Integration of Neutrosophic Methods into Adaptive Control of Nonlinear Systems Using Neuro-Fuzzy Networks With B-Spline Functions

Abstract

This paper addresses the problem of adaptive control of nonlinear dynamic systems operating under parametric uncertainty, external disturbances, and partial or contradictory information about the system state – conditions under which classical linear Model Reference Adaptive Control (MRAC) and conventional neuro-fuzzy controllers exhibit degraded performance, slow adaptation, and oscillatory behavior. To overcome these limitations, a novel Neuro-Neutrosophic Model Reference Adaptive Controller (NN-MRAC) is proposed, implemented using a neutrosophic neuro-fuzzy network with B-spline basis functions. The key innovation of the proposed approach lies in integrating neutrosophic logic into the adaptive control architecture by explicitly using a three-component uncertainty representation – truth, indeterminacy, and falsity – which enables robust control synthesis in the presence of incomplete, noisy, and conflicting data. In contrast to traditional neuro-fuzzy controllers, the proposed NN-MRAC combines localized B-spline approximation with neutrosophic weighting of local models and an adaptive decomposition into lower-dimensional submodels, effectively mitigating the curse of dimensionality and reducing computational complexity. Comparative simulation studies with a classical linear MRAC demonstrate that the proposed controller reduces the mean-square tracking error by approximately 59%, decreases overshoot by more than 3 times, shortens the transient response time by nearly 1.8 times, and lowers control energy consumption by about 18%. The results confirm that the proposed neuro-neutrosophic MRAC ensures stable, smooth, and energy-efficient control in the presence of noise and deep uncertainty, making it a promising solution for intelligent control of complex nonlinear systems.

ABSTRAK: Kajian ini mencadangkan masalah kawalan adaptif bagi sistem dinamik bukan linear yang beroperasi pada ketidakpastian parameter, gangguan luaran, serta maklumat separa atau bercanggah mengenai keadaan sistem, di mana kaedah linear klasik Model Kawalan Suai Rujukan (MRAC) dan kawalan konvensional neural-fuzi menunjukkan prestasi terhad, kadar penyesuaian perlahan, dan tingkah laku berayun. Bagi mengatasi kekangan ini, satu Model Kawalan Suai Rujukan Neuro-Neutrosofik (NN-MRAC) yang baharu dicadangkan, dilaksanakan berasaskan rangkaian neural-fuzi neutrosofik dengan fungsi asas alur-B. Inovasi utama pendekatan ini terletak pada pengintegrasian logik neutrosofik ke dalam seni bina kawalan suai melalui penggunaan perwakilan terkecuali pada tiga komponen ketidakpastian – kebenaran, ketidakpastian, dan kepalsuan – membolehkan sintesis kawalan yang teguh dalam keadaan data tidak lengkap, bising, dan bercanggah. Berbeza dengan pengawal neural-fuzi tradisional, NN-MRAC yang dicadangkan menggabungkan penghampiran setempat berasaskan alur-B dengan pemberat neutrosofik bagi model setempat serta penguraian suai kepada submodel berdimensi rendah, sekaligus mengurangkan kerumitan pengiraan dan mengatasi masalah “kutukan dimensi”. Kajian simulasi perbandingan dengan MRAC linear klasik menunjukkan bahawa cadangan kawalan mencapai pengurangan ralat min kuasa dua (MSE) kira-kira 59%, penurunan lebihan (overshoot) lebih daripada tiga kali ganda, pemendekan masa tindak balas sementara hampir 1.8 kali, serta pengurangan penggunaan tenaga kawalan sekitar 18%. Keputusan ini mengesahkan bahawa MRAC neuro-neutrosofik yang dicadangkan mampu memastikan kawalan stabil, licin, dan cekap tenaga di bawah keadaan hingar dan ketidakpastian mendalam, menjadikannya satu penyelesaian berpotensi pada sistem kawalan pintar bukan linear yang kompleks.