• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.130-139
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• 2002

In this paper, at first, we investigate existing algorithms for finding the minimum infinity-norm solution of consistent linear equations and then propose a new algorithm. The proposed algorithm is intended to includes the advantages of computational efficiency as well as geometric explicitness. As a practical application example, optimum trajectory planning for redundant robot manipulators is considered. Also, an efficient approach avoiding discontinuity in trajectory is proposed by resolving the non-uniqueness problem of minimum infinity-norm solution. To be specific, the proposed method for checking possible discontinuity does not need any other algorithms in checking the possibility of discontinuity while previous work needs specially designed checking courses. To show the usefulness of the proposed techniques, an example calculating minimum infinity-norm solution for comparing the computational efficiency as well as the trajectory planning for a redundant robot manipulator are included.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1609-1612
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• 1997

Kinematically redundantant manipulators have a nimber of potential advantages over nonredundant ones. Questions associated with manipulability measures for (non)redundant manipulators derived by minimum 2-norm solution and minimum infinity-norm solution in unit joint velocity are examined in detail.

• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.229-244
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• 2015

H-infinity norm relates to the maximum in the frequency response function and H-infinity control method focuses on the case that the vibration is excited at the fundamental frequency, while 2-norm relates to the output energy of systems with the input of pulses or white noises and 2-norm control method weighs the overall vibration performance of systems. The trade-off between the performance in frequency-domain and that in time-domain may be achieved by integrating two indices in the mixed vibration control method. Based on the linear fractional state space representation in the modal space for a piezoelectric flexible structure with uncertain modal parameters and un-modeled residual high-frequency modes, a mixed dynamic output feedback control design method is proposed to suppress the structural vibration. Using the linear matrix inequality (LMI) technique, the initial populations are generated by the designing of robust control laws with different H-infinity performance indices before the robust 2-norm performance index of the closed-loop system is included in the fitness function of optimization. A flexible beam structure with a piezoelectric sensor and a piezoelectric actuator are used as the subject for numerical studies. Compared with the velocity feedback control method, the numerical simulation results show the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.811-814
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• 1997

In this paper, the torque optimization of a kinematically redundant manipulator for minimizing the torque demands is discussed. The minimum torque solution based on a local optimization has been known to encounter the instability problem and then the global torque optimization was suggested as one of the alternatives. Herein, by adopting the infinity-norm rather than the 2-norm for the magnitude of torques, we are to propose a new cost function more advantageous to the avoidance of torque limits. By the way, a solution to the global torque optimization formulated with the new cost function can not be obtained by the previous methods due to their difficulties such as inability to treat discontinuous cost functions and various constraints on the joint variables. Thus, to overcome those deficiencies, we are developing a new approach using the dynamic programming. The effectiveness of the proposed method is shown through simulation examples for a 3-link planar redundant manipulator.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.58 no.3
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• pp.241-250
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• 2022

This paper describes the design of H-infinity controller for robust control of a DC motor system. The suggested controller can ensure robustness against disturbance and model uncertainty by minimizing H-infinity norm of the transfer function from exogenous input to performance output and applying the small gain theorem. In particular, the controller was designed to reduce the effects of disturbance and model uncertainty simultaneously by formalizing these problems as a mixed sensitivity problem. The validity of the proposed controller was demonstrated by computer simulations and real experiments. Moreover, the effectiveness of the proposed controller was confirmed by comparing its performance with PI controller, which was tested under the same experimental condition as the H-infinity controller.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.56-59
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• 1996

Worst-case state estimation will be proposed in this paper. By using the worst-case disturbance and worst-case state estimation, we can obtain right/left constrained coprime factors. If constrained coprime factors are used in designing a controller, the infinity-norm of closed-loop transfer matrix can be smaller than any constant .gamma.(> .gamma.$_{opt}$) without matrix dilation optimization. The derivation of left/right constrained coprime factors is achieved by doubly coprime factorization for the plant constrained by the infinity norm. And the parameterization of stabilizing controllers gives us easily understanding for H$_{\infty}$ control theory.ry.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.867-875
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• 1998

In this paper we prove that any continuous function on a bounded closed interval of can be approximated by the superposition of a bounded sigmoidal function with a fixed weight. In addition we show that any continuous function over $\mathbb{R}$ which vanishes at infinity can be approximated by the superposition f a bounded sigmoidal function with a weighted norm. Our proof is constructive.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.205-212
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• 1998

We investigate the behavior of $L^2$ harmonic one forms on complete manifolds and as an application, we show the space of $L^2$harmonic one forms on a complete Riemannian manifold of nonnegative Ricci curvature outside a compact set with bounded $n/2$-norm of Ricci curvature satisfying the Sobolev inequality is finite dimensional.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1754-1757
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• 2004

For the anti-sway control of traveling cranes, there are several solutions, i.e., by fuzzy control, by optimal control theory, etc. Each of them is reported to be effective. And, H infinity control and $H_2$ control can be also used. However, the full order observer which estimates all states in the controlled object is used in these methods. Therefore, the orders of these controllers are apt to be higher than that of the optimal controller, etc. Because the conventional H2 controller which minimizes $H_2$ norm consists of two parts, that is: feedback gains which make the controlled object stable and the full order observer which estimate those states. If the minimal order observer is used instead of the full order one, the order of the controller can be reduced. In this paper, we propose a new method based on the minimalization of $H_2$ norm using the minimal order observer. And, we confirm the effect of a new $H_2$ controller in the experiments of the anti-sway control of a traveling crane.

• Journal of Aerospace System Engineering
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• v.2 no.3
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• pp.1-6
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• 2008

The tilt rotor aircraft has the flight characteristics which takes off vertically like a helicopter and flies forward like an airplane. Especially, the transition process from a helicopter to an airplane mode requires not only the mixing of control inputs but also the stability and controllability augmentation system(SCAS) in order to keep the safe flight because there are compound flight dynamic characteristics of a helicopter and an airplane including non-linearity, uncertainty. This paper describes the design of SCAS in a lateral motion for the tilt rotor aircraft based on the $H_{\infty}$ control method, which was performed from mathematical model with weighting matrix based on the relationship between the $H_{\infty}$ norm and the sensitivity function. Through simulation analysis for the controller designed on the $H_{\infty}$ control theory, it was shown that this method may be applied to the control design of the tilt rotor aircraft.