블럭펄스 變換에 의한 非線型系의 最適 制御를 위한 새로운 接近方法에 關한 硏究 = New approach to optimal control of nonlinear systems via block pulse transformations

다국어 초록 (Multilingual Abstract)

This paper present a new approach methods for analysis and optimal control of nonlinear system including time-varying parameters.
Concerned with those problems, this paper uses the adaptive approach scheme and block pulse transformations for solving state equation and the Riccati differential equation which is usually quite difficult.
Recently block pulse function finds application in a variety of fields such as analysis and design of nonlinear systems, solution of distributed systems and identification problems because computer control is usually implemented on the basis of the discrete time where the step functions produced by sampling and holding can be precisely expressed by finite block pulse function series.
To obtain the new abaptive approach method, the following steps are used :
First, the nonlinear system is modeled as x(t)=A(x, t)x(t) + B(x, t)u(t). Second, systems matrices A(x, t) and B(x, t) are considered constant at their present time t_(i). Third, optimal control vector is determined by intergrating the matrix Riccati equation backward from final time t_(f) to present time t_(i) via block pulse transformations. Fourth, the nonlinear system is controlled for a short time until some new present time t_(i+1)=t_(i) +Δt is reached. Fifth, at this new t_(i+1) the state and system parameters are updated and the optimal control vector is recalculated as the same manners. These steps are processed reculsively for present time t_(i) is reached to final t_(f).
This proposed method is applied to linear and nonlinear system examples and the viabiity of this method is established with simulation results for comparision with other approach method.
The method proposed in this paper is simple and computationally advantageous. Furthermore this method is very applicable to analysis and optimal control problems of nonlinear systems.

목차 (Table of Contents)

• 목차 = ⅰ
• 표목차 = ⅳ
• 그림목차 = ⅴ
• 기호설명 = ⅵ
• 제 1 장 서론 = 1
• 1.1 연구배경
• 1.2 연구목적
• 1.3 연구방법 및 내용
• 제 2 장 블럭펄스변환 = 7
• 2.1 블럭펄스 함수 = 7
• 2.2 블럭펄스 함수의 적분연산 = 8
• 2.3 블럭펄스 변환 = 10
• 제 3 장 비선형계의 해석 및 최적제어 = 11
• 3.1 비선형계의 선형근사화 = 11
• 3.2 비선형계의 최적제어 = 15
• 제 4 장 블럭펄스 변환에 의한 비선형계의 적응형 해석 및 최적제어 = 17
• 4.1 비선형계의 적응형 해석 = 17
• 4.2 비선형계의 적응형 최적제어 = 27
• 제 5 장 시뮬레이션 = 40
• 5.1 비선형계의 해석 및 최적제어 = 40
• 5.1.1 적용예 1 : Van Der Pol 방정식 = 40
• 5.1.2 적용예 2 : Volterra Predator-prey 방정식 = 52
• 5.1.3 적용예 3 : Rayleigh 방정식 = 61
• 5.1.4 적용예 4 : 타여자 직류전동기 시스템 = 70
• 5.2 선형계의 해석 및 최적제어 = 79
• 5.2.1 적용예 5 : 선형 시변계 = 79
• 제 6 장 검토 및 고찰 = 88
• 제 7 장 결론 = 105
• 참고문헌 = 107
• 부록: 적용예에 대한 시뮬레이션 프로그램 = 112
• Abstract = 126