Title Page

ABSTRACT

Contents

Symbols and Acronyms 10

Chapter 1. Introduction 12

Chapter 2. Problem Formulation 18

Chapter 3. Preliminaries 21

3.1. Control Lyapunov-barrier Function 21

3.2. Sontag's Universal Formula 24

Chapter 4. Controller Design 26

4.1. Construction of Control Lyapunov-barrier Function 27

4.2. Modified Sontag's Universal Formula 31

4.3. Disturbance Observer and Composite Control Law 34

Chapter 5. Mathematical Analysis 38

5.1. System Description in Singularly Perturbed Form 39

5.2. Proof of Theorem 5.1 42

5.3. Comparison with Other Safety-guaranteed Control 47

Chapter 6. Simulation: Inverted Pendulum on a Cart 50

6.1. Case 1: Simulation with Pulse Disturbance 54

6.2. Case 2: Simulation with Sine Disturbance 60

Chapter 7. Conclusion 63

BIBLIOGRAPHY 64

APPENDIX 67

A.1. Connected Set 67

A.2. Comparison Lemma 68

국문초록 69

Table 6.1. Detailed parameters used for CLBF design 53

Table 6.2. Supremum of Wn(x(t)) and x₁(t) in Figure 6.2[이미지참조] 56

Table 6.3. RMS of x₁(t) in Figure 6.5(a) and (c) 58

Table 6.4. RMS of d(t)-d(t) in Figure 6.5(b) and (d)[이미지참조] 58

Table 6.5. RMS of x₁(t) in Figure 6.6 59

Table 6.6. RMS of x₁(t) in Figure 6.7 61

Table 6.7. RMS of x₁(t) in Figure 6.8(a) and (c) 62

Table 6.8. RMS of d(t)-d(t) in Figure 6.8(b) and (d)[이미지참조] 62

Figure 1.1. Example of robot manipulator operated with some objects or human 13

Figure 1.2. Graphical description of a barrier function on ℝ² 13

Figure 2.1. Inverted pendulum on a cart 20

Figure 3.1. An example of CLBF 24

Figure 4.1. Block diagrams of (a) the overall system and (b) the nominal closed-loop system 27

Figure 5.1. Conceptual sketch of Proof of Theorem 5.1 43

Figure 6.1. Figures representing CBF Bn.[이미지참조] 52

Figure 6.2. Simulation results selecting the design parameters (γ＝2, η＝10, and τ＝0.02) with an initial condition x(0)＝... 56

Figure 6.3. Simulation results under variation of initial states. 57

Figure 6.4. Simulation results under variation of uncertainty. 57

Figure 6.5. Simulation results under variation of τ. 58

Figure 6.6. Simulation results under variation of various design parameters γ and η. 59

Figure 6.7. Simulation results under variation of magnitudes and frequencies of disturbance. 61

Figure 6.8. Simulation results under variation of τ with sine disturbance. 62

Figure A.1. Graphical explanation of connected and disconnected set: The sets are shaded in sky blue color, while the elements in red el-... 67