• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.5
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• pp.482-489
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• 1988

In this paper, we proposed a generalized model reference adaptive control theory which can be applied to single-input single-output discrete system by using V.M.Popov's hyperstability theory. As the result of theoretical analysis, it is proved that the discrete adaptive control scheme proposed by Narendra is a special case of the adaptive control schemes proposed in this paper. Also we suggest a variety of parameter adaptiations methods of controller through hyperstability theory.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1827-1838
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• 2015

We give some results on hyperstability for the general linear equation. Namely, we show that a function satisfying the linear equation approximately (in some sense) must be actually the solution of it.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.107-123
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• 2023

In this paper, we present some hyperstability results for a general quintic functional equation and a general septic functional equation.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.901-917
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• 2018

In this paper, we first introduce the notions of (2, ${\beta}$)-Banach spaces and we will reformulate the fixed point theorem [10, Theorem 1] in this space. We also show that this theorem is a very efficient and convenient tool for proving the new hyperstability results of the general linear equation in (2, ${\beta}$)-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. Our results are improvements and generalizations of the main results of Piszczek [34], Brzdęk [6, 7] and Bahyrycz et al. [2] in (2, ${\beta}$)-Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.147-156
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• 2020

The functional equation related to a distance measure f(pr, qs) + f(ps, qr) = M(r, s)f(p, q) + M(p, q)f(r, s) can be generalized a sum form functional equation as follows $${\frac{1}{n}}{\sum\limits_{i=0}^{n-1}}f(P{\cdot}{\sigma}_i(Q))=M(Q)f(P)+M(P)f(Q)$$ where f, g is information measures, P and Q are the set of n-array discrete measure, and σ_i is a permutation for each i = 0, 1, ⋯, n-1. In this paper, we obtain the hyperstability of the above type functional equation.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.343-359
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• 2021

The aim of this paper is to obtain the general solution of the 2-variable radical functional equations $f({\sqrt[k]{x^k+z^k}},\;{\sqrt[{\ell}]{y^{\ell}+w^{\ell}}})=f(x,y)+f(z,w)$, x, y, z, w ∈ ℝ, for f a mapping from the set of all real numbers ℝ into a vector space, where k and ℓ are fixed positive integers. Also using the fixed point result of Brzdęk and Ciepliński [11, Theorem 1] in (2, 𝛽)-Banach spaces, we prove the generalized hyperstability results of the 2-variable radical functional equations. In the end of this paper we derive some consequences from our main results.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.391-409
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• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.469-485
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• 2023

In this paper, we investigate the Hyers-Ulam-Rassias stability for a Drygas functional equation g(u + v) + g(u - v) = 2g(u) + g(v) + g(-v) in the setting of quasi-Banach space using fixed point approach. Also, we give general results on hyperstability of a Drygas functional equation. The results obtain in this paper extend various previously known results in the setting of quasi-Banach space. Some examples are also illustrated.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.21 no.10
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• pp.73-81
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• 2007

To improve the capability of instantaneous torque control, a design method of an MRAC-based adaptive current controller for a PMSM servo motor is proposed. In the synchronous frame current controller, a new control inputs can be obtained through the decoupling compensation. Using this, a desired controller bandwidth can be assigned However, the control performance may be degraded due to disturbances caused by the parameter variations or dead time of the switch. To improve these drawbacks, an adaptive current controller is proposed and the design method is obtained using the hyperstability theory. The asymptotic stability is proved and the effectiveness is verified through simulations and experiments using DSP TMS320C31.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.6
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• pp.1346-1360
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• 1989

본 연구에서는 기준 모델 적응제어 방식에서 직접 적응제어 방식을 사용하여 부하의 변동 및 외란이 발생할 경우에도 매니퓰레이터의 정확한 궤적의 추종 및 속도 의 실시간 제어가 가능한 적응제어시스템을 설계하고자 한다. 제2절에서는 로봇 매니퓰레이터의 기구학적 이론 및 동적 모델링에 대한 기본이론을 전개하고, 제3절 에서는 제어시스템의 설계를 위한 제어 알고리즘과 초안정(hyperstability)이론을 통한 안정성 해석을 다룬다. 그리고 제4절에서는 제안된 제어기의 성능 평가를 위해 6관절 로봇인 스탠포드 로봇 매니퓰레이터에 대한 시뮬레이션을 통한 결과를 토오크 계산법(computed torque method)에 의한 결과와 비교 검토함으로서 제안된 제어기의 성능을 예증한다.