• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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• pp.429-434
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• 2016

This paper introduces a stabilization condition for polynomial fuzzy systems that guarantees $H_{\infty}$ performance under the imperfect premise matching. An $H_{\infty}$ control of polynomial fuzzy systems attenuates the effect of external disturbance. Under the imperfect premise matching, a polynomial fuzzy model and controller do not share the same membership functions. Therefore, a polynomial fuzzy controller has an enhanced design flexibility and inherent robustness to handle parameter uncertainties. In this paper, the stabilization conditions are derived from the polynomial Lyapunov function and numerically solved by the sum-of-squares (SOS) method. A simulation example and comparison of the performance are provided to verify the stability analysis results and demonstrate the effectiveness of the proposed stabilization conditions.

• Journal of information and communication convergence engineering
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• v.16 no.3
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• pp.166-172
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• 2018

A pseudo-random sequence generated by using a primitive polynomial, trace function, and Legendre symbol has been researched in our previous work. Our previous sequence has some interesting features such as period, autocorrelation, and linear complexity. A pseudo-random sequence widely used in cryptography. However, from the aspect of the practical use in cryptographic systems sequence needs to generate swiftly. Our previous sequence generated by utilizing a primitive polynomial, however, finding a primitive polynomial requires high calculating cost when the degree or the characteristic is large. It’s a shortcoming of our previous work. The main contribution of this work is to find some relation between the generated sequence and irreducible polynomials. The purpose of this relationship is to generate the same sequence without utilizing a primitive polynomial. From the experimental observation, it is found that there are (p - 1)/2 kinds of polynomial, which generates the same sequence. In addition, some of these polynomials are non-primitive polynomial. In this paper, these relationships between the sequence and the polynomials are shown by some examples. Furthermore, these relationships are proven theoretically also.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.208-211
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• 2007

In a recently proposed method of model reduction for discrete interval systems, the denominator polynomial of a reduced model is computed by applying interval arithmetic to dominant poles of the original system. However, the denominator polynomial obtained via interval arithmetic usually has poles with larger intervals than desired ones. Hence an unstable polynomial can be derived from the stable polynomial. In this paper a simple technique is presented to partially overcome such a stability problem by accurately preserving desired real dominant poles.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.4
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• pp.295-303
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• 2004

Previously it has been shown that the all pole systems resulting good time responses can be characterized by so called K-polynomial. The polynomial is defined in terms of the principal characteristic ratio $\alpha_1$ and the generalized time constant $\tau$ . In this paper, Part II presents several sensitivity analyses of such systems with respect to $\alpha_1$ and $\tau$ changes. We first deal with the root sensitivity to the perturbation of $\alpha_1$ . By way of determining the unnormalized function sensitivity, both time response sensitivity and frequency response sensitivity are derived. Finally, the root sensitivity relative to $\tau$ change is also analyzed. These results provide some useful insight and background theory when we select of and l to compose a reference model of which denominator is a K-polynomial, which is illustrated by examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.327-332
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• 2005

We investigatea new fuzzy-neural networks-Hybrid Fuzzy set based polynomial Neural Networks (HFSPNN). These networks consist of genetically optimized multi-layer with two kinds of heterogeneous neurons thatare fuzzy set based polynomial neurons (FSPNs) and polynomial neurons (PNs). We have developed a comprehensive design methodology to determine the optimal structure of networks dynamically. The augmented genetically optimized HFSPNN (namely gHFSPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of gHFSPNN leads to the selection leads to the selection of preferred nodes (FSPNs or PNs) available within the HFSPNN. In the sequel, the structural optimization is realized via GAs, whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFSPNN is quantified through experimentation where we use a number of modeling benchmarks synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.130-133
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• 2000

In this paper, a new design methodology named FNNN(Fuzzy Polynomial Neural Network) algorithm is proposed to identify the structure and parameters of fuzzy model using PNN(Polynomial Neural Network) structure and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and modified quadratic besides the biquadratic polynomial used in the GMDH. The premise of fuzzy inference rules defines by triangular and gaussian type membership function. The fuzzy inference method uses simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture Several numerical example are used to evaluate the performance of out proposed model. Also we used the training data and testing data set to obtain a balance between the approximation and generalization of proposed model.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.101-106
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• 2003

In the area of tracking control, it is important to design not only the controllers but also the trajectories to which a system has to follow. $5^{th}$ order polynomial is often used with constraints of initial and final states. Smooth ending with possible minimum time is important for many systems because of vibration or jerky motions. Examples are increased with development of technology in smaller, more accurate systems. On the base of a polynomial like trajectory generation method from a paper in ACC2002 and RIC(Robust Internal-loop Compensator) control scheme of Robotics and Bio-mechanics lab. of POSTECH, generalized and expanded polynomial like trajectory generation method is showed.

• Journal of Korea Society of Industrial Information Systems
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• v.8 no.1
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• pp.92-96
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• 2003

본 논문에서는 비대칭 터보부호를 사용 무선 ATM환경에서 ATM셀을 전송할 때 비트 오류확률, 셀 손실확률을 대칭 터보부호와 비교하였다. 일반적으로 터보부호기는 동일한 재귀 컨벌루션코드(Resursive Systematic Convolution Code)로 구성된다. 비대칭 터보부호와 대칭적 터보부호를 비교하기 위한 생성다항식을 Primitive Polynomial과 Non-Primitive Polynomial 의 4가지 조합을 고려하여 시뮬레이션을 수행하였다. Feedback 다항식이 Primitive 다항식인 사용된 터보부호기가 Non-Primitive다항식이 사용된 터보부호기와 비교하여 1.2dB이상 성능 향상을 보였고, Primitive Polynomial과 Non-Primitive Polynomial이 같이 사용된 비대칭 터보부호기는 Non-Primitive Polynomial이 사용된 대칭 터보부호기와 비교하여 0.7dB 성능 향상을 보였다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.483-487
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• 2005

We introduce a new architecture of hetero-hybridized feed-forward neural networks composed of fuzzy set-based polynomial neural networks (FSPNN) and polynomial neural networks (PM) that are based on a genetically optimized multi-layer perceptron and develop their comprehensive design methodology involving mechanisms of genetic optimization and Information Granulation. The construction of Information Granulation based HFSPNN (IG-HFSPNN) exploits fundamental technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks, and genetic algorithms(GAs) and Information Granulation. The architecture of the resulting genetically optimized Information Granulation based HFSPNN (namely IG-gHFSPNN) results from a synergistic usage of the hybrid system generated by combining new fuzzy set based polynomial neurons (FPNs)-based Fuzzy Neural Networks(PM) with polynomial neurons (PNs)-based Polynomial Neural Networks(PM). The design of the conventional genetically optimized HFPNN exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being tuned by using Genetie Algorithms throughout the overall development process. However, the new proposed IG-HFSPNN adopts a new method called as Information Granulation to deal with Information Granules which are included in the real system, and a new type of fuzzy polynomial neuron called as fuzzy set based polynomial neuron. The performance of the IG-gHFPNN is quantified through experimentation.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.33-38
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• 2006

In this paper, we propose a new architecture of Fuzzy Polynomial Neural Networks(FPNN) by means of genetically optimized Fuzzy Polynomial Neuron(FPN) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially Genetic Algorithms(GAs). The conventional FPNN developed so far are based on mechanisms of self-organization and evolutionary optimization. The design of the network exploits the extended Group Method of Data Handling(GMDH) with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The proposed FPNN gives rise to a structurally optimized network and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. It is shown that the proposed advanced genetic algorithms based Fuzzy Polynomial Neural Networks is more useful and effective than the existing models for nonlinear process. We experimented with Medical Imaging System(MIS) dataset to evaluate the performance of the proposed model.