Applied and Computational Control, Signals, and Circuits: Volume 1 Book

Foreword from the Editors
Preface
Acknowledgments
Contributors

1 Discrete Event Systems: The State of the Art and New Directions
-C.G. Cassandras and S. Lafortune
1.1 Introduction
1.2 DES Modeling Framework
1.3 Review of the State of the Art in DES Theory
Supervisory Control
Max-Plus Algebra
Sample Path Analysis and Performance Optimization
1.4 New Directions in DES Theory
1.5 Decentralized Control and Optimization
Some Key Issues
Decentralized Optimization Problem Formulation
Distributed Estimation
Weak Convergence Analysis
1.6 Failure Diagnosis
Statement of the Problem
Survey of Recent Literature
Presentation of One Approach to Failure Diagnosis
Some Issues for Future Research
1.7 Nondeterministic Supervisory Control
Nondeterminism and semantics of untimed models
The failure semantics
The trajectory semantics
The bisimulation semantics
The isomorphism semantics
Discussion
1.8 Hybrid Systems and Optimal Control
Statement of the Problem
Using Optimal Control in systems with Event-Driven Dynamics
References

2 Array Algorithms for H² and H^∞ Estimation
-B. Hassibi, T. Kailath and A.H. Sayed
2.1 Introduction
2.2 H² Square-Root Array Algorithm
Kalman Filtering
Square-Root Arrays
2.3 H^∞ Square-Root Array Algorithms
H^∞ Filtering
A Krein Space Formulation
J-Unitary Transformations
Square-Root Array Algorithms
The Central Filters
2.4 H² Fast Array Algorithms
2.5 H^∞ Fast ArrayAlgorithms
The General Case
The Central Filters
2.6 Conclusion
References
2.A Unitary and Hyperbolic Rotations
Elementary Householder Transformations
Elementary Circular or Givens Rotations
Fast Givens Transformations
Hyperbolic Transformations
2.B Krein Spaces
A Geometric Interpretation

3 Non-uniqueness, Uncertainty and Complexity in Modeling
-H. Kimura
3.1 Introduction
3.2 Issues of Models and Modeling
3.3 Non-Uniqueness
3.4 Uncertainty
3.5 Complexity
3.6 Formulation of Model Set Identification
3.7 Learning or Optimization?
3.8 Conclusion
References

4 Iterative Learning Control - An Expository Overview
-K.L. Moore
4.1 Introduction
4.2 Generic Description of ILC
4.3 Two Illustrative Examples of ILC Algorithms
A Linear Example
An Adaptive ILC Algorithm for a Robotic Manipulator
4.4 The Literature, Context, Terminology of ILC
Classifications of ILC Literature
Connections to Other Control Paradigms
4.5 ILC Algorithms and Results
Basic Ideas
Nonlinear Systems
Robotics and Other Applications
Some New Approaches to ILC Algorithms
4.6 Example: Combining Some New ILC Approaches
GMAW Model
ILC-Based Control Strategy
4.7 Conclusion: The Past, Present, and Future of ILC
References

5 FIR Filter Design via Spectral Factorization and Convex Optimization
-S-P. Wu, S. Boyd and L. Vandenberghe
5.1 Introduction
5.2 Spectral factorization
5.3 Convex semi-infinite optimization
5.4 Lowpass filter design
5.5 Log-Chebychev approximation
5.6 Magnitude equalizer design
5.7 Linear antenna array weight design
5.8 Conclusions
References
5.A Appendix: Spectral factorization

6 Algorithms for Subspace State Space System Identification - An Overview
-B. De Moor, P. Van Overschee and W. Favoreel
6.1 System identification: To measure is to know!
6.2 Linear subspace identification: an overview
Re-discovering the state
The subspace structure of linear systems
The two basic steps in subspace identification
6.3 Comparing PEM with subspace methods
6.4 Statistical consistency results
6.5 Extensions
Deterministic systems
Closed-loop subspace system identification
Frequency domain subspace identification
Subspace identification of bilinear systems
6.6 Software and DAISY
6.7 Conclusions and open research problems
References

7 Iterative Solution Methods for Large Linear Discrete Illposed Problems
-D. Calvetti, L. Reichel and Q. Zhang
7.1 Introduction
7.2 Krylov subspace iterative methods
The standard conjugate gradient algorithm
Conjugate gradient methods for inconsistent systems
7.3 Tikhonov regularization
Factorization methods
Algorithms based on the conjugate gradient method
Explicit approximation of the filter function
A comparison of conjugate gradient and expansion methods
Methods based on the total variation norm
7.4 An exponential filter function
7.5 Iterative methods based on implicitly defined filter functions
Landweber iteration
Truncated conjugate gradient iteration
Regularizing preconditioned conjugate gradient methods
7.6 Towards a black box
Computation of the regularization parameter
Two algorithms for Tikhonov regularization
7.7 Computed examples
References

8 Wavelet-Based Image Coding: An Overview
-G. Davis and A. Nosratinia
8.1 Introduction
Image compression
8.2 Quantization
Vector Quantization
Optimal Vector Quantizers
Sphere Covering and Density Shaping
Cross-Variable Dependencies
Fractional Bitrates
8.3 Transform Coding
The Karhunen-Loève transform
Optimal bit allocation
Optimality of the Karhunen-Loève Transform
The Discrete Cosine Transform
Subband transforms
8.4 Wavelets: A Different Perspective
Multiresolution Analyses
Wavelets
Recurrence Relations
Wavelet Transforms vs. Subband Decompositions
Wavelet Properties
8.5 A Basic Wavelet Image Coder
Choice of Wavelet Basis
Boundaries
Quantization
Entropy Coding
Bit Allocation
Perceptually Weighted Error Measures
8.6 Extending the Transform Coder Paradigm
8.7 Zerotree Coding
The Shapiro and Said-Pearlman Coders
Zerotrees and Rate-Distortion Optimization
8.8 Frequency, space-frequency adaptive coders
Wavelet Packets
Frequency Adaptive Coders
Space-Frequency Adaptive Coders
8.9 Utilizing Intra-band Dependencies
Trellis coded quantization
TCQ subband coders
Mixture Modeling and Estimation
8.10 Future Trends
8.11 Summary and Conclusion
References

9 Reduced-Order Modeling Techniques Based on Krylov Subspaces and their Use in Circuit Simulation
-R.W. Freund
9.1 Introduction
9.2 Reduced-Order Modeling of Linear Dynamical Systems
Linear Dynamical Systems
Reduced-Order Modeling
Reduction to One Matrix
9.3 Linear Systems in Circuit Simulation
General Circuit Equations
Linear Subcircuits and Linearized Circuits
Linear RLC Circuits
9.4 Krylov Subspaces and Moment Matching
Assumptions and a Convention
Single Starting Vectors
Connection to Moment Matching
Multiple Starting Vectors
9.5 The Lanczos Process
The Classical Algorithm for Single Starting Vectors
A Lanczos-Type Algorithm for Multiple Starting Vectors
Exploiting Symmetry
9.6 Lanczos-Based Reduced-Order Modeling
The Classical Lanczos-Padé Connection
The Multi-Input Multi-Output Case
Stability and Passivity
PVLp: Post-Processing of PVL
Passive Reduced-Order Models from SyMPVL
How to Achieve Passivity in Practice
Two Other Lanczos-Based Approaches
9.7 The Arnoldi Process
9.8 Arnoldi-Based Reduced-Order Modeling
9.9 Circuit-Noise Computations
The Problem
Reformulation as a Transfer Function
A PVL Simulation
9.10 Concluding Remarks
References

10 SLICOT - A Subroutine Library in Systems and Control Theory
-P. Benner, V. Mehrmann, V. Sima, S. Van Huffel and A. Varga
10.1 Introduction
10.2 Why Do We Need More Than MATLAB Numerics?
Limitations of MATLAB
The need for production quality numerical software
Low level reusability of Fortran libraries
Structure preserving algorithms
10.3 Retrospect
Short history of control subroutine libraries
Standard libraries RASP and SLICOT: present status
RASP/SLICOT mutual compatibility concept
10.4 The Design of SLICOT
Structure of the library
Choice of algorithms
User Manual
Implementation and documentation standards
Benchmarks
10.5 TOC of SLICOT
Current TOC of the library
Development of the public release of SLICOT
In the queue
10.6 Performance Results
10.7 The Future-NICONET
Objectives and exploratory phase of NICONET
Development of performant numerical software for CACSD
Integration of saftware in a user-friendly environment
Benchmarking and testing the software in an industrial environment
Information dissemination and access to control software
Implementation phase
10.8 Concluding Remarks
References
10.A TOC of SLICOT Release 3.0
10.B Electronic Access to the Library and Related Literature