• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.183-194
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• 2003

We will explain a new method for obtaining the nearly optimal domain for optimal shape design problems associated with the solution of a nonlinear wave equation. Taking into account the boundary and terminal conditions of the system, a new approach is applied to determine the optimal domain and its related optimal control function with respect to the integral performance criteria, by use of positive Radon measures. The approach, say shape-measure, consists of two steps; first for a fixed domain, the optimal control will be identified by the use of measures. This function and the optimal value of the objective function depend on the geometrical variables of the domain. In the second step, based on the results of the previous one and by applying some convenient optimization techniques, the optimal domain and its related optimal control function will be identified at the same time. The existence of the optimal solution is considered and a numerical example is also given.

• Structural Engineering and Mechanics
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• 제15권6호
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• pp.669-683
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• 2003

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

• 대한전자공학회논문지TE
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• 제42권3호
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• pp.25-30
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• 2005

대부분의 경우, 비선형 최적 제어 문제는 헤밀톤-야코비 방정식(Hamilton-Jacobi equations)을 풀어야하는데, HJEs는 해석적으로 답을 구하기가 매우 어렵다. 그래서 이러한 어려움은 비선형 시스템에 피드백 선형화를 적용하여, 선형화된 시스템을 얻고, 선형화된 선형 시스템에 대한 최적 제어 문제를 고려하게 되었다. 본 논문에서는 간단한 비선형 시스템의 예에 최적 제어 설계 기법과 피드백 선형화 제어기, 선형 제어기를 적용하여, 최적 성능을 평가함으로서, 피드백 선형화 최적 제어가 적용되는 비선형 시스템의 조건을 제시한다.

• 제어로봇시스템학회논문지
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• 제7권7호
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• pp.589-596
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• 2001

In this paper, a new design methodology for the optimal control of nonlinear systems described by the TS(Takagi-Sugeno) fuzzy model is proposed. First, a new theorem concerning the optimal stabilizing control of a general nonlinear dynamic system is proposed. Next, based on the proposed theorem and the inverse optimal approach, an optimal controller synthesis procedure for a TS fuzzy system is given, Also, it is shown that the optimal controller can be found by solving a linear matrix inequality problem. Finally, the proposed method is applied to the attitude control of a rigid spacecraft to demonstrate its validity.

• 한국유체기계학회 논문집
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• 제15권2호
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• pp.30-35
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• 2012

Aerodynamic torque of wind turbine has nonlinear properties. Nonlinearity of aerodynamic torque is very important in wind turbine in the aspect of control. The traditional torque control method using optimal mode gain has been applied in many wind turbines but its response is slower as wind turbine size is larger. In this paper, a torque control method using a nonlinear parameter of rotor speed among nonlinear properties of aerodynamic torque. Simulink model is implemented to obtain the nonlinear parameter of rotor speed and numerical simulations for a 2MW wind turbine are carried out and simulation results for the traditional and proposed torque control methods are compared.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.388-388
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• 2000

The complexity of nonlinear systems makes it difficult to ascertain their behavior using classical methods of analysis. Many efforts have been focused on the advanced algorithms and techniques that hold the promise of improving real-time optimal control while at the same time providing higher accuracy. In this paper, a fuzzy cell mapping method of real-time optimal control far nonlinear dynamical systems is proposed. This approach combines fuzzy logic with cell mapping techniques in order to find the optimal input level and optimal time interval in the finite set which change the state of a system to achieve a desired obiective. In order to illustrate this method, we analyze the behavior of an inverted pendulum using fuzzy cell mapping.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• Smart Structures and Systems
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• 제23권3호
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• pp.307-318
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• 2019

The frequently excessive vibrations presented in civil structures during seismic events or service conditions may result in users' discomfort, or worst, in structures failure, producing economic and even human casualties. This work contributes in proposing the synthesis of a nonlinear optimal control strategy for semiactive structural control, with the main characteristic that the synthesis considers both the structure model and the semiactive actuator nonlinear dynamics, which produces a nonlinear system that requires a nonlinear controller design. The aim is to reduce the unwanted vibrations in the response of civil structures, by means of intelligent fluid semiactive actuator such as the Magnetorheological Damper (MRD), which is a device with a low level of power consumption. The civil structures for which the proposed control methodology can be applied are those admitting a state-dependent coefficient factorized representation model, such as buildings, bridges, among others. A scaled model of a three storey building is analyzed as a case study, whose dynamical response involves displacement, velocity and acceleration of each one of the storeys, subjected to the North-South component of the September 19th., 2017, Puebla-Morelos (7.1M), Mexico earthquake. The investigation rests on comparing the structural response over time for two different conditions: with no control device installed and with one MRD installed between the first floor and the ground, where a nonlinear optimal signal for the MRD input voltage is determined. Simulation results are presented to show the effectiveness of the proposed controller for reducing the building's dynamical response.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.327-330
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• 1989

Two recent nonlinear control methods of nonlinear geometric method and nonlinear optimal control method are applied to a pH control system with severe nonlinear characteristics. Simulations and experiments show that their performances are very good and robust for various realistic situations such as model parameter mismatches.

• 한국전자통신학회논문지
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• 제7권5호
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• pp.1133-1138
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• 2012

본 논문은 최적제어에 기초하여 비선형 슬라이딩 평면을 설계하는 것이다. 최적제어입력에 의한 상태 궤적을 Frobenius 정리와 matrix decomposition 방법에 의해 구하였고, 이 궤적을 시스템의 슬라이딩 평면으로 설정하였다. 상태는 초기부터 슬라이딩 평면을 유지하며, 그 결과 초기상태 단계로부터 전 영역까지 시스템의 강인성은 보장 받을 수 있으며, 도달시간 동안 발생 될 수 있는 불확실성과 외란의 영향을 제거되고, 큰 제어 입력의 문제도 해결할 수 있었다. 그리고 최적경로를 슬라이딩 평면으로 설정함으로 추적시간을 줄일 수 있었다. 역진자 시스템을 사용하여 그 타당성을 보인다.