RBFNN Adaptive Sampled-Data Control for Nonlinear Plants: A Validity Analysis

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-06-26 DOI:10.1137/23m1595035

Hao Yu, Tongwen Chen

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Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1908-1932, June 2024.
Abstract. This paper investigates adaptive sampled-data control for strict-feedback nonlinear plants with unmatched uncertainties by means of radial basis function neural networks (RBFNNs). First, the continuous-time plant is locally discretized as a disturbed strict-feedback model by using the approximate Euler model approach. Then, as a basis of rigorous stability analysis, the concept of validity is proposed, which, considering the locality of the universal approximation capacity in RBFNNs, requires that the argument of each RBFNN be inside the corresponding compact set all the time. Meanwhile, to address the noncausality issue, delayed signals are utilized in the backstepping method for discrete-time plants. Subsequently, the validity and stability are proved rigorously; meanwhile, a practical output tracking problem is solved under a time-varying reference signal, the order of whose continuous derivatives is the same as the plants. This is the first time the interdependence on the design of sampling periods and RBFNNs in different design steps has been shown. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

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非线性植物的 RBFNN 自适应采样数据控制：有效性分析

SIAM 控制与优化期刊》第 62 卷第 3 期第 1908-1932 页，2024 年 6 月。摘要本文通过径向基函数神经网络（RBFNN）研究了具有不匹配不确定性的严格反馈非线性工厂的自适应采样数据控制。首先，利用近似欧拉模型方法将连续时间工厂局部离散为受干扰的严格反馈模型。然后，作为严格稳定性分析的基础，提出了有效性概念，考虑到 RBFNN 中通用近似能力的局部性，要求每个 RBFNN 的参数始终在相应的紧凑集内。同时，为了解决非因果性问题，在离散时间植物的反步法中使用了延迟信号。随后，严格证明了其有效性和稳定性；同时，解决了时变参考信号（其连续导数的阶数与植物相同）下的实际输出跟踪问题。这是首次展示了不同设计步骤中采样周期和 RBFNN 设计之间的相互依存关系。最后，还提供了仿真结果，以说明所获结果的效率和可行性。

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.