Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

Li, Xiaofei; Qin, Chuan; Zhu, Quanxin

doi:10.1155/2018/3034794

Cited by 2 publications

(1 citation statement)

References 41 publications

(51 reference statements)

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“…e conventional adaptive law for training neural networks and feedback control is linear feedback which makes the system exponential stabile [16,17] or exponentially bounded [18][19][20]. Finite time [21,22] and fixed-time [14] stable results are more meaningful for uncertain nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

U-Model Based Adaptive Neural Networks Fixed-Time Backstepping Control for Uncertain Nonlinear System

Zhang

Fei

et al. 2020

Mathematical Problems in Engineering

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Under U-model control design framework, a fixed-time neural networks adaptive backstepping control is proposed. The majority of the previously described adaptive neural controllers were based on uniformly ultimately bounded (UUB) or practical finite stable (PFS) theory. For neural networks control, it makes the control law as well as stability analysis highly lengthy and complicated because of the unknown ideal weight and unknown approximation error. Moreover, there has been very limited research focus on adaptive law for neural networks adaptive control in finite time. Based on fixed-time stability theory, a fixed-time bounded theory is proposed for fixed-time neural networks adaptive backstepping control. The most outstanding novelty is that fixed-time adaptive law for training weights of neural networks is proposed for fixed-time neural networks adaptive control. Furthermore, by combining fixed-time adaptive law and Lyapunov-based arguments, a valid fixed-time controller design algorithm is presented with universal approximation property of neural networks to ensure the system is fixed-time bounded, rather than PFS or UUB. The controller guarantees closed-loop system fixed-time bounded in the Lyapunov sense. The benchmark simulation demonstrated effectiveness and efficiency of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

U-Model Based Adaptive Neural Networks Fixed-Time Backstepping Control for Uncertain Nonlinear System

Zhang

Fei

et al. 2020

Mathematical Problems in Engineering

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Formation Tracking for Nonaffine Nonlinear Multiagent Systems Using Neural Network Adaptive Control

Zhao

Wang

Zhang

2020

Mathematical Problems in Engineering

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Adaptive tracking control for distributed multiagent systems in nonaffine form is considered in this paper. Each follower agent is modeled by a nonlinear pure-feedback system with nonaffine form, and a nonlinear system is unknown functions rather than constants. Radial basis function neural networks (NNs) are employed to approximate the unknown nonlinear functions, and weights of NNs are updated by adaptive law in finite-time form. Then, the adaptive finite NN approach and backstepping technology are combined to construct the consensus tracking control protocol. Numerical simulation is presented to demonstrate the efficacy of suggested control proposal.

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Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

Cited by 2 publications

References 41 publications

U-Model Based Adaptive Neural Networks Fixed-Time Backstepping Control for Uncertain Nonlinear System

U-Model Based Adaptive Neural Networks Fixed-Time Backstepping Control for Uncertain Nonlinear System

Formation Tracking for Nonaffine Nonlinear Multiagent Systems Using Neural Network Adaptive Control

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