vibration damping of a lumped aeroelastic wing model with translational linear and torsional nonlinear spring elements considering different actuation scenarios. The wing models have two degrees of freedom (DoFs) representing translational and torsional oscillations. On the other hand, the flap angles represent the control inputs that attempt to regulate the wing vibrations. Depending on the number of flaps designed, three actuation scenarios are investigated including fully actuated, overactuated, and underactuated wing models. For a fully actuated wing system (Scenario 1), conventional adaptive control strategies can be used for damping wing oscillations;however, adaptive approximation control is adopted in this work due to its capabilities for controlling (regulating) the dynamic system in the presence of the unknown system parameters. On the other hand, in the overactuated wing model (Scenario 2), the wing system has more control inputs than the DoFs and hence infinite solutions for the control input response are obtained. The Pseudoinverse matrix is a powerful tool to resolve this problem. In Scenario 3, the control inputs are less than the DoFs and hence a partial feedback linearization control strategy with an adaptive approximation compensator is used for regulation purposes;however, the internal dynamics of the underactuated wing system should be stable. Simulation experiments are performed to prove the effectiveness of control methods of the investigated scenarios. © 2023, Pleiades Publishing, Ltd.

关键词： adaptive approximation control fully actuated system function approximation technique overactuated system underactuated system Vibration damping

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Compliant adaptive control of human upper-limb exoskeleton robot with unknown dynamics based on a Modified function approximation technique (MFAT)

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ROBOTICS AND AUTONOMOUS SYSTEMS 2019年 117卷 92-102页

作者： Brahmi, Brahim Laraki, Mohamed Hamza Saad, Maarouf Rahman, M. H. Ochoa-Luna, Cristobal Brahmi, Abdelkrim Ecole Technol Super 1100 Rue Notre Dame Ouest Montreal PQ H3C 1K3 Canada Univ Wisconsin 3200 N Cramer St Milwaukee WI 53211 USA

Rehabilitation robots have shown a high potential for improving the patients' mobility, improving their functional movements and assisting in daily activities. However, this technology is still an emerging field and suffers from several challenges like compliance control and dynamic uncertain caused by the human-robot collaboration. The main challenge addressed in this paper is to ensure that the exoskeleton robot provides a suitable compliance control that allows it to cooperate perfectly with humans even if the dynamic model of the exoskeleton robot is uncertain. To achieve that, an adaptive tracking controller based on Modified function approximation technique (FAT) is proposed to approximate the dynamic model of the exoskeleton robot. Unlike a conventional FAT, the required use of basis functions in estimations law of dynamic model and the acceleration feedback is eliminated in the proposed modified FAT. Additionally, the desired trajectory is designed based on the designer's prediction of the motion intention of the human, using the Damped Least Square method in order to reduce the error between the actual position of the robot and the motion intention of the human which help the subject move the exoskeleton arm easily in active rehabilitation tasks. The stability analysis is formulated and demonstrated based on Lyapunov function. An experimental physiotherapy session and comparison study with a healthy subject was performed to test the effectiveness and robustness of the proposed adaptive control. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Rehabilitation robots function approximation technique Active assistive motion Human inverse kinematics

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function approximation technique based Sliding Mode Controller Adaptive Control of Robotic Arm with Time-Varying Uncertainties

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Procedia Computer Science 2015年 76卷 87-94页

作者： Mst. Nafisa Tamanna Shanta Norsinnira Zainul Azlan Department of Mechatronics Engineering International Islamic University Malaysia Jalan Gombak 53100 Kuala Lumpur Malaysia

The controlling of robotic arm is really challenging due to the involvement of various uncertainties such as- time varying payload, friction and disturbances. These challenges attract many researchers to develop advanced control strategies for robot arm. However, most of the developed controllers focus on time invariant uncertainties. This paper presents the formulation of a new Sliding Mode Control- function approximation technique (SMC-FAT) based adaptive controller for a robot arm carrying unknown time-varying payload with the presence of time-varying disturbance and friction. The limitation of previous controllers to cope up with wide range time-varying uncertainty is solved using FAT expression. The stability of the controller can be proven by selecting a proper Lyapunov function and the update law can be derived easily. Three different time-varying uncertainties in sinusoidal, sawtooth and random functions have been considered as the payload and disturbance in the computer simulation to evaluate the controller's performance. The results with error less than 0.02 percentages proved the effectiveness of the proposed controller.

关键词： adaptive control sliding mode control function approximation technique robot arm uncertainties disturbance

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function approximation technique Based Immersion and Invariance Control for Motor Servo System

Function Approximation Technique Based Immersion and Invaria...

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第40届中国控制会议

作者： Wei Chen Jian Hu Weirong Nie School of Mechanical Engineering Nanjing University of Science and Technologe

In the motor servo system,structured and unstructured uncertainties are the main reasons to limit motion *** nonlinear controllers discuss structured and unstructured uncertainties separately,which increases the complexity of controller *** this paper,a function approximation technique based immersion and invariance（IIFAT） adaptive controller is proposed for the motor servo *** this method,both the structured and unstructured uncertainties of the system are regarded as unmodeled dynamics,and the unmodeled dynamics are fitted by weighted basis functions and a remainder *** updated law of the weight of the basis function is designed by the immersion and invariant *** the one hand,the function approximation technique simplifies the design of the controller,on the other hand,the immersion and invariance adaptive method enhances the robustness of the *** addition,the reliability of the controller theory is proved by Lyapunov stability analysis,and the good performance of the controller under different working conditions is verified by simulation experiments.

关键词： Adaptive control Immersion and invariance function approximation technique motor servo system

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Coordinated manipulation and robust adaptive object handling by multiple manipulators, relying on the q-Szasz-Schurer operators as uncertainty approximator

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2025年第2期47卷 1-26页

作者： Izadbakhsh, Alireza Islamic Azad Univ Dept Elect Engn Garmsar Branch Garmsar Iran

In industrial applications, the use of multiple robotic manipulators for collaborative tasks significantly enhances operational flexibility and agility. However, as the number of robotic arms increases, so do the system's complexity and nonlinearity, leading to uncertainties and unmodeled dynamics. Moreover, external factors such as disturbances can further degrade system performance. This study focuses on developing a robust adaptive control strategy for a robotic system composed of multiple cooperative arms carrying an object. Specifically, it introduces the use of q-Szasz-Schurer operators as uncertainty approximators. To the best of the authors' knowledge, this is the first instance where these operators have been employed adaptively, as no prior research has provided adaptation rules for q-Szasz-Schurer operators. These powerful mathematical tools approximate system uncertainties, including unmodeled dynamics and external disturbances. Adaptive laws, derived through stability analysis, are used to adjust the coefficients of the q-Szasz-Schurer operators. The Lyapunov direct method ensures that all force and position tracking errors are uniformly ultimately bounded (UUB). The proposed controller/approximator is evaluated on a two-arm robotic system tasked with cooperative object manipulation, demonstrating its effectiveness. The numerical simulation results are also compared with an advanced approximation method, highlighting the accuracy and effectiveness of the proposed controller design. Both approximators yield almost identical results, with the exception that the q-Szasz-Schurer-based controller has a lower computational load compared to the RBFNN-based controller.

关键词： Adaptive controller Cooperative robotic arms function approximation technique q-Szasz-Schurer operator

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Nonlinear robust adaptive object manipulation by coordinated robotic arms employing Bleimann, Butzer, and Hahn operators for uncertainty estimation

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ASIAN JOURNAL OF CONTROL 2025年

作者： Mobayen, Saleh Izadbakhsh, Alireza Natl Yunlin Univ Sci & Technol Grad Sch Intelligent Data Sci Touliu Taiwan Islamic Azad Univ Dept Elect Engn Ga C Garmsar Iran

function approximation techniques (FAT) are a potent mathematical tool recently applied to create controllers for handling objects with multiple manipulators without relying on a specific model. However, its effectiveness is contingent on having velocity measurements, which might not be accessible in numerous real-world scenarios. This paper addresses the issue by introducing a robust adaptive controller using Bleimann, Butzer, and Hahn operators as uncertainty approximators without velocity measurements. Utilizing the Lyapunov lemma, the error signals in the controlled system are guaranteed to remain Uniformly Ultimately Bounded (UUB). The proposed controller will eventually be implemented in a cooperative system where two arms handle a rigid object. The efficiency and effectiveness of the proposed approach are demonstrated through simulation results.

关键词： adaptive controller Bleimann, Butzer, and Hahn operators cooperative robotic arms function approximation technique

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