• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.729-733
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• 1988

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problems (LQ-problem) is proposed. In LQ problems, the quadratic weighting matrices are usually decided on trial and error in order to get a good response. But using the proposed method, the quadratic weights are decided in such a way that all poles of the closed loop system are located in a desired area for good responses as well as for stability and values of the quadratic cost functional are kept less then a specified value. The closed loop systems constructed by this method have merits of LQ problems as well as those of pole assignment problems. Taking into consideration that little is known about the relationship among the quadratic weights, the poles and the values of cost functional, this procedure is also interesting from the theoretical point of view.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay equations and general boundary conditions. The basic new idea of this paper is to Introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.884-889
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• 1989

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problem (LQ-problem) is proposed. In LQ-problems, the quadratic weighting matrices are usually decided on trial and error in order to get a good response. But using the proposed method, the quadratic weights are decided in such a way that all poles of the closed loop system are located in a desired region for good responses as well as for stability and values of the quadratic cost function are kept less then a specified value.

• Journal of Astronomy and Space Sciences
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• v.19 no.2
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• pp.107-122
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• 2002

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems ad-dressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.845-858
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• 2008

In this paper, we consider a terminal, linear control system with delay, subject to unknown but bounded disturbances. For this system, we consider the problem of constructing a worst-case optimal feedback control policy, which can be corrected at fixed, intermediate time instants. The policy should guarantee that for all admissible uncertainties the system states are in prescribed neighborhoods of predefined system states, at all fixed, intermediate time instants, and in the neighborhood of a given state at a terminal time instant, and the value of the cost function is the best guaranteed value. Simple explicit rules(which can be easily implemented on-line) for constructing the optimal control policy in the original control problem are derived.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.2
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• pp.134-139
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• 2010

In order to overcome some problems of existing anti-windup methods, this paper defines LQ (Linear Quadratic) observer and proposes a new anti-windup method using the LQ observer. LQ observer is derived by linear quadratic optimization in order to calculate controller states, which make the controller outputs equal to the plant inputs. And we propose an algorithm so that it can be implemented by a digital controller easily. The relationship between the design parameters and the anti-windup performance is shown via some numerical examples, which cover the cases with the anti-windup method using LQ observer designed and the case without it. Finally, the anti-windup performance of the proposed method is exemplified via comparison with the existing model-based conditioning scheme method[4].

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.7
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• pp.655-660
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• 2009

In many real applications, the discrepancy problem between controller outputs and plant inputs or the abrupt variation problem of controller outputs can occur. These problems have a negative effect on control performance and stability. It is well-known that two phenomena called 'windup' and 'bump' cause these problems. So far these problems have been studied separately in each side of the anti-windup and the bumpless transfer. This paper proposes a new unified method combines the anti-windup and the bumpless transfer method using the linear quadratic minimization and a proper state space model representation for the anti-windup controller. The proposed method has a feature that it takes account of both the anti-windup and the bumpless transfer in one formula. Finally, we exemplify the performance of the proposed method via numerical examples using the controller switching between the anti-windup PID controller and the anti-windup LQ controller.

• Coupled systems mechanics
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• v.13 no.1
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• pp.73-93
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• 2024

In this work, we propose combining an advanced optimal control algorithm with a geometrically exact beam model. For simplicity, the 2D Reissner beam model is chosen to represent large displacements and rotations. The difficulty pertains to the nonlinear nature of beam kinematics affecting the tangent stiffness matrix, making it non-constant, which compromises direct use of optimal control methods for linear problems. Thus, we seek to accommodate a time varying control using linear-quadratic regulator (LQR) algorithm with the proposed geometrically nonlinear beam model. We provide a detailed theoretical formulation and its numerical implementation in a variational format form. Several illustrative numerical examples are provided to confirm an excellent performance of the proposed methodology.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.365-386
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• 2015

In this article, the linear quadratic (LQ) optimal guidance laws with arbitrary weighting functions are introduced. The optimal guidance problems in conjunction with the control effort weighed by arbitrary functions are formulated, and then the general solutions of these problems are determined. Based on these investigations, we can know a lot of previous optimal guidance laws belong to the proposed results. Additionally, the proposed results are compared with other results from the generalization standpoint. The potential importance on the proposed results is that a lot of useful new guidance laws providing their outstanding performance compared with existing works can be designed by choosing weighting functions properly. Accordingly, a new optimal guidance law is derived based on the proposed results as an illustrative example.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.393-399
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• 2015

W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.