Applied and Computational Control, Signals, and Circuits Volume 1

The purpose of this annual series, Applied and Computational Control, Signals, and Circuits, is to keep abreast of the fast-paced developments in computational mathematics and scientific computing and their increasing use by researchers and engineers in control, signals, and circuits. The series is dedicated to fostering effective communication between mathematicians, computer scientists, computational scientists, software engineers, theorists, and practicing engineers. This interdisciplinary scope is meant to blend areas of mathematics (such as linear algebra, operator theory, and certain branches of analysis) and computational mathematics (numerical linear algebra, numerical differential equations, large scale and parallel matrix computations, numerical optimization) with control and systems theory, signal and image processing, and circuit analysis and design. The disciplines mentioned above have long enjoyed a natural synergy. There are distinguished journals in the fields of control and systems the­ ory, as well as signal processing and circuit theory, which publish high quality papers on mathematical and engineering aspects of these areas; however, articles on their computational and applications aspects appear only sporadically. At the same time, there has been tremendous recent growth and development of computational mathematics, scientific comput­ ing, and mathematical software, and the resulting sophisticated techniques are being gradually adapted by engineers, software designers, and other scientists to the needs of those applied disciplines.

1 Discrete Event Systems: The State of the Art and New Directions.- 1.1 Introduction.- 1.2 DES Modeling Framework.- 1.3 Review of the State of the Art in DES Theory.- 1.4 New Directions in DES Theory.- 1.5 Decentralized Control and Optimization.- 1.6 Failure Diagnosis.- 1.7 Nondeterministic Supervisory Control.- 1.8 Hybrid Systems and Optimal Control.- References.- 2 Array Algorithms forH2andH?Estimation.- 2.1 Introduction.- 2.2H2Square Root Array Algorithms.- 2.3HO?Square Root Array Algorithms.- 2.4H2Fast Array Algorithms.- 2.5HO?Fast Array Algorithms.- References.- 2.A Unitary and Hyperbolic Rotations.- 2.B Krein Spaces.- 3 Nonuniqueness, Uncertainty, and Complexity in Modeling.- 3.1 Introduction.- 3.2 Issues of Models and Modeling.- 3.3 Nonuniqueness.- 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.- 4.1 Introduction.- 4.2 Generic Description of ILC.- 4.3 Two Illustrative Examples of ILC Algorithms.- 4.4 The Literature, Context, and Terminology of ILC.- 4.5 ILC Algorithms and Results.- 4.6 Example: Combining Some New ILC Approaches.- 4.7 Conclusion: The Past, Present, and Future of ILC.- References.- 5 FIR Filter Design via Spectral Factorization and Convex Optimization.- 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.- 6.1 System Identification: To Measure Is To Know’.- 6.2 Linear SubspaceIdentification: An Overview.- 6.3 Comparing PEM with Subspace Methods.- 6.4 Statistical Consistency Results.- 6.5 Extensions.- 6.6 Software and DAISY.- 6.7 Conclusions and Open Research Problems.- References.- 7 Iterative Solution Methods for Large Linear Discrete Ill-Posed Problems.- 7.1 Introduction.- 7.2 Krylov Subspace Iterative Methods.- 7.3 Tikhonov Regularization.- 7.4 An Exponential Filter Function.- 7.5 Iterative Methods Based on Implicitly Defined Filter Functions.- 7.6 Toward a Black Box.- 7.7 Computed Examples.- References.- 8 Wavelet-Based Image Coding: An Overview.- 8.1 Introduction.- 8.2 Quantization.- 8.3 Transform Coding.- 8.4 Wavelets: A Different Perspective.- 8.5 A Basic Wavelet Image Coder.- 8.6 Extending the Transform Coder Paradigm.- 8.7 Zerotree Coding.- 8.8 Frequency and Space-Frequency Adaptive Coders.- 8.9 Utilizing Intra-band Dependencies.- 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.- 9.1 Introduction.- 9.2 Reduced-Order Modeling of Linear Dynamical Systems.- 9.3 Linear Systems in Circuit Simulation.- 9.4 Krylov Subspaces and Moment Matching.- 9.5 The Lanczos Process.- 9.6 Lanczos-Based Reduced-Order Modeling.- 9.7 The Arnoldi Process.- 9.8 Arnoldi-Based Reduced-Order Modeling.- 9.9 Circuit-Noise Computations.- 9.10 Concluding Remarks.- References.- 10 SLICOT—A Subroutine Library in Systems and Control Theory.- 10.1 Introduction.- 10.2 Why Do We Need More Than MATLAB Numerics?.- 10.3 Retrospect.- 10.4 The Design of SLICOT.- 10.5 Contents of SLICOT.- 10.6 Performance Results.- 10.8 Concluding Remarks.- References.- 10.A Contents of SLICOT Release 3.0.- 10.B Electronic Access to the Library and Related Literature.