선형행렬부등식을 이용한 비선형 시스템의 최적 제어
Optimal Control of Uncertain Nonlinear Systems Using Linear Matrix Inequalities
- 주제(키워드) optimal control + linear matrix inequality + guaranteed cost control + adaptive control + actuator saturation + hard nonlinearity
- 발행기관 아주대학교
- 지도교수 홍석교
- 발행년도 2006
- 학위수여년월 2006. 8
- 학위명 박사
- 학과 및 전공 일반대학원 제어계측공학과
- 본문언어 영어
초록/요약
In this thesis, the problem of guaranteed cost control (GCC) for some classes of uncertain nonlinear systems is considered. In particular, the thesis considers two types of problems in this direction: the problem of GCC for uncertain systems subject to actuator saturation and the problem of adaptive GCC for a class of uncertain nonlinear systems which may include systems with hard nonlinearities such as the Coulomb friction. Based on LMI techniques, the thesis proposes new conditions for GCC design, which admit norm-bounded uncertainties and some classes of nonlinearities. The resulting LMI conditions are further used for solving convex optimization problems which minimize the upper-bounds of cost functions associated with the given systems. The solution for the first problem leads to a state-feedback controller that minimizes the upper-bound of the cost function in the presence of uncertainties and actuator saturation. The solution for the second problem leads to an adaptive state-feedback controller that compensates for the effects of uncertain nonlinearities while minimizing the upper-bound of the given cost function. The effectiveness and applicability of the proposed methods is illustrated by using simulation examples, in which an uncertain helicopter model in a vertical plane subject to actuator saturation is considered for the first problem and a 1-DOF mechanical oscillator subject to uncertain Coulomb friction is considered for the second problem.
more목차
Acknowledgments --- v
Table of Contents --- viii
List of Figures --- x
List of Tables --- xii
Abstract --- xiii
1 Introduction --- 1
1.1 Background and Motivation --- 1
1.2 Organization of the Thesis --- 4
2 Guaranteed Cost Control Using Linear Matrix Inequalities --- 6
2.1 Linear Matrix Inequalities --- 6
2.1.1 Useful Results in LMIs --- 8
2.1.2 Standard Problems Involving LMIs --- 10
2.2 Guaranteed Cost Control for Linear Systems --- 12
2.2.1 Guaranteed Cost Control for Nominal Linear Systems --- 13
2.2.2 Guaranteed Cost Control for Uncertain Linear Systems --- 15
3 Optimal Guaranteed Cost Control for Uncertain Systems with Actuator Saturation --- 17
3.1 Introduction --- 17
3.2 Problem Statements and Preliminary Results --- 20
3.3 Guaranteed Cost Controller Design --- 24
3.3.1 Sufficient Condition for Controller Design --- 24
3.3.2 Optimization --- 27
3.4 Illustrative Example --- 30
3.4.1 Case When $|u| \leq 1$ Without Uncertainties --- 32
3.4.2 Case When $|u| \leq 1$ With Constant Uncertainties --- 36
3.4.3 Case When $|u| \leq 1$ With Sinusoidal Uncertainties --- 36
3.4.4 Case When $|u| \leq 0.165$ With Sinusoidal Uncertainties --- 40
3.5 Summary --- 41
4 Adaptive Guaranteed Cost Control for Uncertain Systems with Hard Nonlinearities --- 49
4.1 Introduction --- 49
4.2 Problem Statements --- 51
4.3 Adaptive Guaranteed Cost Controller Design --- 53
4.3.1 Sufficient Condition for Controller Design --- 53
4.3.2 Optimization --- 55
4.4 Illustrative Example --- 57
4.5 Summary --- 59
5 Conclusions --- 62
5.1 Contributions of the Thesis --- 63
5.2 Directions for Future Research --- 64
Bibliography --- 65
Appendix. MATLAB Code --- 70
Abstract in Korean --- 76
