Adaptive control of a class of uncertain nonlinear systems using brain emotional learning and Legendre polynomials

IF 1.7 4区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS Transactions of the Institute of Measurement and Control Pub Date : 2023-11-08 DOI:10.1177/01423312231203270
Fatemeh Amiri, Saeed Khorashadizadeh
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Abstract

In this paper, an adaptive controller for a class of uncertain nonlinear systems is presented using a combination of Legendre polynomials and brain emotional learning-based intelligent controller (BELBIC). Recently, some versions of BELBIC have been presented with the aim of satisfying the universal approximation property using Gaussian basis function. However, the size of regressor vector is too large that imposes a heavy computational load to the processor. The novelty of this paper is presenting a new version of BELBIC with less computational burden using Legendre polynomials. Moreover, there are very few tuning parameters in Legendre polynomials. Another contribution of this paper is editing the stability analysis presented in recent related works. Due to the intrinsic non-differentiability of the adaptation rules of BELBIC, the second time derivative of Lyapunov function is undefined and thus, the Barbalat’s lemma cannot be applied to verify the asymptotic convergence of the error function. Therefore, bounded-input-bounded-output (BIBO) stability can only be claimed for this controller. Simulation results on different case studies show that Legendre polynomials can improve the universal approximation property of BELBIC with less tuning parameters. Moreover, in the absence of the robust control term in the control law, the performance Legendre polynomials will not deteriorate, while the performance degrade in Gaussian basis function is quite considerable.
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基于脑情感学习和勒让德多项式的一类不确定非线性系统自适应控制
本文将Legendre多项式与基于大脑情绪学习的智能控制器(BELBIC)相结合,提出了一类不确定非线性系统的自适应控制器。最近,为了满足高斯基函数的全称逼近性质,提出了一些版本的BELBIC。然而,回归向量的大小太大,给处理器带来了沉重的计算负担。本文的新颖之处在于利用勒让德多项式提出了一种计算量更小的新版本BELBIC。此外,在勒让德多项式中很少有调谐参数。本文的另一个贡献是编辑了最近相关工作中的稳定性分析。由于BELBIC自适应规则的内在不可微性,Lyapunov函数的二阶导数是无定义的,因此不能用Barbalat引理来验证误差函数的渐近收敛性。因此,有界输入-有界输出(BIBO)稳定性只能用于该控制器。不同实例的仿真结果表明,Legendre多项式可以在较少的调谐参数下提高BELBIC的普遍逼近性能。此外,当控制律中没有鲁棒控制项时,勒让德多项式的性能不会下降,而在高斯基函数中性能下降相当大。
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来源期刊
CiteScore
4.10
自引率
16.70%
发文量
203
审稿时长
3.4 months
期刊介绍: Transactions of the Institute of Measurement and Control is a fully peer-reviewed international journal. The journal covers all areas of applications in instrumentation and control. Its scope encompasses cutting-edge research and development, education and industrial applications.
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