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Keywords = barrier lyapunov function

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24 pages, 840 KB  
Article
Adaptive Event-Triggered Full-State Constrained Control of Multi-Agent Systems Under Cyber Attacks
by Jinxia Wu, Pengfei Cui, Juan Wang and Yuanxin Li
Actuators 2025, 14(9), 448; https://doi.org/10.3390/act14090448 - 11 Sep 2025
Viewed by 390
Abstract
For multi-agent systems under Denial-of-Service (DoS) attacks, a relative threshold strategy for event triggering and a state-constrained control method with prescribed performance are proposed. Within the framework of combining graph theory with the leader–follower approach, coordinate transformation is utilized to decouple the multi-agent [...] Read more.
For multi-agent systems under Denial-of-Service (DoS) attacks, a relative threshold strategy for event triggering and a state-constrained control method with prescribed performance are proposed. Within the framework of combining graph theory with the leader–follower approach, coordinate transformation is utilized to decouple the multi-agent system. Inspired by the three-way handshake technology of TCP communication, a DoS detection system is designed based on event-triggering. This system is used to detect DoS attacks, prevent the impacts brought by DoS attacks, and reduce the update frequency of the controller. Fuzzy logic systems are employed to approximate the unknown nonlinear functions within the system. By using a first-order filter to approximate the derivative of the virtual controller, the computational complexity issue in the backstepping method is addressed. Furthermore, The Barrier Lyapunov Function (BLF) possesses unique mathematical properties. When the system state approaches the pre-set boundary, it can exhibit a special variation trend, thereby imposing a restrictive effect on the system state. The Prescribed Performance Function (PPF), on the other hand, defines the expected performance standards that the system aims to achieve in the tracking task, covering key indicators such as tracking accuracy and response speed. By organically integrating these two functions, the system can continuously monitor and adjust its own state during operation. When there is a tendency for the tracking error to deviate from the specified range, the combined function mechanism will promptly come into play. Through the reasonable adjustment of the system’s control input, it ensures that the tracking error always remains within the pre-specified range. Finally, through Lyapunov analysis, the proposed control protocol ensures that all closed-loop signals remain bounded under attacks, with the outputs of all followers synchronizing with the leader’s output in the communication graph. Full article
(This article belongs to the Special Issue Advanced Technologies in Actuators for Control Systems)
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27 pages, 5105 KB  
Article
Performance of Double Pipe Heat Exchanger—Partially Occupied by Metal Foam—Is Better Enhanced Using Robust Adaptive Barrier Function-Based Sliding Mode Control
by Luma F. Ali, Shibly A. AL-Samarraie and Amjad J. Humaidi
Energies 2025, 18(17), 4671; https://doi.org/10.3390/en18174671 - 3 Sep 2025
Viewed by 905
Abstract
Numerous thermal practical applications utilize shell and tube heat exchanger appliances to transfer heat energy between hot and cold working fluids. Incorporating metal foam to the outer periphery of inner tube improves the heat transfer process from hot water in the tube side [...] Read more.
Numerous thermal practical applications utilize shell and tube heat exchanger appliances to transfer heat energy between hot and cold working fluids. Incorporating metal foam to the outer periphery of inner tube improves the heat transfer process from hot water in the tube side to cold water in the shell side and consequently improves heat exchanger performance. In this study, the integration of use of a porous material together with designing a robust adaptive controller could efficiently regulate the outlet cold water temperature to the desired value. This is achieved with respect to the time required for cold water to reach the desired temperature (settling time) and the amount of hot water volume flow during a certain time span. A barrier function-based adaptive sliding mode controller (BF-based adaptive SMC) is proposed, which requires only the information of temperature measurement of cold water. The stability of BF-based adaptive SMC is proved utilizing Lyapunov function analysis. The effectiveness of proposed controller is verified via numerical results, which showed that the proposed controller could achieve considerable accuracy of cold water temperature using suitable design parameters. In addition, the robustness of controller against variation in inlet temperature is also verified. Another improvement to performance of heat exchanger system is achieved by adding the metal foam of aluminum material on inner pipe perimeter with wide range of metal foam to outer inner pipe diameters ratio (1s1.8). The results showed that the settling time is significantly reduced which enables outlet cold water to reach the required temperature faster. With respect of the case of non-adding metal foam on inner pipe outer circumference, when s=1.2, the settling time and hot water temperature are reduced by 1/2 and 17.3%, respectively, while for s=1.8, they are decreased by 1/20 and 35.3% correspondingly. Accordingly, the required volume flow for hot water is reduced considerably. Full article
(This article belongs to the Special Issue Heat Transfer Analysis: Recent Challenges and Applications)
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30 pages, 15851 KB  
Article
Parameter Tuning of Barrier Lyapunov Function-Based Controllers in Electric Drive Systems
by Marcin Jastrzębski and Jacek Kabziński
Energies 2025, 18(16), 4301; https://doi.org/10.3390/en18164301 - 12 Aug 2025
Viewed by 476
Abstract
This paper refers to fast and accurate electric servo control in the presence of position and velocity constraints. This problem, one of the most common nowadays in industrial automation, is often addressed by controllers derived using barrier Lyapunov functions (BLFs). This popular and [...] Read more.
This paper refers to fast and accurate electric servo control in the presence of position and velocity constraints. This problem, one of the most common nowadays in industrial automation, is often addressed by controllers derived using barrier Lyapunov functions (BLFs). This popular and effective technique is burdened with several difficulties, such as complex feasibility conditions and the inapplicability of the derived controller because of control constraints. In this contribution, we propose a novel, BLF-based, adaptive controller for an electric servo (linear or rotational) with modeling uncertainties, solving a tracking problem. The controller derivation is completed by the tuning procedure, which enables safe system operation in the presence of active control constraints, measurement errors, and noise. The selection of the best combination of BLFs is a part of this procedure. Also, all feasibility issues are solved by the proposed approach. The derivation is completed by extensive numerical simulations and real-life implementation using two different servo systems—the first with a linear permanent magnet motor and the second with a rotational PMSM. Full article
(This article belongs to the Section F: Electrical Engineering)
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22 pages, 4827 KB  
Article
Development of a Multifunctional Mobile Manipulation Robot Based on Hierarchical Motion Planning Strategy and Hybrid Grasping
by Yuning Cao, Xianli Wang, Zehao Wu and Qingsong Xu
Robotics 2025, 14(7), 96; https://doi.org/10.3390/robotics14070096 - 15 Jul 2025
Viewed by 2316
Abstract
A mobile manipulation robot combines the navigation capability of unmanned ground vehicles and manipulation advantage of robotic arms. However, the development of a mobile manipulation robot is challenging due to the integration requirement of numerous heterogeneous subsystems. In this paper, we propose a [...] Read more.
A mobile manipulation robot combines the navigation capability of unmanned ground vehicles and manipulation advantage of robotic arms. However, the development of a mobile manipulation robot is challenging due to the integration requirement of numerous heterogeneous subsystems. In this paper, we propose a multifunctional mobile manipulation robot by integrating perception, mapping, navigation, object detection, and grasping functions into a seamless workflow to conduct search-and-fetch tasks. To realize navigation and collision avoidance in complex environments, a new hierarchical motion planning strategy is proposed by fusing global and local planners. Control Lyapunov Function (CLF) and Control Barrier Function (CBF) are employed to realize path tracking and to guarantee safety during navigation. The convolutional neural network and the gripper’s kinematic constraints are adopted to construct a learning-optimization hybrid grasping algorithm to generate precise grasping poses. The efficiency of the developed mobile manipulation robot is demonstrated by performing indoor fetching experiments, showcasing its promising capabilities in real-world applications. Full article
(This article belongs to the Section Sensors and Control in Robotics)
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22 pages, 2867 KB  
Article
Hierarchical Deep Reinforcement Learning-Based Path Planning with Underlying High-Order Control Lyapunov Function—Control Barrier Function—Quadratic Programming Collision Avoidance Path Tracking Control of Lane-Changing Maneuvers for Autonomous Vehicles
by Haochong Chen and Bilin Aksun-Guvenc
Electronics 2025, 14(14), 2776; https://doi.org/10.3390/electronics14142776 - 10 Jul 2025
Viewed by 1173
Abstract
Path planning and collision avoidance are essential components of an autonomous driving system (ADS), ensuring safe navigation in complex environments shared with other road users. High-quality planning and reliable obstacle avoidance strategies are essential for advancing the SAE autonomy level of autonomous vehicles, [...] Read more.
Path planning and collision avoidance are essential components of an autonomous driving system (ADS), ensuring safe navigation in complex environments shared with other road users. High-quality planning and reliable obstacle avoidance strategies are essential for advancing the SAE autonomy level of autonomous vehicles, which can largely reduce the risk of traffic accidents. In daily driving scenarios, lane changing is a common maneuver used to avoid unexpected obstacles such as parked vehicles or suddenly appearing pedestrians. Notably, lane-changing behavior is also widely regarded as a key evaluation criterion in driver license examinations, highlighting its practical importance in real-world driving. Motivated by this observation, this paper aims to develop an autonomous lane-changing system capable of dynamically avoiding obstacles in multi-lane traffic environments. To achieve this objective, we propose a hierarchical decision-making and control framework in which a Double Deep Q-Network (DDQN) agent operates as the high-level planner to select lane-level maneuvers, while a High-Order Control Lyapunov Function–High-Order Control Barrier Function–based Quadratic Program (HOCLF-HOCBF-QP) serves as the low-level controller to ensure safe and stable trajectory tracking under dynamic constraints. Simulation studies are used to evaluate the planning efficiency and overall collision avoidance performance of the proposed hierarchical control framework. The results demonstrate that the system is capable of autonomously executing appropriate lane-changing maneuvers to avoid multiple obstacles in complex multi-lane traffic environments. In computational cost tests, the low-level controller operates at 100 Hz with an average solve time of 0.66 ms per step, and the high-level policy operates at 5 Hz with an average solve time of 0.60 ms per step. The results demonstrate real-time capability in autonomous driving systems. Full article
(This article belongs to the Special Issue Intelligent Technologies for Vehicular Networks, 2nd Edition)
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19 pages, 1219 KB  
Article
Control Design for Flexible Manipulator Model with Nonlinear Input and State Constraints Based on Symmetric Barrier Lyapunov Function
by Yukun Song, Yongjun Wu and Yang Chen
Symmetry 2025, 17(7), 1035; https://doi.org/10.3390/sym17071035 - 1 Jul 2025
Cited by 1 | Viewed by 391
Abstract
Flexible manipulators are widely applied in many fields. Here, the control design for a simplified flexible manipulator model with nonlinear inputs and state constraints is studied. The impact of two inputs and disturbances on the system was considered. One torque input comes from [...] Read more.
Flexible manipulators are widely applied in many fields. Here, the control design for a simplified flexible manipulator model with nonlinear inputs and state constraints is studied. The impact of two inputs and disturbances on the system was considered. One torque input comes from the joint motor, and the other input force comes from the linkage actuator tip. The input constraints of a dead zone are applied to both inputs to the manipulator. To offset the effect of the nonlinear input, we first linearize the dead zone and convert it into a linear-input characteristic and a finite error value. Then, the adaptive rate is designed to compensate for the effects of the nonlinear input. For the state constraints, an adaptive controller is proposed based on a symmetric tangent-type barrier Lyapunov function which can operate under closer constraint conditions, and parameter tunability offers flexibility in balancing the constraints’ tightness and performance. The stability proof ensures that all states are within the given constraint range. The provided simulation results indicate that the system is not sensitive to the initial values, and when the initial values are taken to be between open intervals (−0.4, 0.34), this ensures the stability of the system and does not violate the constraint bounds. Full article
(This article belongs to the Section Mathematics)
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22 pages, 4907 KB  
Article
Predefined Time Control of State-Constrained Multi-Agent Systems Based on Command Filtering
by Jianhua Zhang, Xuan Yu, Quanmin Zhu and Zhanyang Yu
Mathematics 2025, 13(13), 2151; https://doi.org/10.3390/math13132151 - 30 Jun 2025
Viewed by 547
Abstract
This paper resolves the predefined-time control problem for multi-agent systems under predefined performance metrics and state constraints, addressing critical limitations of traditional methods—notably their inability to enforce strict user-specified deadlines for mission-critical operations, coupled with difficulties in simultaneously guaranteeing transient performance bounds and [...] Read more.
This paper resolves the predefined-time control problem for multi-agent systems under predefined performance metrics and state constraints, addressing critical limitations of traditional methods—notably their inability to enforce strict user-specified deadlines for mission-critical operations, coupled with difficulties in simultaneously guaranteeing transient performance bounds and state constraints while suffering prohibitive stability proof complexity. To overcome these challenges, we propose a predefined performance control methodology that integrates Barrier Lyapunov Functions command-filtered backstepping. The framework rigorously ensures exact convergence within user-defined time independent of initial conditions while enforcing strict state constraints through time-varying BLF boundaries and further delivers quantifiable performance such as overshoot below 5% and convergence within 10 s. By eliminating high-order derivative continuity proofs via command-filter design, stability analysis complexity is reduced by 40% versus conventional backstepping. Stability proofs and dual-case simulations (UAV formation/smart grid) demonstrate over 95% tracking accuracy under disturbances and constraints, validating broad applicability in safety-critical multi-agent systems. Full article
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41 pages, 3731 KB  
Article
Neural Optimization Techniques for Noisy-Data Observer-Based Neuro-Adaptive Control for Strict-Feedback Control Systems: Addressing Tracking and Predefined Accuracy Constraints
by Abdulaziz Garba Ahmad and Taher Alzahrani
Fractal Fract. 2025, 9(6), 389; https://doi.org/10.3390/fractalfract9060389 - 17 Jun 2025
Viewed by 867
Abstract
This research proposes a fractional-order adaptive neural control scheme using an optimized backstepping (OB) approach to address strict-feedback nonlinear systems with uncertain control directions and predefined performance requirements. The OB framework integrates both fractional-order virtual and actual controllers to achieve global optimization, while [...] Read more.
This research proposes a fractional-order adaptive neural control scheme using an optimized backstepping (OB) approach to address strict-feedback nonlinear systems with uncertain control directions and predefined performance requirements. The OB framework integrates both fractional-order virtual and actual controllers to achieve global optimization, while a Nussbaum-type function is introduced to handle unknown control paths. To ensure convergence to desired accuracy within a prescribed time, a fractional-order dynamic-switching mechanism and a quartic-barrier Lyapunov function are employed. An input-to-state practically stable (ISpS) auxiliary signal is designed to mitigate unmodeled dynamics, leveraging classical lemmas adapted to fractional-order systems. The study further investigates a decentralized control scenario for large-scale stochastic nonlinear systems with uncertain dynamics, undefined control directions, and unmeasurable states. Fuzzy logic systems are employed to approximate unknown nonlinearities, while a fuzzy-phase observer is designed to estimate inaccessible states. The use of Nussbaum-type functions in decentralized architectures addresses uncertainties in control directions. A key novelty of this work lies in the combination of fractional-order adaptive control, fuzzy logic estimation, and Nussbaum-based decentralized backstepping to guarantee that all closed-loop signals remain bounded in probability. The proposed method ensures that system outputs converge to a small neighborhood around the origin, even under stochastic disturbances. The simulation results confirm the effectiveness and robustness of the proposed control strategy. Full article
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20 pages, 820 KB  
Article
Fixed-Time Adaptive Event-Triggered Control for Uncertain Nonlinear Systems Under Full-State Constraints
by Yue Zhang, Jietao Dai, Zhenzhang Liu, Ruizhi Tang, Guoxiong Zheng and Jianhui Wang
Actuators 2025, 14(5), 231; https://doi.org/10.3390/act14050231 - 5 May 2025
Cited by 1 | Viewed by 917
Abstract
The problem of adaptive event-triggered control for uncertain nonlinear systems with full-state constraints was investigated. State constraints can significantly affect system performance, especially when time-varying external disturbances are present, potentially leading to instability. Thus, a fixed-time disturbance observer was designed. It estimated unknown [...] Read more.
The problem of adaptive event-triggered control for uncertain nonlinear systems with full-state constraints was investigated. State constraints can significantly affect system performance, especially when time-varying external disturbances are present, potentially leading to instability. Thus, a fixed-time disturbance observer was designed. It estimated unknown uncertainties within a predetermined time. Meanwhile, an asymmetric barrier Lyapunov function was developed. It ensured the stability of the system state under constraints. Furthermore, to reduce the utilization rate of the system’s communication resources, an adaptive event-triggered control scheme was proposed, and an integrated control method was established to preset the convergence time of the system’s state error, greatly improving the convergence speed. Theoretical analysis and simulations demonstrated the effectiveness of the proposed approach. The results show that the system achieved stable control within a fixed time, even under full-state constraints and external disturbances, while using fewer communication resources. Full article
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23 pages, 2147 KB  
Article
Precision Fixed-Time Formation Control for Multi-AUV Systems with Full State Constraints
by Yuanfeng Chen, Haoyuan Wang and Xiaodong Wang
Mathematics 2025, 13(9), 1451; https://doi.org/10.3390/math13091451 - 28 Apr 2025
Cited by 2 | Viewed by 619
Abstract
The trajectory tracking the control of autonomous underwater vehicle (AUV) systems faces considerable challenges due to strong inter-axis coupling and complex time-varying external disturbances. This paper proposes a novel fixed-time control scheme incorporating a switching threshold-based event-driven strategy to address critical issues in [...] Read more.
The trajectory tracking the control of autonomous underwater vehicle (AUV) systems faces considerable challenges due to strong inter-axis coupling and complex time-varying external disturbances. This paper proposes a novel fixed-time control scheme incorporating a switching threshold-based event-driven strategy to address critical issues in multi-AUV formation control, including full-state constraints, unmeasurable states, model uncertainties, limited communication resources, and unknown time-varying disturbances. A rapid and stable dimensional augmented state observer (RSDASO) was first developed to achieve fixed-time convergence in estimating aggregated disturbances and unmeasurable states. Subsequently, a logarithmic barrier Lyapunov function was constructed to derive a fixed-time control law that guarantees bounded system errors within a predefined interval while strictly confining all states to specified constraints. The introduction of a switching threshold event-triggering mechanism (ETM) significantly reduced communication resource consumption. The simulation results demonstrate the effectiveness of the proposed method in improving control accuracy while substantially lowering communication overhead. Full article
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16 pages, 3434 KB  
Article
Adaptive Terminal Sliding Mode Control for a Quadrotor System with Barrier Function Switching Law
by Jiangting Zhu, Xionghui Long and Quan Yuan
Mathematics 2025, 13(8), 1344; https://doi.org/10.3390/math13081344 - 19 Apr 2025
Cited by 3 | Viewed by 812
Abstract
This study presents a novel finite-time robust control framework for quadrotor systems subjected to model uncertainties and unknown external disturbances. A fast terminal sliding mode (FTSM) manifold is first constructed to achieve finite-time convergence of tracking errors. To address the challenges posed by [...] Read more.
This study presents a novel finite-time robust control framework for quadrotor systems subjected to model uncertainties and unknown external disturbances. A fast terminal sliding mode (FTSM) manifold is first constructed to achieve finite-time convergence of tracking errors. To address the challenges posed by uncertain system dynamics, a radial basis function neural network (RBFNN) is integrated for real-time approximation of unknown nonlinearities. In addition, an adaptive gain regulation mechanism based on a barrier Lyapunov function (BLF) is developed to ensure boundedness of system trajectories while enhancing robustness without requiring prior knowledge of disturbance bounds. The proposed control scheme guarantees finite-time stability, strong robustness, and precise trajectory tracking. Numerical simulations substantiate the efficacy and superiority of the proposed method in comparison with existing control approaches. Full article
(This article belongs to the Special Issue Deep Learning and Adaptive Control, 3rd Edition)
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17 pages, 3681 KB  
Article
Control of Vehicle Lateral Handling Stability Considering Time-Varying Full-State Constraints
by Lizhe Wu and Dingxuan Zhao
Mathematics 2025, 13(8), 1217; https://doi.org/10.3390/math13081217 - 8 Apr 2025
Cited by 1 | Viewed by 1056
Abstract
Lateral handling stability control is crucial for ensuring vehicle driving safety. To address this issue, this paper proposes a lateral handling stability control method that considers time-varying full-state constraints. By constructing a time-varying symmetric Barrier Lyapunov Function (TS-BLF), this method imposes time-varying nonlinear [...] Read more.
Lateral handling stability control is crucial for ensuring vehicle driving safety. To address this issue, this paper proposes a lateral handling stability control method that considers time-varying full-state constraints. By constructing a time-varying symmetric Barrier Lyapunov Function (TS-BLF), this method imposes time-varying nonlinear constraints on both the sideslip angle and yaw rate, thereby ensuring full-state constrained stability control of vehicles under complex operating conditions. Additionally, a second-order command filtering technique with an error compensation mechanism is introduced to reduce the computational complexity of control laws while mitigating filter-induced errors that may degrade system performance. To validate the effectiveness and robustness of the proposed method, the vehicle’s dynamic response is analyzed under different speeds on both dry asphalt pavement and dry gravel surfaces. The simulation results demonstrate that the proposed method effectively suppresses understeer and oversteer, enhances the dynamic stability margin under extreme operating conditions, and improves vehicle adaptability in complex environments. Full article
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26 pages, 12220 KB  
Article
Preassigned Fixed-Time Synergistic Constrained Control for Fixed-Wing Multi-UAVs with Actuator Faults
by Jianhua Lu, Zehao Yuan and Ning Wang
Drones 2025, 9(4), 268; https://doi.org/10.3390/drones9040268 - 1 Apr 2025
Viewed by 472
Abstract
This study focuses on the distributed fixed-time fault-tolerant control problem for a network of six-degree-of-freedom (DOF) fixed-wing unmanned aerial vehicles (UAVs), which are subject to full-state constraints and actuator faults. The novelty of the proposed design lies in the incorporation of an enhanced [...] Read more.
This study focuses on the distributed fixed-time fault-tolerant control problem for a network of six-degree-of-freedom (DOF) fixed-wing unmanned aerial vehicles (UAVs), which are subject to full-state constraints and actuator faults. The novelty of the proposed design lies in the incorporation of an enhanced asymmetric time-varying tan-type barrier Lyapunov function (BLF), which is applicable in both constrained and unconstrained scenarios. This function ensures that the UAV states remain within compact sets at all times while achieving fixed-time convergence. Additionally, a fixed-time performance function (FTPF) is developed to eliminate the dependency on exponential functions commonly used in traditional fixed-time control methods. The adverse effects of actuator faults, including lock-in-place and loss of effectiveness, are mitigated through a bounded uniform tracking control design. A rigorous Lyapunov function analysis demonstrates that all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with both velocity and attitude tracking errors converging to residual sets near the origin. Experimental validation tests are conducted to confirm the effectiveness of the theoretical findings. Full article
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19 pages, 2561 KB  
Article
Prescribed Performance Bounded-H Control for Flexible-Joint Manipulators Without Initial Condition Restriction
by Ye Zhang, Ruibo Sun and Jie Shang
Sensors 2025, 25(7), 2195; https://doi.org/10.3390/s25072195 - 30 Mar 2025
Viewed by 616
Abstract
Flexible-joint manipulators have a lightweight nature, compact structure, and high flexibility, making them widely applicable in industrial manufacturing, biomedical instruments, and aerospace fields. However, the inherent flexibility of single-link flexible-joint manipulators (SLFJMs) poses substantial control challenges. Compared to traditional control algorithms, prescribed performance [...] Read more.
Flexible-joint manipulators have a lightweight nature, compact structure, and high flexibility, making them widely applicable in industrial manufacturing, biomedical instruments, and aerospace fields. However, the inherent flexibility of single-link flexible-joint manipulators (SLFJMs) poses substantial control challenges. Compared to traditional control algorithms, prescribed performance control (PPC) algorithms provide superior transient response and steady-state performance by defining a prescribed performance function. However, existing PPC algorithms are limited to a specific range of system initial states, which reduces the joint manipulator’s operational workspace and weakens the robustness of the control algorithm. To address this issue, this study proposes a prescribed performance bounded-H fault-tolerant controller for SLFJMs. By designing an improved tangent-type barrier Lyapunov function (BLF), a prescribed performance controller that is independent of the initial state of the SLFJM is developed. An input control function (ICF) is employed to mitigate the impulse response of the control input, ensuring a smooth transition from zero. Furthermore, the improved tangent-type BLF enables the tracking error to rapidly converge to a small neighborhood of zero. Finally, a stabilization control simulation experiment is conducted; the results validate the effectiveness of the proposed prescribed performance bounded-H controller. Full article
(This article belongs to the Section Sensors and Robotics)
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22 pages, 2883 KB  
Article
Zero-Error Prescribed-Time Tracking Control for Switched Non-Square MIMO Nonlinear Systems Subject to Asymmetric Time-Varying Output Constraints
by Ying Liu, Hui Wang, Quanxin Zhu and Fujin Jia
Mathematics 2025, 13(6), 986; https://doi.org/10.3390/math13060986 - 17 Mar 2025
Cited by 1 | Viewed by 493
Abstract
Previous studies typically assume that output constraints are symmetric or time-invariant. However, effectively addressing asymmetric and time-varying output constraints remains an unsolved issue, especially in the case of switched non-square multi-input multi-output (MIMO) nonlinear systems. To tackle this challenge, this paper first establishes [...] Read more.
Previous studies typically assume that output constraints are symmetric or time-invariant. However, effectively addressing asymmetric and time-varying output constraints remains an unsolved issue, especially in the case of switched non-square multi-input multi-output (MIMO) nonlinear systems. To tackle this challenge, this paper first establishes a prescribed-time (PT) Lyapunov criterion for switched nonlinear systems. Second, an asymmetric nonlinear mapping (ANM) method is proposed to handle asymmetric time-varying output constraints. Compared to the barrier Lyapunov function (BLF) approach, the ANM method relaxes the initial output conditions and the constraint functions are not necessarily required to be opposite in sign. Finally, a PT tracking controller is designed for a class of switched MIMO nonlinear systems with a non-square control coefficient matrix by using the time-varying gain technique. This controller achieves zero-error tracking within the prescribed time while ensuring that output constraints are satisfied. The effectiveness of the proposed control strategy is validated through numerical and simulation examples. Full article
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