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Journal articles on the topic 'Barrier Lyapunov functionals'

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Author: Grafiati

Published: 6 September 2023

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Li, Dong-Juan, Jing Li, and Shu Li. "Adaptive control of nonlinear systems with full state constraints using Integral Barrier Lyapunov Functionals." Neurocomputing 186 (April 2016): 90–96. http://dx.doi.org/10.1016/j.neucom.2015.12.075.

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Wu, Yuxiang, Tian Xu, and Hongqiang Mo. "Adaptive tracking control for nonlinear time-delay systems with time-varying full state constraints." Transactions of the Institute of Measurement and Control 42, no. 12 (March 6, 2020): 2178–90. http://dx.doi.org/10.1177/0142331220908987.

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This paper presents an adaptive tracking control approach for a class of uncertain nonlinear strict-feedback systems subject to time-varying full state constraints and time-delays. To stabilize such systems, an adaptive tracking controller is structured by combining the neural networks and the backstepping technique. To guarantee all states do not violate the time-varying constraint sets, the appropriate time-varying Barrier Lyapunov functions are employed at each stage of the backstepping procedure. By using the Lyapunov-Krasovskii functionals, the effect of time delay is eliminated. It is proved that the output follows the desired signal well without violating any constraints, and all the signals in the closed-loop system are semiglobal uniformly ultimately bounded by using the Lyapunov analysis. Finally, a comparison study simulation is provided to illustrate the effectiveness of the proposed control strategy.

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Liu, Yan-Jun, Shaocheng Tong, C. L. Philip Chen, and Dong-Juan Li. "Adaptive NN Control Using Integral Barrier Lyapunov Functionals for Uncertain Nonlinear Block-Triangular Constraint Systems." IEEE Transactions on Cybernetics 47, no. 11 (November 2017): 3747–57. http://dx.doi.org/10.1109/tcyb.2016.2581173.

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Li, Dongjuan, Dongxing Wang, and Ying Gao. "Adaptive Neural Control and Modeling for Continuous Stirred Tank Reactor with Delays and Full State Constraints." Complexity 2021 (October 7, 2021): 1–12. http://dx.doi.org/10.1155/2021/9948044.

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In this paper, an adaptive neural network control method is described to stabilize a continuous stirred tank reactor (CSTR) subject to unknown time-varying delays and full state constraints. The unknown time delay and state constraints problem of the concentration in the reactor seriously affect the input-output ratio and stability of the entire system. Therefore, the design difficulty of this control scheme is how to debar the effect of time delay in CSTR systems. To deal with time-varying delays, Lyapunov–Krasovskii functionals (LKFs) are utilized in the adaptive controller design. The convergence of the tracking error to a small compact set without violating the constraints can be identified by the time-varying logarithm barrier Lyapunov function (LBLF). Finally, the simulation results on CSTR are shown to reveal the validity of the developed control strategy.

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Ai, Xiang, Ya Zhang, and Yang-Yang Chen. "Spherical Formation Tracking Control of Non-Holonomic UAVs with State Constraints and Time Delays." Aerospace 10, no. 2 (January 26, 2023): 118. http://dx.doi.org/10.3390/aerospace10020118.

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This paper addresses a novel spherical formation tracking control problem of multiple UAVs with time-varying delays in the directed communication network, where the dynamics of each UAV is non-holonomic and in the presence of spatiotemporal flowfields. The state constraints (that is, position and velocity constraints) are derived from our previous differential geometry method and the F–S formulas. The state constraints and time delays in the directed communication network bring many difficulties to controller design. To this end, a virtual-structure-like design is given to achieve a formation with delayed information by using Lyapunov–Krasovskii functionals, and then proposing a barrier Lyapunov function for the satisfaction of state constraints to design a novel spherical formation tracking algorithm. The general assumption of the rate of change of time-varying delays, and a certain initial position and velocity adjustment range are given. Simulation results show the feasibility and effectiveness of the proposed algorithm.

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Li, Menghan, Shaobo Li, Junxing Zhang, Fengbin Wu, and Tao Zhang. "Neural Adaptive Funnel Dynamic Surface Control with Disturbance-Observer for the PMSM with Time Delays." Entropy 24, no. 8 (July 26, 2022): 1028. http://dx.doi.org/10.3390/e24081028.

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This paper suggests an adaptive funnel dynamic surface control method with a disturbance observer for the permanent magnet synchronous motor with time delays. An improved prescribed performance function is integrated with a modified funnel variable at the beginning of the controller design to coordinate the permanent magnet synchronous motor with the output constrained into an unconstrained one, which has a faster convergence rate than ordinary barrier Lyapunov functions. Then, the specific controller is devised by the dynamic surface control technique with first-order filters to the unconstrained system. Therein, a disturbance-observer and the radial basis function neural networks are introduced to estimate unmatched disturbances and multiple unknown nonlinearities, respectively. Several Lyapunov-Krasovskii functionals are constructed to make up for time delays, enhancing control performance. The first-order filters are implemented to overcome the “complexity explosion” caused by general backstepping methods. Additionally, the boundedness and binding ranges of all the signals are ensured through the detailed stability analysis. Ultimately, simulation results and comparison experiments confirm the superiority of the controller designed in this paper.

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Zhao, Wei, Yanjun Liu, and Lei Liu. "Observer-Based Adaptive Fuzzy Tracking Control Using Integral Barrier Lyapunov Functionals for A Nonlinear System With Full State Constraints." IEEE/CAA Journal of Automatica Sinica 8, no. 3 (March 2021): 617–27. http://dx.doi.org/10.1109/jas.2021.1003877.

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Wei, Yan, Pingfang Zhou, Yueying Wang, Dengping Duan, and Jiwei Tang. "Adaptive finite-time neural backstepping control for multiple-input–multiple-output uncertain nonlinear systems with full state constraints." Transactions of the Institute of Measurement and Control 43, no. 11 (February 7, 2021): 2450–60. http://dx.doi.org/10.1177/0142331221989121.

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This paper investigates the issue of finite-time tracking control for multiple-input–multiple-output nonlinear systems subject to uncertainties and full state constraints. To deal with full state constraints directly, integral barrier Lyapunov functionals (iBLF) are introduced. By using finite-time stability theory, an iBLF-based adaptive finite-time neural control scheme is presented. To solve the problem of “explosion of complexity” in the design of traditional backstepping control, a new finite-time convergent differentiator is presented. Through stability analysis, all closed-loop signals are proved to be semi-globally uniformly ultimately bounded, the finite time convergence can be guaranteed, and the state constraints are never violated. Finally, the attitude tracking simulations for an autonomous airship are conducted to verify the effectiveness of the proposed scheme.

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Xu, Tian, Yuxiang Wu, Haoran Fang, and Fuxi Wan. "Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation." Transactions of the Institute of Measurement and Control 44, no. 9 (December 30, 2021): 1824–35. http://dx.doi.org/10.1177/01423312211065851.

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This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.

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Luo, Zhenguo, Liping Luo, Liu Yang, Zhenghui Gao, and Yunhui Zeng. "Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses." Journal of Applied Mathematics 2014 (2014): 1–21. http://dx.doi.org/10.1155/2014/592543.

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An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.

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Kim, Bong Su, and Sung Jin Yoo. "Adaptive control of nonlinear pure-feedback systems with output constraints: Integral barrier Lyapunov functional approach." International Journal of Control, Automation and Systems 13, no. 1 (December 18, 2014): 249–56. http://dx.doi.org/10.1007/s12555-014-0018-3.

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Yu, Tianqi, Lei Liu, and Yan-Jun Liu. "Observer-based adaptive fuzzy output feedback control for functional constraint systems with dead-zone input." Mathematical Biosciences and Engineering 20, no. 2 (2022): 2628–50. http://dx.doi.org/10.3934/mbe.2023123.

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<abstract><p>This paper develops an adaptive output feedback control for a class of functional constraint systems with unmeasurable states and unknown dead zone input. The constraint is a series of functions closely linked to state variables and time, which is not achieved in current research results and is more general in practical systems. Furthermore, a fuzzy approximator based adaptive backstepping algorithm is designed and an adaptive state observer with time-varying functional constraints (TFC) is constructed to estimate the unmeasurable states of the control system. Relying on the relevant knowledge of dead zone slopes, the issue of non-smooth dead-zone input is successfully solved. The time-varying integral barrier Lyapunov functions (iBLFs) are employed to guarantee that the states of the system remain within the constraint interval. By Lyapunov stability theory, the adopted control approach can ensure the stability of the system. Finally, the feasibility of the considered method is conformed via a simulation experiment.</p></abstract>

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Rauh, Alexander. "Analytical Localization Lengths in an One-Dimensional Disordered Electron System." Zeitschrift für Naturforschung A 64, no. 3-4 (April 1, 2009): 205–21. http://dx.doi.org/10.1515/zna-2009-3-407.

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Abstract Analytical approximations of the Lyapunov exponent are derived for a random displacement model with equal potential barriers and random positions of the scatterers. Two asymptotic regions are considered corresponding to high and low reflectivity of the single scattering potential. The analytical results are in terms of a distribution function W for certain phases of the transfer matrices. A functional equation for W is derived and numerically solved. This serves to validate the analytical asymptotic formulas which turn out to be accurate in the high and low reflectivity regions with dimensionless wave number K < 2 and K > 6, respectively. The high wave number asymptotics allows for an analytical examination of the sufficient conditions for Anderson localization

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Yuan, Fengyi, Yan-Jun Liu, Lei Liu, Jie Lan, Dapeng Li, Shaocheng Tong, and C. L. Philip Chen. "Adaptive Neural Consensus Tracking Control for Nonlinear Multiagent Systems Using Integral Barrier Lyapunov Functionals." IEEE Transactions on Neural Networks and Learning Systems, 2021, 1–11. http://dx.doi.org/10.1109/tnnls.2021.3112763.

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Jiang, Dao-gen, Wei Jiang, Xiao-dong Zhu, and Xiang-yuan Yin. "Adaptive control for full-states constrained nonlinear systems with unknown control direction using Barrier Lyapunov Functionals." Transactions of the Institute of Measurement and Control, May 21, 2022, 014233122210938. http://dx.doi.org/10.1177/01423312221093826.

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In this paper, a new adaptive back-stepping (BS) control technique based on barrier Lyapunov functions (BLFs) is proposed to manage a class of full-state constrained nonlinear systems subject to totally unknown directions and uncertain time-varying parameters. BLFs guarantee that all the system states are constrained in a predefined compact set and the tracking error can converge to a small zero neighborhood. Nussbaum’s gain technique is utilized to tackle the unknown control direction issue. Besides, a sufficiently smooth projection algorithm is adopted to estimate the unknown time-varying parameters, so as to ensure that the adaption laws are differentiable and bounded. The developed controller not only makes all the system states restrained in the compact set but also assures the smoothness and boundedness of all the signals of the closed-loop system. In addition, the sufficiently smooth projection algorithm and Nussbaum gain technique are combined with the BLF-BS control method for the nonlinear systems. Finally, the simulation example results verify the effectiveness and feasibility of the proposed control scheme.

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Wu, Yuxiang, Tian Xu, and Haoran Fang. "Command filtered adaptive neural tracking control of uncertain nonlinear time-delay systems with asymmetric time-varying full state constraints and actuator saturation." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, December 6, 2020, 095965182097526. http://dx.doi.org/10.1177/0959651820975265.

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This article investigates the command filtered adaptive neural tracking control for uncertain nonlinear time-delay systems subject to asymmetric time-varying full state constraints and actuator saturation. To stabilize such a class of systems, the radial basis function neural networks and the backstepping technique are used to structure an adaptive controller. The command filter is utilized to overcome the complexity explosion problem in backstepping. By employing the Lyapunov–Krasovskii functionals, the effect of time-delay is eliminated. The asymmetric time-varying barrier Lyapunov functions are designed to ensure full state constraint satisfaction. Moreover, the hyperbolic tangent function and an instrumental variable are introduced to deal with actuator saturation. All signals in the closed-loop system are proved to be bounded and the tracking error converges to a small neighborhood of the origin. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

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Isaly, Axton, Brendon C. Allen, Ricardo G. Sanfelice, and Warren E. Dixon. "Encouraging Volitional Pedaling in Functional Electrical Stimulation-Assisted Cycling Using Barrier Functions." Frontiers in Robotics and AI 8 (November 24, 2021). http://dx.doi.org/10.3389/frobt.2021.742986.

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Stationary motorized cycling assisted by functional electrical stimulation (FES) is a popular therapy for people with movement impairments. Maximizing volitional contributions from the rider of the cycle can lead to long-term benefits like increased muscular strength and cardiovascular endurance. This paper develops a combined motor and FES control system that tasks the rider with maintaining their cadence near a target point using their own volition, while assistance or resistance is applied gradually as their cadence approaches the lower or upper boundary, respectively, of a user-defined safe range. Safety-ensuring barrier functions are used to guarantee that the rider’s cadence is constrained to the safe range, while minimal assistance is provided within the range to maximize effort by the rider. FES stimulation is applied before electric motor assistance to further increase power output from the rider. To account for uncertain dynamics, barrier function methods are combined with robust control tools from Lyapunov theory to develop controllers that guarantee safety in the worst-case. Because of the intermittent nature of FES stimulation, the closed-loop system is modeled as a hybrid system to certify that the set of states for which the cadence is in the safe range is asymptotically stable. The performance of the developed control method is demonstrated experimentally on five participants. The barrier function controller constrained the riders’ cadence in a range of 50 ± 5 RPM with an average cadence standard deviation of 1.4 RPM for a protocol where cadence with minimal variance was prioritized and used minimal assistance from the motor (4.1% of trial duration) in a separate protocol where power output from the rider was prioritized.

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