Approximation of Hessian Matrix for Second-order SPSA Algorithm ...

CONTENTS
2.13 Simulation 70
2.13.1 Simulation 1 70
2.13.2 Simulation 2 72
2.13.3 Simulation 3 75
3. Vibration Suppression Control of a Flexible Arm using
Non-linear Observer with SPSA 79
3.1 Introduction 79
3.2 Dynamic Modeling of a Single Link Robot Arm 81
-3.2.1 Dynamic Model 81
-3.2.2 Equation of Motion and State Equations 84
3.3 Design of Non-Linear Observer 85
3.4 Model Reference Sliding Model Controller 87
3.5 Simulation 91
4. Lattice IIR Adaptive Filter Structure Adapted by SPSA Algorithm
9 9
4.1 Introduction 99
4.2 Procedure of Improved Algorithm 101
4.3 Lattice Structure 104
4.4 Adaptive Algorithm 105
-4.4.1 SHARF Algorithm 105
-4.4.2 Steiglitz-McBride Algorithm 108
4.5 Simulation 109
-4.5.1 SHARF Algorithm 109
-4.5.2 Steiglitz-McBride Algorithm 110
5. Parameters Estimation using a Modified Version of
SPSA Algorithm Applied to State-Space Models 113
5.1 Introduction 113
5.2 Implementation of SPSA Toward Proposed Model 115
-5.2.1 State-Space Model 115
-5.2.2 Gradient-free Maximum Likelihood Estimation 118
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