• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.5
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• pp.470-477
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• 1990

Singh's multi-level method is extended to the optimal tracking control of a large interconnected dynamical system which has coupled states and coupled inputs. The steady-state tracking error and a convergence condition for the extended multi-level method are derived analytically and the results show that the steady-state tracking error and a convergence rate have to be compromised. Also, a new multi-level method which is advantageous over the Singh's method in steady-state tracking error and computational burden is proposed by introducing nominal inputs into the performance index. The resulting feedback gain matrix and the compensation vector are optimal for all initial conditions so that eventual on-line computation is minimal.

• Proceedings of the KIEE Conference
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• 2003.11a
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• pp.297-299
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• 2003

This paper proposes a totally new method in the chaos characteristics analysis of power systems, the introduction of topological invariants. Using a return histogram the bifurcation graph was drawn, the periodic orbits and topological invariants the local crossing number, relative rotation rates, and linking number during the process of period-doubting bifurcation and chaos were extracted. This study also examined the effect on the topological invariants when the sensitive parameters were varied. In addition, the topological invariants of a three-dimensional embedding of the strange attractor was extracted and the result was compared with those obtained from differential equations. This could be a new way for a state detection and fault diagnosis in a dynamical system.

• Proceedings of the KIEE Conference
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• 2003.07d
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• pp.2190-2192
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• 2003

In this paper, a state observer based direct adaptive fuzzy controller for unknown nonlinear dynamical system is presented. The adaptive parameters of the direct adaptive fuzzy controller can be tuned by using a projection algorithm on-line based on the Lyapunov synthesis approach. A maximum control is used to guarantee the robustness of system. A stability analysis of the overall adaptive scheme is discussed based on the sense of Lyapunov. The inverted pendulum simulation example shows that proposed control algorithm can be used for the tracking problem of nonlinear system.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2320-2322
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• 2001

This paper describes the design of a robust adaptive neural-net(NN) observer for uncertain nonlinear dynamical system. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property of the state estimation error, as well as of all other signals in the closed-loop system. Especially, for reducing the dynamic oder of the observer, we propose a new method in which no strictly positive real(SPR) condition is needed with on-line estimation of weights of the NNs. No a priori knowledge of an upper bounds on the uncertain terms is required. The theoretical results are illustrated through a simulation example.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.97-104
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• 2008

Most of engine control systems for helicopter turboshaft engines are equipped with dual sensors. For the system with dual redundancy, analytic methods are used to detect faults based on the system dynamical model. Helicopter engine dynamics are affected by aerodynamic torque induced from the dynamics of the main rotor. In this paper an engine model including the rotor dynamics is constructed for the T700-GE-700 turboshaft engine powering UH-60 helicopter. The singular value decomposition(SVD) method is applied to the developed model in order to detect sensor faults. The SVD method which do not need an additional computation to generate residual uses the characteristics that the system outputs in direction of the left singular vector if an input is applied in direction of the right singular vector. Simulations show that the SVD method works well in detecting and isolating the sensor faults.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.197-224
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• 2019

Let A be a $JB^*$-triple with Banach dual space $A^*$ and bi-dual the $JBW^*$-triple $A^{**}$. Elements x of $A^*$ of norm one may be regarded as normalised 'Q-measures' defined on the complete ortho-lattice ${\tilde{\mathcal{U}}}(A^{**})$ of tripotents in $A^{**}$. A Q-measure x possesses a support e(x) in ${\tilde{\mathcal{U}}}(A^{**})$ and a compact support $e_c(x)$ in the complete atomic lattice ${\tilde{\mathcal{U}}}_c(A)$ of elements of ${\tilde{\mathcal{U}}}(A^{**})$ compact relative to A. Necessary and sufficient conditions for an element v of ${\tilde{\mathcal{U}}}_c(A)$ to be a compact support tripotent $e_c(x)$ are given, one of which is related to the Q-covering numbers of v by families of elements of ${\tilde{\mathcal{U}}}_c(A)$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.4
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• pp.331-350
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• 2020

Exploding gradient is a widely known problem in training recurrent neural networks. The explosion problem has often been coped with cutting off the gradient norm by some fixed value. However, this strategy, commonly referred to norm clipping, is an ad hoc approach to attenuate the explosion. In this research, we opt to view the problem from a different perspective, the discrete-time optimal control with infinite horizon for a better understanding of the problem. Through this perspective, we fathom the region at which gradient explosion occurs. Based on the analysis, we introduce a gradient-explosion-free algorithm that keeps the training process away from the region. Numerical tests show that this algorithm is at least three times faster than the clipping strategy.

• Earthquakes and Structures
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• v.22 no.4
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• pp.421-430
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• 2022

This paper addresses the stochastic control problem of robots within the framework of parameter uncertainty and uncertain noise covariance. First of all, an open circle deterministic trajectory optimization issue is explained without knowing the unequivocal type of the dynamical framework. Then, a Linear Quadratic Gaussian (LQG) controller is intended for the ostensible trajectory-dependent linearized framework, to such an extent that robust hereditary NN robotic controller made out of the Kalman filter and the fuzzy controller is blended to ensure the asymptotic stability of the non-continuous controlled frameworks. Applicability and performance of the proposed algorithm shown through simulation results in the complex systems which are demonstrate the feasible to improve the performance by the proposed approach.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.50.1-50.1
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• 2021

Gravitational instability (GI) can produce massive gas giants on wide orbits by fragmentation of protoplanetary disks (PPDs). While most previous works focus on PPDs around solar mass stars, gas giants have been observed in systems with a wide range of stellar masses including M dwarfs. We use the GIZMO code to perform global three-dimensional simulations of self-gravitating disks around low-mass stars. Our models consider heating by turbulent viscosity and stellar irradiation and the β cooling occurring over the dynamical time. We run various models with differing disk-to-star mass ratio q and disk temperature. We find that strongly gravitating disks either produce spirals or undergo fragmentation. The minimum q value for fragmentation is 0.2-0.7, with a smaller value corresponding to a more massive star and/or a smaller disk. The critical q value depends somewhat sensitively on the disk temperature, suggesting that the stellar irradiation is an important factor in determining GI. We discuss our results in comparison with previous work as well as recent ALMA observations.