Least squares support vector regression for differential equations on unbounded domains

Pakniyat, Ali; Parand, Kourosh; Jani, Mostafa

doi:10.1016/j.chaos.2021.111232

Cited by 10 publications

(2 citation statements)

References 34 publications

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“…In order to improve the control accuracy of AUVs in demanding operation tasks, a LSSVR interactive network composed of two modules is designed to improve the accuracy of AUV motion control by virtue of the outstanding ability of LSSVR in learning of small samples [39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

A LSSVR Interactive Network for AUV Motion Control

Jiang

Wan

Zhang

et al. 2023

JMSE

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In view of the requirements on control precision of autonomous underwater vehicles (AUVs) in different operations, the improvement of AUV motion control accuracy is the focus of this paper. In regard to the unsatisfying robustness of traditional control methods, an interactive network based on Least Square Support Vector Regression (LSSVR) is therefore put forward. The network completed the identification of the strong nonlinear AUV dynamic characteristics based on the LSSVR theory and by virtue of the interactions between the offline and online modules, it achieved offline design and online optimization of the AUV control law. In addition to contrastive numerical simulations and sea trials with the classic S-plane method in AUV velocity and heading control, the LSSVR network was also tested in path following and long-range cruise. The precision and robustness and of the proposed network were verified by the high-accuracy control results of the aforesaid simulations and trials. The network can be of practical use in AUV control especially under unfamiliar water conditions with access to a limited number of control samples or little information of the operation site.

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Section: Introductionmentioning

confidence: 99%

A LSSVR Interactive Network for AUV Motion Control

Jiang

Wan

Zhang

et al. 2023

JMSE

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“…Authors in [24] solved nonlinear stochastic differential equations by variable fractional Brownian motion via the Chelyshkov least squares support vector regression method. Pakniyat et al [25] developed least squares support vector regression for differential equations on unbounded domains.…”

Section: Introductionmentioning

confidence: 99%

Bernoulli wavelet least squares support vector regression: Robust numerical method for systems of fractional differential equations

Rahimkhani¹,

Ordokhani

Sabermahani

2023

Math Methods in App Sciences

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In this study, a new hybrid method is developed to solve linear or nonlinear systems of fractional differential equations using Bernoulli wavelets (Bws) and the least squares support vector regression (LS‐SVR). The numerical methods based on operational matrices for solving various kinds of fractional equations have been widely studied in the last decade. In contrast to the existing methods, here we derive the operator of fractional integration, aiming to remove the approximation error. For this purpose, we present Bw operator of Riemann–Liouville fractional integration and use it in our scheme. In the proposed technique, we approximate the unknown functions via Bws, and then with the help of Bw operator of fractional integration and LS‐SVR, we reduce the problem to an algebraic system. In this way, we simplify the computation of the considered system. The error analysis of our method is proposed. Finally, we demonstrate the applicability of the present scheme by solving several numerical examples.

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