Modeling, Estimation and Control

Festschrift in Honor of Giorgio Picci on the Occasion of his Sixty-Fifth Birthday

By: Augusto Ferrante (Editor), Stefano Pinzoni (Editor), Alessandro Chiuso (Editor)

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Paperback | 21 August 2007

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This Festschrift is intended as a homage to our esteemed colleague, friend and maestro Giorgio Picci on the occasion of his sixty-?fth birthday. We have knownGiorgiosince our undergraduatestudies at the University of Padova, wherewe ?rst experiencedhisfascinatingteachingin theclass ofSystem Identi?cation. While progressing through the PhD program, then continuing to collaborate with him and eventually becoming colleagues, we have had many opportunitiesto appreciate the value of Giorgio as a professor and a scientist, and chie?y as a person. We learned a lot from him and we feel indebted for his scienti?c guidance, his constant support, encouragement and enthusiasm. For these reasons we are proud to dedicate this book to Giorgio. The articles in the volume will be presented by prominent researchers at the "- ternational Conference on Modeling, Estimation and Control: A Symposium in Honor of Giorgio Picci on the Occasion of his Sixty-Fifth Birthday", to be held in Venice on October 4-5, 2007. The material covers a broad range of topics in mathematical systems theory, esti- tion, identi?cation and control, re?ecting the wide network of scienti?c relationships established during the last thirty years between the authors and Giorgio. Critical d- cussion of fundamental concepts, close collaboration on speci?c topics, joint research programs in this group of talented people have nourished the development of the ?eld, where Giorgio has contributed to establishing several cornerstones.

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Coefficients of Variations in Analysis of Macro-policy Effects: An Example of Two-Parameter Poisson-Dirichlet Distributions	p. 1
Introduction	p. 1
The Model	p. 2
Asymptotic Properties of the Number of Sectors	p. 2
The Coefficients of Variation	p. 3
The Number of Sectors	p. 3
The Number of Sectors of Specified Size	p. 3
Discussion	p. 3
References	p. 4
How Many Experiments Are Needed to Adapt?	p. 5
Introduction	p. 5
Worst-Case Approach to Adaptation	p. 7
Worst-Case Performance	p. 7
Adaptive Design	p. 8
The Experimental Effort Needed for Adaptation	p. 9
A Numerical Example	p. 11
Conclusions	p. 13
References	p. 14
A Mutual Information Based Distance for Multivariate Gaussian Processes	p. 15
Introduction	p. 15
Model Class	p. 17
Principal Angles, Canonical Correlations and Mutual Information	p. 19
Principal Angles and Directions	p. 20
Canonical Correlations	p. 20
Mutual Information	p. 21
Application to Stochastic Processes	p. 21
A Distance Between Multivariate Gaussian Processes	p. 25
Definition and Metric Properties	p. 25
Computation	p. 26
Special Case of Scalar Processes	p. 26
Relation with Subspace Angles Between Scalar Stochastic Processes	p. 27
Relation with a Cepstral Distance	p. 27
The Cepstral Nature of the Mutual Information Distance	p. 28
Multivariate Power Cepstrum and Cepstral Distance	p. 28
The Cepstral Nature of the Mutual Information Distance	p. 29
Conclusions and Open Problems	p. 30
Conclusions	p. 30
Open Problems	p. 31
References	p. 31
Differential Forms and Dynamical Systems	p. 35
Introduction	p. 35
Planar Dynamical Systems	p. 36
The Principle of the Torus for Autonomous Systems	p. 40
Lyapunov-Like Differential Forms for the Existence of Cross Sections	p. 41
Necessary and Sufficient Conditions for Existence of Periodic Orbits	p. 42
Stability and Robustness of Periodic Orbits	p. 43
References	p. 44
An Algebraic Framework for Bayes Nets of Time Series	p. 45
Introduction	p. 45
Conditional Independence and Stochastic Realization	p. 46
Lattice Conditionally Independence and Stochastic Realization	p. 48
Lattices of Subspaces	p. 48
Lattice Conditionally Orthogonal Stochastic Hilbert Spaces	p. 49
Spatially Patterned Infinite Bayes Nets	p. 53
References	p. 56
A Birds Eye View on System Identification	p. 59
Introduction	p. 59
Structure Theory	p. 61
Estimation for a Given Subclass	p. 64
Model Selection	p. 67
Linear Non-mainstream Cases	p. 68
Nonlinear Systems	p. 69
Present State and Future Developments	p. 69
References	p. 70
Further Results on the Byrnes-Georgiou-Lindquist Generalized Moment Problem	p. 73
Introduction	p. 73
A Generalized Moment Problem	p. 74
Kullback-Leibler Criterion	p. 75
Optimality Conditions and the Dual Problem	p. 76
An Existence Theorem	p. 77
A Descent Method for the Dual Problem	p. 79
References	p. 81
Factor Analysis and Alternating Minimization	p. 85
Introduction	p. 85
The Model	p. 86
Lifting of the Original Problem	p. 87
The First Partial Minimization Problem	p. 88
The Second Partial Minimization Problem	p. 89
The Link to the Original Problem	p. 91
Alternating Minimization Algorithm	p. 92
The Algorithm	p. 92
Proof of Proposition 1	p. 94
References	p. 95
Appendix	p. 95
Multivariate Normal Distribution	p. 95
Partitioned Matrices	p. 95
Tensored Polynomial Models	p. 97
Introduction	p. 97
Tensored Models	p. 98
Preliminaries	p. 98
Tensored Polynomial and Rational Models	p. 99
Module Structures on Tensored Models	p. 101
Duality	p. 103
Homomorphisms of Tensored Models	p. 104
Applications	p. 105
The Space of Intertwining Maps	p. 105
The Polynomial Sylvester Equation	p. 106
Solving the Sylvester Equation	p. 107
Invariant Factors of the Sylvester Map	p. 109
References	p. 112
Distances Between Time-Series and Their Autocorrelation Statistics	p. 113
Introduction	p. 113
Interpretation of the L[subscript 1] Distance	p. 114
A Distance Between Covariance Matrices	p. 115
An Example	p. 118
Approximating Sample Covariances	p. 120
Comparison with the von Neumann Entropy	p. 120
Structured Covariances	p. 121
References	p. 122
Global Identifiability of Complex Models, Constructed from Simple Submodels	p. 123
Introduction	p. 123
The Problem	p. 124
A Simple Example of Interconnected Modules	p. 126
Preliminary Considerations and Tools	p. 127
Identifiability Analysis	p. 128
A Formal Theorem on Identifiability from Sub-models	p. 131
Global Identifiability	p. 131
Local Identifiability	p. 132
Conclusions	p. 132
References	p. 133
Identification of Hidden Markov Models - Uniform LLN-s	p. 135
Introduction	p. 135
Hidden Markov Models	p. 136
L-Mixing Processes	p. 138
Asymptotic Properties of the Log-Likelihood Function	p. 139
The Case of Primitive Q-s	p. 141
The Derivative of the Predictive Filter	p. 144
Uniform Laws of Large Numbers	p. 147
Estimation of Hidden Markov Models	p. 149
References	p. 149
Identifiability and Informative Experiments in Open and Closed-Loop Identification	p. 151
Introduction	p. 151
The Prediction Error Identification Setup	p. 153
Identifiability, Informative Data, and All That Jazz	p. 154
Analysis of the Information Matrix	p. 157
Expressions of the Pseudoregression Vector	p. 157
The Range and Kernel of Rank-One Vector Processes	p. 158
Regularity Conditions for I([theta]): A First Analysis	p. 159
Rich and Exciting Signals	p. 161
Regularity of I([theta]) for ARMAX and BJ Model Structures	p. 166
Conclusions	p. 169
References	p. 169
On Interpolation and the Kimura-Georgiou Parametrization	p. 171
Introduction	p. 171
Interpolation Conditions as Matrix Equations	p. 172
The Connection with the Kimura-Georgiou Parametrization	p. 177
References	p. 182
The Control of Error in Numerical Methods	p. 183
Introduction	p. 183
A Simple Example	p. 184
Four-Step Adams-Bashforth	p. 186
Statistical Analysis	p. 190
Conclusion	p. 192
References	p. 192
Contour Reconstruction and Matching Using Recursive Smoothing Splines	p. 193
Introduction	p. 193
Problem Formulation and Motivation	p. 194
Some Theoretical Properties	p. 196
Proper Periodicity Conditions	p. 196
Continuous Time, Continuous Data	p. 197
Continuous Time, Discrete Data	p. 199
Continuous Time, Discrete Data Iterated	p. 200
Data Set Reconstruction	p. 200
Evaluation of Recursive Spline Method	p. 202
Conclusions	p. 205
References	p. 206
Role of LQ Decomposition in Subspace Identification Methods	p. 207
Introduction	p. 207
State-Input-Output Matrix Equation	p. 208
MOESP Method	p. 209
N4SID Method	p. 211
Zero-Input Responses	p. 211
Relation to Ho-Kalman's Method	p. 214
State Vector and Zero-State Response	p. 214
Zero-State Response	p. 215
Conclusions	p. 216
References	p. 217
Canonical Operators on Graphs	p. 221
Introduction	p. 221
Graphs	p. 222
The Geometry of Graphs and Digraphs	p. 222
Operator Theory on Graphs and Digraphs	p. 224
Differences, Divergences, Laplacians and Dirac Operators	p. 227
Operators on Weighted Graphs	p. 230
The Incidence Operator and Its Kin	p. 232
The Drift of a Digraph	p. 235
References	p. 236
Prediction-Error Approximation by Convex Optimization	p. 239
Introduction	p. 239
Prediction-Error Approximation	p. 240
Prediction-Error Approximation in Restricted Model Classes	p. 241
The Kullback-Leibler Criterion and Maximum-Likelihood Identification	p. 245
Prediction-Error Approximation by Analytic Interpolation	p. 246
Conclusion	p. 248
References	p. 248
Patchy Solutions of Hamilton-Jacobi-Bellman Partial Differential Equations	p. 251
Hamilton Jacobi Bellman PDEs	p. 251
Other Approaches	p. 255
New Approach	p. 255
One Dimensional HJB PDEs	p. 256
One Dimensional Example	p. 260
HJB PDEs in Higher Dimensions	p. 261
Two Dimensional Example	p. 268
Conclusion	p. 269
References	p. 269
A Geometric Assignment Problem for Robotic Networks	p. 271
Introduction	p. 271
Geometric and Stochastic Preliminaries	p. 272
The Euclidean Traveling Salesperson Problem	p. 273
Bins and Balls	p. 273
Random Geometric Graphs	p. 273
Network Model and Problem Statement	p. 274
Robotic Network Model	p. 274
The Target Assignment Problem	p. 274
Sparse and Dense Environments	p. 275
Sparse Environments	p. 275
Assignment-Based Algorithms with Lower Bound Analysis	p. 275
The ETSP AssgmtAlgorithm with Upper Bound Analysis	p. 276
Dense Environments	p. 279
The Grid AssgmtAlgorithm with Complexity Analysis	p. 279
A Sensor Based Version	p. 282
Congestion Issues	p. 282
Conclusion and Extensions	p. 283
References	p. 283
On the Distance Between Non-stationary Time Series	p. 285
Introduction	p. 285
Formalization	p. 286
Introducing Nuisances	p. 287
Dynamic Time Warping	p. 288
Dynamics, or Lack Thereof, in DTW	p. 289
Time Warping Under Dynamic Constraints	p. 290
Going Blind	p. 292
Computing the Distance	p. 293
Correlation Kernels for Non-stationary Time Series	p. 294
Invariance Via Canonization	p. 295
Discussion	p. 297
References	p. 298
Stochastic Realization for Stochastic Control with Partial Observations	p. 301
Introduction	p. 301
Problem Formulation	p. 302
The Classical Approach	p. 303
The Stochastic Realization Approach to Stochastic Control with Partial Observations	p. 305
Special Cases	p. 306
Concluding Remarks	p. 312
References	p. 312
Experiences from Subspace System Identification - Comments from Process Industry Users and Researchers	p. 315
Introduction	p. 315
Questions and Answers from the User	p. 317
Comments from the Researchers	p. 320
Input Design	p. 321
Merging Data	p. 322
Merging of Models	p. 324
Conclusion	p. 326
References	p. 326
Recursive Computation of the MPUM	p. 329
Introduction	p. 329
Problem Statement	p. 330
Subspace Identification	p. 333
State Construction by Past/Future Partition	p. 334
The Hankel Structure and the Past/Future Partition	p. 336
The Left Kernel of a Hankel Matrix	p. 338
Recursive Computation of a Module Basis	p. 339
Concluding Remarks	p. 341
Subspace ID	p. 341
State Construction by Shift-and-Cut	p. 342
Return to the Data	p. 343
Approximation and Balanced Reduction	p. 343
The Complementary System	p. 343
References	p. 344
New Development of Digital Signal Processing Via Sampled-Data Control Theory	p. 345
Foreword	p. 345
Introduction	p. 345
The Shannon Paradigm	p. 346
Problems in the Shannon Paradigm	p. 347
Control Theoretic Formulation	p. 349
Application to Images	p. 352
Concluding Remarks and Related Work	p. 354
References	p. 355
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Modeling, Estimation and Control

Festschrift in Honor of Giorgio Picci on the Occasion of his Sixty-Fifth Birthday

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