I= STATE-SPACE RECURSIVE LEAST-SQUARES
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Title of Thesis
STATE-SPACE RECURSIVE LEAST-SQUARES

Author(s)
Muhammad Bilal Malik
Institute/University/Department Details
National University of Science and Technology
Session
2004
Subject
Electrical Engineering
Number of Pages
120
Keywords (Extracted from title, table of contents and abstract of thesis)

Abstract
This thesis presents “state-space recursive least squares (SSRLS)” algorithm. SSRLS allows a designer to incorporate an appropriate model for the environment. The result is a marked improvement in its tracking performance over the standard RLS and least mean square (LMS) filters. Another attribute of SSRLS is its state-space formulation, which makes it’s a suitable state estimator in control systems.

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926.6 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 Contents
67.43 KB
2 1 Introduciton 1
86.33 KB
  1.1 Estimation and Tracking 1
  1.2 Deterministic Signals 2
  1.3 Nonlinear Control Systems 4
  1.4 Requirement of a New Algorithm 8
  1.5 Overview of the Thesis 8
3 2 State-Space Recursive Least-Squares Estimation 11
141.39 KB
  2.1 Btch-Processing Least-Squares Approach 11
  2.2 Recursive Algorithm 13
  2.3 Steady-State Solution of SSRLS 19
  2.4 Special Cases 21
  2.5 Example (Tracking a Single Tone ) 26
4 3 Stability and Convergence Analysis 29
155.08 KB
  3.1 Estimation Error 30
  3.2 Convergence of Difference Lyapunov Equation 30
  3.3 The Algebraic Riccati Equation (ARE) 33
  3.4 The Difference Riccati Equation (DRE ) 33
  3.5 Convergence of SSRLS to Steady-State SSRLS 34
  3.6 BIBO Stability of SSRLS 37
  3.7 Convergence Analysis of Steady-State SSRLS 41
  3.8 Convergence Analysis of Steady-State SSRLS 46
5 4 SSRLS with Adaptive Memory 50
76.39 KB
  4.1 Adaptive Memory 51
  4.2 Approximate Solution 54
  4.3 Initialization 56
  4.4 Example of Tacking a Noisy Chirp 56
6 5 Performance of SSRLS in presence of Model 60
99.5 KB
  5.1 Estimator Error 60
  5.2 Some Properties of Square Matrices 61
  5.3 Steady-State Mean Error 63
  5.4 Mean Square Error 66
  5.5 Neutrally Stable Systems 68
7 6 Sampled-Data Control of Nonlinear System Using High-Gain SSRLS 74
202.97 KB
  6.1 A Perview of High-Gain Observers 75
  6.2 SSRLS as an Approximate Discrete Differentiator 80
  6.3 Disturbance Rejection Property of High-Gain SSRLS 81
  6.4 Discrete Equivalent of the Plant 82
  6.5 SSRLS as a Discrete High-Gain Observer 85
  6.6 Output Feedback Sampled-Data Control of Full-State Feedback Linearizable Systems Using SSRLS 87
  6.7 Tracking a Reference with Unknown Model and Unknown Derivatives 97
  6.8 Example (Inverted Pendulum ) 98
  6.9 Extensionof MIMO Systems 99
  6.10 Systems with Relative Degree 99
8 7 SSRLS in stochastic Nonlinear Control Systems 101
109.51 KB
  7.1 Simultaneous Disturbance and Noise Rejection Property of SSRLS with Adaptive Memory 102
  7.2 State Estimation in Presence of Observation Noise 105
  7.3 Tracking a Noisy Reference with Unknown Model and Derivatives 109
  7.4 A Note on Performance of Continuous High-Gain Observers 111
9 8 Conclusions and future suggestions 114
29.66 KB
  8.1 Conclusions 114
  8.2 Future Suggestions 115
10 9 References 117
48.17 KB
11 10 Appendix-A PhD-5 Form (Doctoral Defense ) 121
81.74 KB
  10.1 Appendix-B PhD-4 Form (Doctoral Thesis work ) 122