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18 pages, 713 KiB

Open AccessArticle

Cooperative Control for Multi-Agent Systems with Deception Attack Based on an Attack Detection Mechanism

by Shuhan Zhang, Kai Zhang and Zhijian Hu

Energies 2025, 18(11), 2962; https://doi.org/10.3390/en18112962 - 4 Jun 2025

Viewed by 479

This study highlights the security control challenge for multi-agent systems (MASs) with integrated attack detectors under deception attacks (DAs). We develop an adaptive backstepping security control strategy designed to simultaneously detect DAs and maintain cooperative system performance. First, a DA detection mechanism is [...] Read more.

This study highlights the security control challenge for multi-agent systems (MASs) with integrated attack detectors under deception attacks (DAs). We develop an adaptive backstepping security control strategy designed to simultaneously detect DAs and maintain cooperative system performance. First, a DA detection mechanism is proposed using a state observer. The analytical results reveal that observer errors grow unbounded under DAs but converge to zero in attack-free scenarios, enabling effective attack identification. Following detection, we integrate a Nussbaum function into the backstepping control framework to manage unknown time-varying output gains. Additionally, adaptive parameters, dynamically adjusted based on DA signals, are designed to compensate for actuator and sensor deviations induced by attacks. Rigorous Lyapunov-based analysis proves that the proposed controller ensures output tracking under deception attacks, the timely detection of attack signals, and the boundedness of all closed-loop signals. Numerical simulations further confirm the theoretical findings and demonstrate the effectiveness of the proposed method. Full article

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20 pages, 3873 KiB

Open AccessArticle

Neural Unilateral Nussbaum Gain Sliding Mode Control for Uncertain Ship Course Keeping with an Unknown Control Direction

by Guoxin Ma, Dongliang Li, Qiang Wei and Lei Song

J. Mar. Sci. Eng. 2025, 13(5), 846; https://doi.org/10.3390/jmse13050846 - 24 Apr 2025

Viewed by 287

Abstract

This paper focuses on the ship control system and studies the problem of unknown control directions. Considering that the traditional Nussbaum gain method has to consider the complex situation where the gain converges to both positive and negative infinity when proving the stability [...] Read more.

This paper focuses on the ship control system and studies the problem of unknown control directions. Considering that the traditional Nussbaum gain method has to consider the complex situation where the gain converges to both positive and negative infinity when proving the stability of a system, a unilateral Nussbaum function is defined in this paper. By constructing this function, the design and proof process of the adaptive Nussbaum gain method are simplified. Taking the ship course–keeping control system as the research object, a course angle tracking controller is designed by combining neural network, robust adaptive, and sliding mode control techniques. A dual-input RBF single-output neural network is used to approximate the uncertain part of the system, and the robust adaptive control is adopted to deal with the unknown disturbance. The simulation results at the end of the article show that when the direction suddenly switches, the overshoot of the system reaches 40%, and the adjustment time is approximately 3 s. However, the system can still adapt to the change of the control direction and maintain stability, indicating that the method proposed in this paper is reasonable and effective. And the proposed method can effectively cope with the problems of the unknown control direction and its jump, keeping the system stable, which has great theoretical and engineering application value. Full article

(This article belongs to the Special Issue Autonomous Marine Vehicle Operations—3rd Edition)

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18 pages, 1623 KiB

Open AccessArticle

Adaptive Internal Model Backstepping Control for a Class of Second-Order Electromagnetic Micromirror with Output Performance Constraints and Anomaly Control

by Huasen Gan, Yi Qin, Jinfeng Zhang, Cixing Lv, Zhonghua Chen and Yaohua Hu

Micromachines 2024, 15(7), 925; https://doi.org/10.3390/mi15070925 - 19 Jul 2024

Cited by 1 | Viewed by 1083

Abstract

This paper investigates the asymptotic tracking problem for a class of second-order electromagnetic micromirror model with output performance constraints and anomaly control, which is subject to model parameter uncertainties and external disturbances. Specifically, this paper formulates the trajectory tracking control problem of an [...] Read more.

This paper investigates the asymptotic tracking problem for a class of second-order electromagnetic micromirror model with output performance constraints and anomaly control, which is subject to model parameter uncertainties and external disturbances. Specifically, this paper formulates the trajectory tracking control problem of an electromagnetic micromirror as a closed-loop control trajectory tracking problem based on the general solution framework of output regulation. Moreover, the extended internal model is introduced to reformulate the closed-loop control problem into a state stabilization problem of the augmented system. Based on the augmented system, an internal model backstepping controller is proposed by integrating the barrier Lyapunov Functions (BLF) and the Nussbaum gain function with the backstepping structure.This controller not only satisfies the output performance constraints of the micromirror, but also maintains the control performance in anomalous control situations. The final performance simulation demonstrates the efficacy of the proposed controller. Full article

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30 pages, 3867 KiB

Open AccessArticle

Distributed Dynamic Surface Control for a Class of Quadrotor UAVs with Input Saturation and External Disturbance

by Guoqiang Zhu, Laiping Lv, Lingfang Sun and Xiuyu Zhang

Drones 2024, 8(3), 77; https://doi.org/10.3390/drones8030077 - 23 Feb 2024

Cited by 3 | Viewed by 1939

Abstract

An adaptive dynamic surface trajectory tracking control method based on the Nussbaum function is proposed for a class of quadrotor UAVs encountering unknown external disturbances and unidentified nonlinearities. By transforming controller expressions into numerical solutions, the challenge of overly complex controller design expressions [...] Read more.

An adaptive dynamic surface trajectory tracking control method based on the Nussbaum function is proposed for a class of quadrotor UAVs encountering unknown external disturbances and unidentified nonlinearities. By transforming controller expressions into numerical solutions, the challenge of overly complex controller design expressions is addressed, simplifying the overall controller design process and enhancing the efficiency of simulation programs. Additionally, an adaptive controller based on Nussbaum gain is introduced to effectively resolve actuator saturation issues. This approach mitigates complexities associated with traditional control design and ensures smooth operation of the quadrotor UAVs. The proposed methodology offers promising prospects for enhancing the robustness and performance of quadrotor UAVs under uncertain operating conditions. Finally, to validate the effectiveness of the proposed control scheme, a hardware-in-the-loop experimental setup is constructed. The dynamic model of the quadrotor UAVs and the proposed controller scheme are implemented on the Rapid Control Prototype (RCP) and Real-Time Simulator (RTS), respectively. This facilitates a semi-physical simulation experiment, providing a basis for the subsequent application of the control scheme to actual aerial vehicles. The concluding experimental results affirm the effectiveness of the proposed control scheme and highlight its potential for practical applications. Full article

(This article belongs to the Special Issue A UAV Platform for Flight Dynamics and Control System)

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24 pages, 2680 KiB

Open AccessArticle

Observer-Based Adaptive Fuzzy Quantized Control for Fractional-Order Nonlinear Time-Delay Systems with Unknown Control Gains

by Yuwen Dong, Shuai Song, Xiaona Song and Inés Tejado

Mathematics 2024, 12(2), 314; https://doi.org/10.3390/math12020314 - 18 Jan 2024

Cited by 3 | Viewed by 1334

Abstract

This paper investigates the observer-based adaptive fuzzy quantized control problem for a class of fractional-order nonlinear time-delay systems with unknown control gains based on a modified fractional-order dynamic surface control (FODSC) technique and an indirect Lyapunov method. First, a fractional-order, high-gain state observer [...] Read more.

This paper investigates the observer-based adaptive fuzzy quantized control problem for a class of fractional-order nonlinear time-delay systems with unknown control gains based on a modified fractional-order dynamic surface control (FODSC) technique and an indirect Lyapunov method. First, a fractional-order, high-gain state observer is constructed to estimate unavailable state information. Furthermore, the Nussbaum gain technique and a fractional-order filter are adopted to cope with the problem of unknown control gains and to reduce the computational complexity of the conventional recursive procedure, respectively. Moreover, through integration with the compensation mechanism and estimation model, the adaptive fuzzy quantized controllers and adaptive laws are designed to ensure that all the signals of the closed-loop system are bounded. In the end, the proposed controller is applied to a numerical example and a single-machine-infinite bus (SMIB) power system; the simulation results show the validity, superiority, and application potential of the developed control strategy. Full article

(This article belongs to the Special Issue Mathematical Methods for Nonlinear Dynamics)

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17 pages, 4573 KiB

Open AccessArticle

A Novel Nonlinear Filter-Based Robust Adaptive Control Method for a Class of Nonlinear Discrete-Time Systems

by Zeyi Zhao, Zhu Wang and Qian Wang

Processes 2024, 12(1), 171; https://doi.org/10.3390/pr12010171 - 11 Jan 2024

Cited by 1 | Viewed by 1453

Abstract

This paper introduces an innovative adaptive control approach utilizing a nonlinear filter for a specific subset of nonlinear discrete-time systems, considering the presence of both input and output noise. The system can be transformed into a nonlinear autoregressive moving average with exogenous inputs [...] Read more.

This paper introduces an innovative adaptive control approach utilizing a nonlinear filter for a specific subset of nonlinear discrete-time systems, considering the presence of both input and output noise. The system can be transformed into a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model. The concept of discrete Nussbaum gain is introduced to address the theoretical constraint associated with unknown directions of feed-forward or control gains, and the extended adaptive tuning sequence is introduced to facilitate the acceleration of parameter updating. In the case of no noise, asymptotical output tracking and global stability are achieved with the adaptive control. Further, in the presence of input noise and output noise, a novel nonlinear filter is designed to generate a more accurate filtered output, which improves the control system’s ability to adapt and track accurately. Finally, examples are provided to showcase the effectiveness and precision of the method. Full article

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17 pages, 3119 KiB

Open AccessArticle

Adaptive Fuzzy Command Filtered Tracking Control for Flexible Robotic Arm with Input Dead-Zone

by Zhike Zhao, Hao Chang and Caizhang Wu

Appl. Sci. 2023, 13(19), 10812; https://doi.org/10.3390/app131910812 - 28 Sep 2023

Cited by 2 | Viewed by 1546

Abstract

In this paper, an adaptive fuzzy tracking control method is proposed to address the issues of dead-zone and unobservable states in a flexible robotic arm system. The control design process begins with the utilization of a fuzzy logic system to approximate the nonlinear [...] Read more.

In this paper, an adaptive fuzzy tracking control method is proposed to address the issues of dead-zone and unobservable states in a flexible robotic arm system. The control design process begins with the utilization of a fuzzy logic system to approximate the nonlinear functions present in the flexible robotic arm system. To estimate the unobservable states of the system, a state observer is then designed. To alleviate the computational complexity during controller design, the command filtering technique is introduced. Additionally, the Nussbaum function is incorporated to address the unknown control gain problem. The stability of the system can be verified through the design of a Lyapunov function. This study’s simulation results demonstrate that the designed control system can closely track the specified reference signals. The closed-loop system effectively controls the flexible robotic arm, as verified through experimentation. Full article

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19 pages, 2861 KiB

Open AccessArticle

Finite-Time Adaptive Dynamic Surface Asymptotic Tracking Control of Uncertain Multi-Agent Systems with Unknown Control Gains

by Xiongfeng Deng and Chaocheng An

Appl. Sci. 2023, 13(17), 9552; https://doi.org/10.3390/app13179552 - 23 Aug 2023

Cited by 1 | Viewed by 1454

Abstract

In this work, the finite-time asymptotic tracking control problem of uncertain multi-agent systems with unknown control gains is studied. For the unknown control gain of each subsystem in multi-agent systems, we consider using the Nussbaum gain function techniques to handle them. To deal [...] Read more.

In this work, the finite-time asymptotic tracking control problem of uncertain multi-agent systems with unknown control gains is studied. For the unknown control gain of each subsystem in multi-agent systems, we consider using the Nussbaum gain function techniques to handle them. To deal with the unknown uncertain nonlinear dynamics, the radial basis function neural network is introduced in each step of the dynamic surface control design. In addition, a nonlinear compensating term with the estimation of an unknown bounded parameter is designed to avoid repeated differentiation of each virtual control law. Then, based on the neural network control method, dynamic surface control technique, and finite-time control theory, an adaptive neural network finite-time dynamic surface control law is finally designed. Using stability analysis, it is proven that the presented adaptive control law can guarantee all signals of the closed-loop system semi-global practical finite-time stable, and the tracking error of each follower agent can converge to a small neighborhood of zero in finite time. Finally, a class of single-link robot systems is provided to illustrate the effectiveness of the designed control law. Full article

(This article belongs to the Topic Advanced Systems Engineering: Theory and Applications)

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21 pages, 1873 KiB

Open AccessArticle

ESN-Observer-Based Adaptive Stabilization Control for Delayed Nonlinear Systems with Unknown Control Gain

by Shuxian Lun, Zhaoyi Lv, Xiaodong Lu and Ming Li

Mathematics 2023, 11(13), 2965; https://doi.org/10.3390/math11132965 - 3 Jul 2023

Cited by 1 | Viewed by 1119

Abstract

This paper investigates the observer-based adaptive stabilization control problem for a class of time-delay nonlinear systems with unknown control gain using an echo state network (ESN). In order to handle unknown functions, a new recurrent neural network (RNN) approximation method called ESN is [...] Read more.

This paper investigates the observer-based adaptive stabilization control problem for a class of time-delay nonlinear systems with unknown control gain using an echo state network (ESN). In order to handle unknown functions, a new recurrent neural network (RNN) approximation method called ESN is utilized. It improves accuracy, reduces computing cost, and is simple to train. To address the issue of unknown control gain, the Nussbaum function is used, and the Lyapunov–Krasovskii functionals are used to address the delay term. The backstepping strategy and command filtering methodology are then used to create an adaptive stabilization controller. All of the closed-loop system’s signals are predicted to be confined by the Lyapunov stability theory. Finally, a simulation example is used to demonstrate the effectiveness of the suggested control mechanism. Full article

(This article belongs to the Special Issue Applications of Mathematical Modeling and Neural Networks)

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17 pages, 4648 KiB

Open AccessArticle

Adaptive Synchronization Sliding Mode Control for an Uncertain Dual-Arm Robot with Unknown Control Direction

by Duc Thien Tran, Hoang Vu Dao and Kyoung Kwan Ahn

Appl. Sci. 2023, 13(13), 7423; https://doi.org/10.3390/app13137423 - 22 Jun 2023

Cited by 4 | Viewed by 2000

Abstract

In this paper, an adaptive synchronization sliding mode control is proposed for a dual-arm robot against parameter variations, external disturbance, and unknown control directions. The proposed control is designed by using cross-coupling error and sliding mode control to guarantee the position synchronization of [...] Read more.

In this paper, an adaptive synchronization sliding mode control is proposed for a dual-arm robot against parameter variations, external disturbance, and unknown control directions. The proposed control is designed by using cross-coupling error and sliding mode control to guarantee the position synchronization of the dual-arm manipulator. The control objective of the proposed control is to synchronize the movement of both arms beside the trajectory tracking issue. In order to manage the lumped uncertainties caused by the parameter variations, external disturbance, and unknown control directions, an extended state observer is used in the proposed control. It enhances the stability of the controlled system against uncertainties. Additionally, a Nussbaum gain function is integrated into the control algorithm to deal with the issue of unknown control direction. Lyapunov stability theory is used to demonstrate the stability of the controlled system. Finally, some simulations are implemented in MATLAB Simulink with a dual 3-DOF manipulator system. The results of the proposed control are compared to other controllers to verify its effectiveness. Full article

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17 pages, 374 KiB

Open AccessArticle

Distributed Adaptive Consensus Output Tracking Problem of Nonlinear Multi-Agent Systems with Unknown High-Frequency Gain Signs under Directed Graphs

by Jingyu Chen and Zhengtao Ding

Electronics 2023, 12(8), 1830; https://doi.org/10.3390/electronics12081830 - 12 Apr 2023

Cited by 3 | Viewed by 1547

Abstract

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relative degrees are the same. A new [...] Read more.

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relative degrees are the same. A new type of Nussbaum gain is first presented to tackle adaptive consensus control of network-connected systems without the knowledge of the high-frequency gains. Adaptive laws and internal models are then proposed to handle the uncertainties and unknown parameters. An integral Lyapunov function based on sufficient conditions is finally introduced to tackle the asymmetry of the Laplacian matrix of directed graphs, into which we incorporate the new Nussbaum gain and the adaptive internal model to design the controller. It is apparent that the control scheme and the adaptive laws are fully distributed, which means that only the relative information of the neighbourhood subsystems’ outputs is used, and the simulation results validate the effectiveness of the control design, whereby they guarantee the asymptotic convergence of errors to zero as well as the boundedness of the state variables. Full article

(This article belongs to the Special Issue High Performance Control and Industrial Applications)

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22 pages, 5267 KiB

Open AccessArticle

Adaptive Fuzzy Command Filtered Finite-Time Tracking Control for Uncertain Nonlinear Multi-Agent Systems with Unknown Input Saturation and Unknown Control Directions

by Xiongfeng Deng, Yiqing Huang and Lisheng Wei

Mathematics 2022, 10(24), 4656; https://doi.org/10.3390/math10244656 - 8 Dec 2022

Cited by 7 | Viewed by 1717

Abstract

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. [...] Read more.

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called “explosion of complexity” in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

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17 pages, 667 KiB

Open AccessArticle

Adaptive Fault-Tolerant Control for Second-Order Multiagent Systems with Unknown Control Directions via a Self-Tuning Distributed Observer

by Rongrong Gu, Xudong Sun and Dongyi Pu

Electronics 2022, 11(23), 3939; https://doi.org/10.3390/electronics11233939 - 28 Nov 2022

Cited by 4 | Viewed by 1520

Abstract

In this paper, we first design a self-tuning distributed observer for second-order multi-agent systems which is capable of providing the estimation of the leader’s signal to various followers. We then further develop an adaptive sliding-mode controller to solve the cooperative tracking problem between [...] Read more.

In this paper, we first design a self-tuning distributed observer for second-order multi-agent systems which is capable of providing the estimation of the leader’s signal to various followers. We then further develop an adaptive sliding-mode controller to solve the cooperative tracking problem between leader and followers for second-order multi-agent systems subject to time-varying actuator faults and unknown external disturbances, which can ensure that the leader-following cooperative tracking errors converge to zero asymptotically. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed controller. This control law offers three advantages: first, the problem of communication barriers among the leader and followers can be solved by the self-tuning distributed observer, which can calculate the observer gain online; second, a new type of adaptive sliding-mode controller is proposed by introducing a Nussbaum function; and lastly, the bounds of unknown actuator faults and unknown external disturbances can be adaptively estimated. Full article

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20 pages, 3245 KiB

Open AccessArticle

Adaptive Dynamic Surface Control of Strict-Feedback Fractional-Order Nonlinear Systems with Input Quantization and External Disturbances

by Fan Zhang, Xiongfeng Deng and Lisheng Wei

Fractal Fract. 2022, 6(12), 698; https://doi.org/10.3390/fractalfract6120698 - 25 Nov 2022

Cited by 1 | Viewed by 1781

Abstract

In this work, an adaptive dynamic surface control law for a type of strict-feedback fractional-order nonlinear system is proposed. The considered system contained input quantization and unknown external disturbances. The virtual control law is presented by utilizing a dynamic surface control approach at [...] Read more.

In this work, an adaptive dynamic surface control law for a type of strict-feedback fractional-order nonlinear system is proposed. The considered system contained input quantization and unknown external disturbances. The virtual control law is presented by utilizing a dynamic surface control approach at each step, where the nonlinear compensating term with the estimation of unknown bounded parameters is introduced to overcome the influence of unknown external disturbances and surface errors. Meanwhile, the adaptive laws of relevant parameters are also designed. In addition, an improved fractional-order nonlinear filter is developed to deal with the explosion of complexity raised by the recursive process. In the last step, an adaptive dynamic surface control law is proposed to ensure the convergence of tracking error, in which the Nussbaum gain function is applied to solve the problem of the unknown control gain generated by input quantization. Then, the fractional Lyapunov stability theory is applied to verify the stability of the proposed control law. Finally, simulation examples are given to illustrate the effectiveness of the proposed control law. Full article

(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)

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17 pages, 2082 KiB

Open AccessArticle

Adaptive Fuzzy Iterative Learning Control for Systems with Saturated Inputs and Unknown Control Directions

by Qing-Yuan Xu, Wan-Ying He, Chuang-Tao Zheng, Peng Xu, Yun-Shan Wei and Kai Wan

Mathematics 2022, 10(19), 3462; https://doi.org/10.3390/math10193462 - 22 Sep 2022

Cited by 4 | Viewed by 2013

Abstract

An adaptive fuzzy iterative learning control (ILC) algorithm is designed for the iterative variable reference trajectory problem of nonlinear discrete-time systems with input saturations and unknown control directions. Firstly, an adaptive fuzzy iterative learning controller is constructed by combining with the fuzzy logic [...] Read more.

An adaptive fuzzy iterative learning control (ILC) algorithm is designed for the iterative variable reference trajectory problem of nonlinear discrete-time systems with input saturations and unknown control directions. Firstly, an adaptive fuzzy iterative learning controller is constructed by combining with the fuzzy logic system (FLS), which can compensate the loss caused by input saturation. Then, the discrete Nussbaum gain technique is adopted along the iteration axis, which can be embedded to the learning control method to identify the control direction of the system. Finally, based on the nonincreasing Lyapunov-like function, it is proven that the adaptive iterative learning controller can converge asymptotically when the number of iterations tends to infinity, and the system signals always remain bounded in the learning process. A simulation example verifies the feasibility and effectiveness of the learning control method. Full article

(This article belongs to the Special Issue Deep Learning and Adaptive Control)

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