• ETRI Journal
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• v.6 no.1
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• pp.3-9
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• 1984

This paper presents a direct adaptive poleplacement control scheme which is applicable to discrete-time non-minimum phase systems. It is proved that by this scheme the poles can be placed at the desired locations and the overall state vector of the system is uniformly bounded if the reference input is sufficiently rich, and also proved that in case of insufficiently rich reference input the overall system can still be stabilized though the poles may not be placed exactly at the desired locations. The effectiveness of this scheme is verified by digital computer simulations.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.747-756
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• 2018

We study a maximum principle for a uniformly elliptic second order differential operator in nondivergence form. We allow a bounded positive zeroth order coefficient in a certain type of unbounded domains. The results extend a result by J. Busca in a sense of domains, and we present a simple proof based on local maximum principle by Gilbarg and Trudinger with iterations.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.145-153
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• 2021

When {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise negatively superadditive dependent(NSD) for semi-Gaussian random variables and {ani|1 ≤ i ≤ n, n ≥ 1} is an array of constants, we study the almost sure convergence of weighted sums ∑ni=1 aniXni under some appropriate conditions and we obtain some corollaries.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.269-286
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• 2022

In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝ^N , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.43 no.10
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• pp.859-867
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• 2015

This study proposes a robust formation flight control technique of multiple unmanned aerial vehicles(UAVs) using behavior-based decentralized approach. The behavior-based decentralized method has various advantages because it utilizes information of neighboring UAVs only instead of information of whole UAVs in the formation maneuvering. The controllers in this paper are divided into two methods: first one is based on position and velocity of neighboring UAVs, and the other one is based on position of neighboring UAVs and passivity technique. The proposed controllers assure uniformly ultimate boundedness of closed-loops system under time varying bounded disturbances. Numerical simulations are performed to validate the effectiveness of the proposed method.

• Journal of Advanced Marine Engineering and Technology
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• v.18 no.4
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• pp.102-111
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• 1994

This article deals with the problem of designing a robust algorithm for the motion control of robot manipulator whose nonlinear dynamics contain various uncertainties. To ensure high performance of control system, a model-based feedforward compensation with continuous robust control has been developed. The control structure based on the deterministic approach consists of two parts : the nominal control law is first introduced to stabilize the system without uncertainties, then a robust nonlinear control law is adopted to compensate for both the resulting errors(or structured uncertainties) and unstructured uncertainties. The uncertainties assumed in this study are bounded by polynomials in the Euclidean norms of system states with known bounding coefficients. The presented control scheme is relatively simple as well as computationally efficient. With a feasible class of desired trajectories, the proposed control law provides sufficient criteria which guarantee that all possible responses of the closed-loop system are uniformly ultimately bounded in the presence of uncertainties. Therefore, the control algorithm proposed is shown to be robust with respect to the involved uncertainties.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.279-289
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• 2011

Let E be a uniformly convex Banach space with a uniformly Gateaux differentiable norm, C be a nonempty closed convex subset of E and f : $C{\rightarrow}C$ be a fixed bounded continuous strong pseudocontraction with the coefficient ${\alpha}{\in}(0,1)$. Let $\{{\lambda}_t\}_{0<t<1}$ be a net of positive real numbers such that ${\lim}_{t{\rightarrow}0}{\lambda}_t={\infty}$ and S = {$T(s)$ : $0{\leq}s$ < ${\infty}$} be a nonexpansive semigroup on C such that $F(S){\neq}{\emptyset}$, where F(S) denotes the set of fixed points of the semigroup. Then sequence {$x_t$} defined by $x_t=tf(x_t)+(1-t)\frac{1}{{\lambda}_t}{\int_{0}}^{{\lambda}_t}T(s)x{_t}ds$ converges strongly as $t{\rightarrow}0$ to $\bar{x}{\in}F(S)$, which solves the following variational inequality ${\langle}(f-I)\bar{x},\;p-\bar{x}{\rangle}{\leq}0$ for all $p{\in}F(S)$.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.5
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• pp.385-389
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• 2013

This paper proposes the leader-follower based formation control method for multiple mobile robots. The controller is designed using the measurements of the follower robot such as the relative distance and angle between the leader and the follower. This means that the follower robot does not require the information of the leader robot while keeping the desired formation. Therefore, the proposed control method can reduce the communication loss and the cost for hardware. From Lyapunov stability theory, it is shown that all error signals in the closed-loop system are uniformly ultimately bounded. Finally, simulation results demonstrate the effectiveness of the proposed control system.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.107-112
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• 2003

In general, the dynamics of autonomous underwater vehicles(AUVs) are highly nonlinear and time-varying, and the hydrodynamic coefficients of vehicles are hard to estimate accurately because of the variations of these coefficients with different navigation conditions. For this reason, in this paper, the control gain function is assumed to be unknown and the exogenous input term is assumed to be unbounded, although it still satisfies certain restrict condition. And these two kinds of wild assumptions have been seldom handled simultaneously in one system because of the difficulty of stability analysis. Under the above two relaxed assumptions, a robust neural network control scheme is presented for autonomous diving control of an AUV, and can guarantee that all the signals in the closed-loop system are UUB (uniformly ultimately bounded). Some practical features of the proposed control law are also discussed.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.3
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• pp.282-293
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• 2018

This paper attempts to address the motion parameter skip problem associated with three-dimensional trajectory tracking of an underactuated Autonomous Underwater Vehicle (AUV) using backstepping-based control, due to the unsmoothness of tracking trajectory. Through kinematics concepts, a three-dimensional dynamic velocity regulation controller is derived. This controller makes use of the surge and angular velocity errors with bio-inspired models and backstepping techniques. It overcomes the frequently occurring problem of parameter skip at inflection point existing in backstepping tracking control method and increases system robustness. Moreover, the proposed method can effectively avoid the singularity problem in backstepping control of virtual velocity error. The control system is proved to be uniformly ultimately bounded using Lyapunov stability theory. Simulation results illustrate the effectiveness and efficiency of the developed controller, which can realize accurate three-dimensional trajectory tracking for an underactuated AUV with constant external disturbances.