• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.621-639
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• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

• Journal of Power Electronics
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• v.16 no.2
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• pp.598-609
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• 2016

The good control performance of permanent magnet linear synchronous motor (LSM) drive systems is difficult to achieve using linear controllers because of uncertainty effects, such as fictitious forces. A backstepping control system using adaptive modified recurrent Laguerre orthogonal polynomial neural network uncertainty observer (OPNNUO) is proposed to increase the robustness of LSM drive systems. First, a field-oriented mechanism is applied to formulate a dynamic equation for an LSM drive system. Second, a backstepping approach is proposed to control the motion of the LSM drive system. With the proposed backstepping control system, the mover position of the LSM drive achieves good transient control performance and robustness. As the LSM drive system is prone to nonlinear and time-varying uncertainties, an adaptive modified recurrent Laguerre OPNNUO is proposed to estimate lumped uncertainties and thereby enhance the robustness of the LSM drive system. The on-line parameter training methodology of the modified recurrent Laguerre OPNN is based on the Lyapunov stability theorem. Furthermore, two optimal learning rates of the modified recurrent Laguerre OPNN are derived to accelerate parameter convergence. Finally, the effectiveness of the proposed control system is verified by experimental results.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.10
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• pp.779-787
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• 2016

A nonlinear control law for the quad-rotor of a low-complexity, global approximation-free from system uncertainties and external disturbances are described in this paper. The control law guarantees convergence to a small bounded error using a prescribed performance function. The stability of the proposed nonlinear control system is also proven by the Lyapunov stability theorem. The advantage of this technique is that it has a simpler form than any other nonlinear compensators and is applicable to any nonlinear systems without precise knowledge of the systems. In this paper, the proposed approach is applied to attitude/altitude control of a quad-rotor. Numerical simulations are performed to investigate the proposed nonlinear attitude control law by applying it to an uncertain quadcopter system with external disturbances.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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• pp.123-126
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• 1998

The theoretical foundations of GA are the Schema Theorem and the Building Block Hypothesis. In the Meaning of these foundational concepts, simple genetic algorithm(SGA) allocate more trials to the schemata whose average fitness remains above average. Although SGA does well in many applications as an optimization method, still it does not guarantee the convergence of a global optimum. Therefore as an alternative scheme, there is a growing interest in a co-evolutionary system, where two populations constantly interact and co-evolve in contrast with traditional single population evolutionary algorithms. In this paper, we propose a new design method of an optimal fuzzy logic controller using co-evolutionary concept. In general, it is very difficult to find optimal fuzzy rules by experience when the input and/or output variables are going to increase. So we propose a co-evolutionary method finding optimal fuzzy rules. Our algorithm is that after constructing two population groups m de up of rule vase and its schema, by co-evolving these two populations, we find optimal fuzzy logic controller. By applying the proposed method to a path planning problem of autonomous mobile robots when moving objects exist, we show the validity of the proposed method.

• Journal of Power Electronics
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• v.14 no.5
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• pp.1008-1027
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• 2014

An electric scooter with a V-belt continuously variable transmission (CVT) driven by a permanent magnet synchronous motor (PMSM) has a lot of nonlinear and time-varying characteristics, and accurate dynamic models are difficult to establish for linear controller designs. A PMSM servo-drive electric scooter controlled by a novel hybrid modified recurrent Legendre neural network (NN) control system is proposed to solve difficulties of linear controllers under the occurrence of nonlinear load disturbances and parameters variations. Firstly, the system structure of a V-belt CVT driven electric scooter using a PMSM servo drive is established. Secondly, the novel hybrid modified recurrent Legendre NN control system, which consists of an inspector control, a modified recurrent Legendre NN control with an adaptation law, and a recouped control with an estimation law, is proposed to improve its performance. Moreover, the on-line parameter tuning method of the modified recurrent Legendre NN is derived according to the Lyapunov stability theorem and the gradient descent method. Furthermore, two optimal learning rates for the modified recurrent Legendre NN are derived to speed up the parameter convergence. Finally, comparative studies are carried out to show the effectiveness of the proposed control scheme through experimental results.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.4
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• pp.202-208
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• 2015

In this study, we propose a new inference algorithm for a multiclass Gaussian process classification model using a variational EM framework and the Laplace approximation (LA) technique. This is performed in two steps, called expectation and maximization. First, in the expectation step (E-step), using Bayes' theorem and the LA technique, we derive the approximate posterior distribution of the latent function, indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. In the maximization step, we compute the maximum likelihood estimators for hyper-parameters of a covariance matrix necessary to define the prior distribution of the latent function by using the posterior distribution derived in the E-step. These steps iteratively repeat until a convergence condition is satisfied. Moreover, we conducted the experiments by using synthetic data and Iris data in order to verify the performance of the proposed algorithm. Experimental results reveal that the proposed algorithm shows good performance on these datasets.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.37 no.1
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• pp.1-8
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• 2014

This paper proposes an emotion classifier from EEG signals based on Bayes' theorem and a machine learning using a perceptron convergence algorithm. The emotions are represented on the valence and arousal dimensions. The fast Fourier transform spectrum analysis is used to extract features from the EEG signals. To verify the proposed method, we use an open database for emotion analysis using physiological signal (DEAP) and compare it with C-SVC which is one of the support vector machines. An emotion is defined as two-level class and three-level class in both valence and arousal dimensions. For the two-level class case, the accuracy of the valence and arousal estimation is 67% and 66%, respectively. For the three-level class case, the accuracy is 53% and 51%, respectively. Compared with the best case of the C-SVC, the proposed classifier gave 4% and 8% more accurate estimations of valence and arousal for the two-level class. In estimation of three-level class, the proposed method showed a similar performance to the best case of the C-SVC.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.431-436
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• 2000

Adaptive feed forward control algorithms based largely upon LMS approach have developed in recent two decades, and they have been widely applied to practical sound and vibration control problems in the case of the reference signal is available. Feedforward control can be applied only when reference signals can be measured or regenerated, while feedback controllers are used to reduce; sound and vibration when reference signals are not available. In recent years, hybrid control schemes in which adaptive feed forward controllers are combined with feedback ones have been studied based on simulations and experiments. The results have shown that the hybrid control may have better control performances in convergence speed and steady state error than the single control schemes. Hybrid control has the advantages of improving stability and performance as well as the disturbance rejection property. However, little effort has been made to the analysis or interpretation of hybrid control systems. In this study, we discussed the feedback controller effects on the stability of feed forward control algorithm in the presence of uncertain error path and a simple example showed that a stable feedback controller could make the feedforward controller unstable. A design criterion of feedback controllers is proposed in order to guarantee the stability of feedforward algorithms in the presence of error paths with uncertainties.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1461-1484
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• 2021

We deal with the following elliptic equations: $\{-div({\varphi}^{\prime}(\left|{\nabla}z\right|^2){\nabla}z)+V(x)\left|z\right|^{{\alpha}-2}z={\lambda}{\rho}(x)\left|z\right|^{r-2}z+h(x,z),\\z(x){\rightarrow}0,\;as\;\left|x\right|{\rightarrow}{\infty},$ in ℝ^N , where N ≥ 2, 1 < p < q < N, 1 < α ≤ p^*q'/p', α < q, 1 < r < min{p, α}, φ(t) behaves like t^q/2 for small t and t^p/2 for large t, and p' and q' the conjugate exponents of p and q, respectively. Here, V : ℝ^N → (0, ∞) is a potential function and h : ℝ^N × ℝ → ℝ is a Carathéodory function. The present paper is devoted to the existence of at least two distinct nontrivial solutions to quasilinear elliptic problems of Schrödinger type, which provides a concave-convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• Journal of Power Electronics
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• v.19 no.3
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• pp.771-783
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• 2019

Due to nonlinear-synthetic uncertainty including the total unknown nonlinear load torque, the total parameter variation and the fixed load torque, a synchronous reluctance motor (SynRM) driving a continuously variable transmission (CVT) system causes a lot of nonlinear effects. Linear control methods make it hard to achieve good control performance. To increase the control performance and reduce the influence of nonlinear time-synthetic uncertainty, an admixed recurrent Gegenbauer orthogonal polynomials neural network (ARGOPNN) with a modified particle swarm optimization (MPSO) control system is proposed to achieve better control performance. The ARGOPNN with a MPSO control system is composed of an observer controller, a recurrent Gegenbauer orthogonal polynomial neural network (RGOPNN) controller and a remunerated controller. To insure the stability of the control system, the RGOPNN controller with an adaptive law and the remunerated controller with a reckoned law are derived according to the Lyapunov stability theorem. In addition, the two learning rates of the weights in the RGOPNN are regulating by using the MPSO algorithm to enhance convergence. Finally, three types of experimental results with comparative studies are presented to confirm the usefulness of the proposed ARGOPNN with a MPSO control system.