Sinha / Telksnys Stochastic Control

Proceedings of the 2nd IFAC Symposium, Vilnius, Lithuanian SSR, USSR, 19-23 May 1986
1. Auflage 2014
ISBN: 978-1-4832-9807-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 526 Seiten, Web PDF

Reihe: IFAC Symposia Series

Stochastic control, the control of random processes, has become increasingly more important to the systems analyst and engineer. The Second IFAC Symposium on Stochastic Control represents current thinking on all aspects of stochastic control, both theoretical and practical, and as such represents a further advance in the understanding of such systems.

Autoren/Hrsg.

Sinha, N. K.

Telksnys, L. A.

Inhaltsverzeichnis

1;Front Cover;1
2;Stochastic Control;4
3;Copyright Page;5
4;Table of Contents;8
5;2nd IFAC SYMPOSIUM ON STOCHASTIC CONTROL;6
6;PREFACE;7
7;PART 1: PLENARY PAPERS;14
7.1;CHAPTER 1. RECENT TRENDS OF ESTIMATION-CONTROL THEORY OF NONLINEAR STOCHASTIC SYSTEMS AND ITS APPLICATIONS;14
7.1.1;INTRODUCTION;14
7.1.2;QUASI-LINEAR STOCHASTIC DIFFERENTIALS;14
7.1.3;AN APPROXIMATION TO NONLINEAR FILTER DYNAMICS
FOR THE SUBOPTIMAL CONTROL;15
7.1.4;SUBOPTIMAL CONTROL;15
7.1.5;SEPARABILITY, NEUTRALITY AND CERTAINTY EQUIVALENCE;17
7.1.6;OPTIMAL CONTROLS FOR STOCHASTIC DISTRIBUTED
PARAMETER SYSTEMS (SDPSs);17
7.1.7;APPLICATIONS;19
7.1.8;CONCLUSIONS;19
7.1.9;REFERENCES;19
7.2;CHAPTER 2. PROBLEMS OF ANALYSIS AND ON-LINE CONDITIONALLY OPTIMAL FILTERING OF PROCESSES IN NONLINEAR STOCHASTIC SYSTEMS;20
7.2.1;1. TYPES OF SYSTEMS CONSIDERED;20
7.2.2;2. STATEMENT OF PROBLEMS OF ANALYSIS;21
7.2.3;3· STATEMENT OF PROBLEMS OF FILTERING AND EXTRAPOLATION;22
7.2.4;4. SOLUTION OF THE ANALYSIS PROBLEMS;23
7.2.5;5. SOLUTION OF FILTERING AND EXTRAPOLATION PROBLEMS;30
7.2.6;6. CONCLUSIONS;33
7.2.7;REFERENCES;33
7.3;CHAPTER 3. APPLICATION OF M-ESTIMATION IN ROBUST RECURSIVE SYSTEM IDENTIFICATION;36
7.3.1;1.0 INTRODUCTION;36
7.3.2;2.0 M-ESTIMATION (OF LOCATION);36
7.3.3;3.0 THE IDENTIFICATION PROBLEM (EQUATION ERROR APPROACH);36
7.3.4;4.0 ROBUST IDENTIFICATION;36
7.3.5;5.0 EVALUATION OF THE EFFICIENCY OF THE ROBUST ALGORITHM;38
7.3.6;6.0 EXTENSION OF THE PROPOSED TECHNIQUE TO CORRELATION METHOD;38
7.3.7;7.0 HOW TO DECIDE ON M-ESTIMATION?;39
7.3.8;8.0 EXAMPLE;39
7.3.9;9.0 CONCLUSIONS;39
7.3.10;ACKNOWLDGEMENTS;40
7.3.11;REFERENCES;40
7.4;CHAPTER 4. RECOGNITION OF NONSTATIONARY RANDOM PROCESSES;44
7.4.1;INTRODUCTION;44
7.4.2;STATEMENT OF THE PROBLEM;44
7.4.3;THE SOLUTION OF THE PROBLEM;45
7.4.4;ESTIMATION OF RECOGNITION
ACCURACY;47
7.4.5;CONCLUSIONS;48
7.4.6;REFERENCES;48
7.5;CHAPTER 5. SELF-TUNING CONTROL OF STOCHASTIC EXTREMAL PLANTS;50
7.5.1;INTRODUCTION;50
7.5.2;PROBLEM STATEMENT;50
7.5.3;MINIMUM-VARIANCE CONTROLLERS;51
7.5.4;IDENTIFICATION IN A CLOSED LOOP;52
7.5.5;SIMULATION RESULTS;52
7.5.6;APPLICATION;53
7.5.7;CONCLUSIONS;53
7.5.8;REFERENCES;53
8;PART 2: PARAMETER ESTIMATION AND
IDENTIFICATION OF STOCHASTIC
SYSTEMS;56
8.1;CHAPTER 6. A NONLINEAR FILTER FOR ESTIMATION OF STATES OF A CONTINUOUS-TIME SYSTEM WITH DISCRETE MEASUREMENTS;56
8.1.1;I. INTRODUCTION;56
8.1.2;II. STATEMENT OF THE PROBLEM;56
8.1.3;III. SOLUTION OF THE PROBLEM;56
8.1.4;IV. A GENERALIZATION OF THE CSDM FILTER;57
8.1.5;V. A SPECIAL CASE OF CSDM FILTER;58
8.1.6;VI. CSDM LINEAR KALMAN FILTER;59
8.1.7;VII. IMPLEMENTATION ASPECTS;59
8.1.8;VIII. CONCLUSION;60
8.1.9;REFERENCES;60
8.2;CHAPTER 7. A STATISTICALLY OPTIMAL EXPLICIT B°-IDENTIFICATION ALGORITHM FOR NONLINEAR DISTRIBUTED-PARAMETER SYSTEMS;62
8.2.1;INTRODUCTION;62
8.2.2;IDENTIFICATION ALGORITHM;63
8.2.3;NUMERICAL SIMULATION
RESULTS;64
8.2.4;CONCLUSIONS;65
8.2.5;REFERENCES;65
8.3;CHAPTER 8. THE ESTIMATION ALGORITHM FOR SPACE DEPENDENT PARAMETERS IN NOISY DISTRIBUTED PARAMETER SYSTEMS;66
8.3.1;INTRODUCTION;66
8.3.2;ESTIMATION ALGORITHM;67
8.3.3;NUMERICAL EXPERIMENTS;68
8.3.4;CONCLUSIONS;69
8.3.5;REFERENCES;69
8.4;CHAPTER 9. ACCURACY ESTIMATION OF PREDICTION ON THE STOCHASTIC REGRESSION MODEL AT THE RESTRICTED SAMPLE;72
8.4.1;INTRODUCTION;72
8.4.2;THE RAISING OF THE EFFICIENCY OF THE REGRESSION COEFFICIENTS ESTIMATIONS;72
8.4.3;THE RAISING OF THE EFFICIENCY OF THE PREDICTION;73
8.4.4;THE DISTRIBUTION OF THE RESPONSE ESTIMATION UNDER NEW OBSERVATIONS;73
8.4.5;CONCLUSIONS;74
8.4.6;REFERENCES;74
8.4.7;APPENDICES;74
8.5;CHAPTER 10. IDENTIFICATION OF A MULTIDIMENSIONAL SYSTEM UNDER GAUSSIAN NOISE WITH AN UNKNOWN COVARIANCE MATRIX;78
8.5.1;CONCLUSION;83
8.5.2;REFERENCES;83
8.6;CHAPTER 11. NOISE SIGNAL IDENTIFICATION IN HIERARCHICALLY STRUCTURED SYSTEMS;84
8.6.1;INTRODUCTION;84
8.6.2;NOTATIONS AND ASSUMPTIONS;84
8.6.3;DETERMINATION OF THE SPECTRAL
DENSITY MATRICES OF THE NOISE
SIGNALS;85
8.6.4;CONCLUSIONS;87
8.6.5;LITERATURE;87
8.7;CHAPTER 12. DETERMINATION OF SUFFICIENT SAMPLE SIZE FOR LINEAR ESTIMATION PROBLEMS;90
8.7.1;INTRODUCTION;90
8.7.2;THE STOPPING RULE;90
8.7.3;THE RECURSIVE PROCEDURE;91
8.7.4;NUMERICAL EXAMPLES;91
8.7.5;EXPERIMENTAL RESULTS;92
8.7.6;CONCLUSION;92
8.7.7;REFERENCES;92
8.8;CHAPTER 13. ROBUST ADAPTIVE APPROACH TO IDENTIFICATION OF REGRESSION MODELS;94
8.8.1;INTRODUCTION;94
8.8.2;1 STATEMENT OF THE PROBLEM;94
8.8.3;2 THE BASIC CLASSES OF DENSITY
DISTRIBUTIONS IN PROBLEM (5);95
8.8.4;3 SOLUTION OF PROBLEM (5) FOR GLASS;96
8.8.5;4 SOLUTION OF PROBLEM (5) FOR CLASS;97
8.8.6;5 SOLUTION OF PROBLEM (5) FOR CLASS;97
8.8.7;6 SOLUTION OF PROBLEM;98
8.8.8;7 ADAPTIVE PROCEDURES OF ROBUSTESTIMATION;98
8.8.9;CONCLUSIONS;99
8.8.10;REFERENCES;99
8.9;CHAPTER 14. ON IDENTIFICATION OF LINEAR DYNAMIC SYSTEMS IN THE PRESENCE OF MULTIPLICATIVE AND ADDITIVE NOISES IN OBSERVATION;100
8.9.1;INTRODUCTION;100
8.9.2;STATE OF PROBLEM;100
8.9.3;CONSTRUCTION OF THE SEQUENTIAL
DESIGNS. THE MAIN RESULT;100
8.9.4;REFERENCES;103
8.10;CHAPTER 15. SYMMETRY GROUPS OF CORRELATION MODELS AND REDUCTION OF MULTIDIMENSIONAL SAMPLES TO INVARIANT STATISTICS;106
8.10.1;INTRODUCTION;106
8.10.2;UNIVERSAL PARAMETRIZATION;106
8.10.3;TRANSFORMATION TO CANONICAL FORM;107
8.10.4;BASIC INVARIANTS;108
8.10.5;SYMMETRY GROUPS;109
8.10.6;APPLICATIONS;109
8.10.7;CONCLUSIONS;111
8.10.8;REFERENCES;112
8.11;CHAPTER 16. A METHOD OF OBTAINING THE OPTIMAL ESTIMATES OF RANDOM VALUES' NUMERICAL CHARACTERISTICS;114
8.11.1;INTRODUCTION;114
8.11.2;PROBLEM STATEMENT;114
8.11.3;PROBLEM SOLUTION;114
8.11.4;EXAMPLES;117
8.11.5;REPERENCES;119
8.12;CHAPTER 17. IDENTIFIABILITY OF LINEAR AND NONLINEAR PARAMETRIC STOCHASTIC SYSTEMS;120
8.12.1;INTRODUCTION;120
8.12.2;LINEAR PARAMETRIC STOCHASTIC SYSTEMS;120
8.12.3;SYSTEMS LINEAR BY PARAMETERS AND NONLINEAR BY VARIABLES;122
8.12.4;NONLINEAR PARAMETRIC STOCHASTIC SYSTEMS;123
8.12.5;CONCLUSIONS;124
8.12.6;REFERENCES;124
8.13;CHAPTER 18. IDENTIFICATION OF ASYMPTOTICALLY STATIONARY PLANTS;126
8.13.1;INTRODUCTION;126
8.13.2;PLANT IDENTIFICATION WITH A PRESCRIBED MODEL OF PARAMETER DRIFT;127
8.13.3;THE IDENTIFICATION OF ASYMPTOMATICALLY STATIONARY PLANTS;127
8.13.4;CONCLUSIONS;128
8.13.5;APPENDICES;128
8.13.6;REFERENCES;128
8.14;CHAPTER 19. A NEW MODEL FOR NONLINEAR MEMORYLESS MULTIPLE SYSTEM;130
8.14.1;1. INTRODUCTION;130
8.14.2;2. STATEMENT OF THE PROBLEM;130
8.14.3;3. ALGORITHM;131
8.14.4;4. CONVERGENCE PROPERTIES;131
8.14.5;5. EXAMPLE;131
8.14.6;6. CONCLUSION;131
8.14.7;ACKNOWLEDGEMENT;132
8.14.8;REFERENCES;132
8.15;CHAPTER 20. ON THE FOUNDATION OF PRONY'S METHOD;134
8.15.1;INTRODUCTION;134
8.15.2;THE DETERMINATION OF THE CLASS OF FUNCTIONS;134
8.15.3;THE CLASS OF THE FINITE ORDER SEQUENCES;135
8.15.4;THE EXPANSION OF THE
FINITE ORDER FUNCTIONS
INTO THE FORMANTS;137
8.15.5;THE RECONSTRUCTION OF A FINITE ORDER FUNCTION FROM ITS SAMPLES USING PRONY'S METHOD;138
8.15.6;THE ESTIMATION OF THE SPECTRAL
DENSITY BY PRONY'S METHOD;138
8.15.7;CONCLUSIONS;139
8.15.8;REFERENCES;139
9;PART 3: STATE ESTIMATION OF DYNAMIC SYSTEMS;140
9.1;CHAPTER 21. ESTIMATION PROBLEMS FOR ONE PHASE STOCHASTIC STEFAN SYSTEMS;140
9.1.1;1. INTRODUCTION;140
9.1.2;2. MATHEMATICAL FORMULATION OF SYSTEM DYNAMICS;140
9.1.3;3. STATE AND FREE BOUNDARY ESTIMATIONS;142
9.1.4;4. APPROXIMATION TECHNIQUE AND NUMERICAL EXPERIMENTS;142
9.1.5;5. CONCLUSIONS;143
9.1.6;REFERENCES;143
9.2;CHAPTER 22. FINITE-DIMENSIONAL DISTRIBUTIONS OF THE PROCESSES IN STOCHASTIC INTEGRAL AND INTEGRO-DIFFERENTIAL SYSTEMS;146
9.2.1;1· Introduction;146
9.2.2;2. Problem statement;146
9.2.3;3. Main results;147
9.2.4;4- Conclusion;149
9.2.5;REFERENCES;150
9.3;CHAPTER 23. ELLIPSOIDAL STATE ESTIMATION OF DYNAMIC SYSTEMS;152
9.3.1;INTRODUCTION;152
9.3.2;STATEMENT OF THE PROBLEM;152
9.3.3;ELLIPSOIDAL ESTIMATES;153
9.3.4;DISCRETE OBSERVATIONS;153
9.3.5;CONTINUOUS OBSERVATIONS;154
9.3.6;CONCLUSION;155
9.3.7;REFERENCES;155
9.4;CHAPTER 24. ON WEAK, STRONG SOLUTIONS AND PATHWISE BANG-BANG CONTROL FOR NONLINEAR DEGENERATED STOCHASTIC SYSTEMS1;158
9.4.1;INTRODUCTION;158
9.4.2;MAIN RESULTS;158
9.4.3;AUXILIARY THEOREMS;159
9.4.4;PROOF OF THEOREM 1, 2 AND 3;161
9.4.5;CONCLUSION;163
9.4.6;REFERENCES;163
9.5;CHAPTER 25. FILTERING OF MARKOV PROCESSES IN DISCRETE TIME BY MONTE-CARLO METHOD;164
9.5.1;INTRODUCTION;164
9.5.2;1. THE PROCESS WITH DETERMINATED STRUCTURE;165
9.5.3;2. THE PROCESS WITH A RANDOM STRUCTURE;166
9.5.4;3. INTERPOLATION AND TOLERANCE CONTROL;167
9.5.5;CONCLUSIONS;168
9.5.6;REFERENCES;168
9.6;CHAPTER 26. ON THE STABILITY OF LINEAR STOCHASTIC SYSTEMS WITH ADDITIVE NOISE;170
9.6.1;INTRODUCTION;170
9.6.2;STATEMENT OF THE PROBLEM;170
9.6.3;CONDITIONS FOR STABILITY;171
9.6.4;SEMI-STABLE STOCHASTIC SYSTEMS;172
9.6.5;REFERENCES;173
9.7;CHAPTER 27. NON-LINEAR FILTRATION ALGORITHMS BASED ON THE LEAST SQUARE METHOD AND THEIR APPLICATION TO POWER SYSTEM PROCESSES;174
9.7.1;INTRODUCTION;174
9.7.2;DEFINITION OF THE PROBIEM;174
9.7.3;RECURSIVE TECHNIQUES;175
9.7.4;APPLICATION;176
9.7.5;CONCLUSION;177
9.7.6;REFERENCES;177
9.8;CHAPTER 28. ON CORRECTNESS OF FILTERING PROBLEM;180
9.8.1;INTRODUCTION;180
9.8.2;REGULARIZATION;181
9.8.3;THE SEQUENCE OF FILTERS APPROACHING OPTIMAL ACCURACY;183
9.8.4;REFERENCES;183
9.9;CHAPTER 29. LINEAR SYSTEM PARAMETER AND STATE ESTIMATION;186
9.9.1;STATEMENT OF THE PROBLEM;186
9.9.2;THE FILTER TO COMPUTE X (t);186
9.9.3;THE FILTER TO COMPUTE X (t);186
9.9.4;FILTER ADAPTATION;187
9.9.5;CONVERGENCE OF ESTIMATES;187
9.9.6;CONCLUSION;189
9.10;CHAPTER 30. SUBOPTIMAL ESTIMATION WITH NONPARAMETRIC AVERAGING OPERATORS;190
9.10.1;INTRODUCTION;190
9.10.2;SETTING OF THE PROBLEM;190
9.10.3;THE RSE - ALGORITHMS;191
9.10.4;DISCUSSION;191
9.10.5;THE SUBOPTTMAL RECURRENCE ESTIMATION;192
9.10.6;THE LINEARIZED PROCEDURES;192
9.10.7;THE PARAMETRIC IDENTIFICATION;192
9.10.8;THE NUMERIC EXAMPLE;193
9.10.9;REFERENCES;194
9.11;CHAPTER 31. ON PUGACHEV'S FILTERING THEORY FOR STOCHASTIC NONLINEAR SYSTEMS;196
9.11.1;I. INTRODUCTION;196
9.11.2;II. CONTINUOUS-TIME FILTERING;196
9.11.3;III. DISCRETE-TIME FILTERING;198
9.11.4;IV. IMPLEMENTATION METHODS;200
9.11.5;V. CONCLUSIONS;200
9.11.6;REFERENCES;201
9.12;CHAPTER 32. THE NONLINEAR FILTERING PROBLEM FOR A MULTISTAGE SYSTEM WITH STATISTICAL UNCERTAINTY;202
9.12.1;I. PROBLEM FORMULATION;202
9.12.2;II. GENERAL RELATIONS;203
9.12.3;III. THE DYNAMICS AND THE ASYMPTOTIC BEHAVIOUR OF THE ESTIMATES IN THE LINEARGAUSSIAN CASE;205
9.12.4;IV. THE ESTIMATION OF A MARKOV CHAIN WITH A FINITE SET OF STATES;206
9.12.5;REFERENCES;207
10;PART 4: ADAPTIVE METHODS OF PARAMETER ESTIMATION AND IDENTIFICATION;208
10.1;CHAPTER 33. RANDOM SEARCH IN ADAPTATION PROBLEMS OF STOCHASTIC SYSTEMS;208
10.1.1;REDUCING THE PROBLEMS TO A BINARY PROBLEM;209
10.1.2;RANDOM SEARCH WITH
ACCUMULATION;209
10.1.3;METHOD ANALYSIS AND MODIFICATION;209
10.1.4;REFERENCES;209
10.2;CHAPTER 34. ON ADAPTIVE PARAMETERS CONTROL IN STOCHASTIC GRADIENT ALGORITHMS;210
10.2.1;INTRODUCTION;210
10.2.2;QUASI-GRADIENT ALGORITHM WITH PROJECTION;210
10.2.3;PARAMETERS CALCULATION OF THE WINDELECTRICAL
WATERLIFTING COMPLEX;212
10.2.4;QUASI-GRADIENT ALGORITHM WITH VARIABLE
METRIC;213
10.2.5;STOCHASTIC ARR0W-HURWICZ ALGORITHM;213
10.2.6;CONCLUSION;214
10.2.7;REFERENCES;214
10.3;CHAPTER 35. ADAPTIVE FILTRATION OF STOCHASTIC PROCESSES WITH UNKNOWN CHARACTERISTICS: CONVERGENCE ANALYSIS AND FILTER SYNTHESIS WITH METHODS OF TWO-STAGE AVERAGING BY ENSEMBLE;216
10.3.1;1 GENERAL CONCEPT;216
10.3.2;2. QUASI-STATICAL SYNTHESIS OF P-FILTERS BEING TUNED;217
10.3.3;3 ADAPTABILITY CONDITIONS FOR P-FILTERS TUNING;217
10.3.4;4 SYNTHESIS OF THE TUNING F-PILTERS;219
10.3.5;CONCLUSIONS;220
10.3.6;REFERENCE;220
10.4;CHAPTER 36. FILTRATING THE MEAN OF NONSTATIONARY STOCHASTIC PROCESSES UNDER CONDITIONS OF A PRIORI AMBIGUITY;222
10.4.1;INTRODUCTION;222
10.4.2;THE LINEAR TWO-STEP ESTIMATION OF NSP MEAN;222
10.4.3;THE OPTIMAL SMOOTHING WINDOW;223
10.4.4;THE NONLINEAR ESTIMATIONS OF NSP MEAN;223
10.4.5;THE LINEAR FILTRATION OF NSP MEAN UNDER CONDITIONS OF A PRIORI AMBIGUITY;224
10.4.6;CHOOSING THE WIDTH OF SMOOTHING WINDOW;224
10.4.7;RECURRENT FILTER;225
10.4.8;CONCLUSION;225
10.4.9;REFERENCES;225
10.5;CHAPTER 37. DATA PROCESSING UNDER A PRIORI STATISTICAL UNCERTAINTY;226
10.5.1;INTRODUCTION;226
10.5.2;SIMULTANEOUS PARAMETER ESTIMATION OF THE VALID SIGNAL AND THE NOISE MODELS;227
10.5.3;THE NOISE CHARACTERISTICS ESTIMATION BY EXCLUDING THE VALID SIGNAL;228
10.5.4;NUMERICAL EXAMPLE;229
10.5.5;CONCLUSION;230
10.5.6;REFERENCES;230
10.6;CHAPTER 38. RECURSIVE IDENTIFICATION OF NONSTATIONARY RANDOM PROCESSES AND SYSTEMS;232
10.6.1;INTRODUCTION;232
10.6.2;PROBLEM FORMULATION;232
10.6.3;ADAPTIVE PARAMETER ESTIMATION
ALGORITHM;232
10.6.4;MODEL STRUCTURE SELECTION;233
10.6.5;EXPERIMENTAL RESULTS;234
10.6.6;CONCLUSIONS;234
10.6.7;REFERENCES;234
10.7;CHAPTER 39. ON THE USE OF A PRIORI INFORMATION IN NONPARAMETRIC REGRESSION ESTIMATION;236
10.7.1;INTRODUCTION;236
10.7.2;THE STRUCTURE AND ASYMPTOTIC PROPERTIES OF ESTIMATES;236
10.7.3;ADAPTIVE ESTIMATE;237
10.7.4;ILLUSTRATIVE EXAMPLES;238
10.7.5;CONCLUSION;239
10.7.6;APPENDICES;239
10.7.7;REFERENCES;241
10.8;CHAPTER 40. THE ADAPTIVE ALGORITHM OF NONPARAMETRIC REGRESSION;242
10.8.1;INTRODUCTION;242
10.8.2;THE PROBLEM;242
10.8.3;THE MAIN RESULT;243
10.8.4;DISCUSSION;243
10.8.5;THE METHOD OF PROOF;243
10.8.6;APPLICATION IN METALLURGY;244
10.8.7;CONCLUSION;244
10.8.8;REFERENCES;244
10.9;CHAPTER 41. A STATIONARY ADAPTATION PROCEDURE AS AN ALTERNATIVE TO THE STOCHASTICA PPROXIMATION TECHNIQUE;246
10.9.1;INTRODUCTION;246
10.9.2;DRAWBACKS OF THE AVAILABLE SEARCH
ALGORITHMS IN OPERATION UNDER
QUASISTATIONARY CONDITIONS;246
10.9.3;A STATIONARY ADAPTIVE SEARCH ALGORITHM;248
10.9.4;REFERENCES;249
10.9.5;APPENDIX;249
10.10;CHAPTER 42. THE SEARCH PROBLEMS WITH AN IMMOVABLE HIDER;252
10.10.1;REFERENCES;254
10.11;CHAPTER 43. UPDATING OF DAILY LOAD PREDICTION IN POWER SYSTEMS USING AR-MODELS;256
10.11.1;INTRODUCTION;256
10.11.2;MAIN PROPERTIES OF THE REST COMPONENT;256
10.11.3;PREDICTION OF THE REST COMPONENT BY MEANS OF AR-MODEL;257
10.11.4;CONCLUSION;258
10.11.5;REFERENCES;258
10.12;CHAPTER 44. CLUSTERING METHODS IN GLOBAL OPTIMIZATION;260
10.12.1;1 Introduction;260
10.12.2;2 Description of clustering metods;261
10.12.3;3 Discussion;264
10.12.4;References;265
10.13;CHAPTER 45. AXIOMATIC CONSTRUCTION OF THE MODELS OF COMPLICATED FUNCTIONS UNDER UNCERTAINTY;266
10.13.1;INTRODUCTION;266
10.13.2;REPRESENTATION OF INFORMATION ON AN OBJECTIVE FUNCTION;266
10.13.3;DEFINITION OF THE CHARACTERISTICS
OF A STATISTICAL MODEL;267
10.13.4;APPLICATIONS OF THE AXIOMATICALLY
BASED MODELS;267
10.13.5;CONSLUSION;268
10.13.6;REFERENCES;268
11;PART 5: DETECTION AND ESTIMATION OF CHANGES IN STOCHASTIC MODELS;270
11.1;CHAPTER 46. ESTIMATION OF THE CHANGE-POINT IN STATISTICAL MODELS;270
11.1.1;INTRODUCTION;270
11.1.2;THE CHANGE-POINT PROBLEM;270
11.1.3;LIKELIHOOD ESTIMATES OF A CHANGE POINT;271
11.1.4;ASYMPTOTIC BEHAVIOUR OF THE CHANGE POINT ESTIMATE;271
11.1.5;DISCERNIBILITY OF TWO STATIONARYSEQUENCES;272
11.1.6;CONCLUSION;273
11.1.7;REFERENCES;273
11.2;CHAPTER 47. SEQUENTIAL MULTIALTERNATIVE RECOGNITION, DETECTION AND ESTIMATION OF CHANGE-POINTS IN THE STRUCTURE OF DYNAMIC SYSTEMS;274
11.2.1;INTRODUCTION;274
11.2.2;STATEMENT OF THE PROBLEM;274
11.2.3;SEQUENTIAL MULTIALTERNATIVE DISCRIMINANT ANALYSIS OF COMPOSITE OBSERVATIONS;275
11.2.4;RECOGNIZABILITY OF DYNMJIC
SYSTEMS;275
11.2.5;ASYMPTOTICAL £ -RECOGNIZABILITY OF DYNAMIC SYSTEMS;276
11.2.6;CONCLUSION;277
11.2.7;REFERENCES;277
11.3;CHAPTER 48. ON THE DETERMINATION OF CHANGE POINTS IN MULTIVARIATE AUTOREGRESSIVE SEQUENCES;280
11.3.1;INTRODUCTION;280
11.3.2;STATEMENT OF THE PROBLEM;280
11.3.3;SOLUTION OF THE PROBLEM;280
11.3.4;EXAMPLE;281
11.3.5;CONCLUSION;281
11.3.6;REFERENCES;282
11.3.7;APPENDIX. FLOWCHART OF THE MAXIMUM ARGUMENT DETERMINATION PROCEDURE;282
11.4;CHAPTER 49. INEQUALITIES OF THE DEVIATION PROBABILITY FOR THE ESTIMATE OF A CHANGE IN THE PROPERTIES OF A RANDOM SEQUENCE;284
11.4.1;INTRODUCTION;284
11.4.2;STATEMENT OF THE PROBLEM;284
11.4.3;MAIN RESULTS;285
11.4.4;APPENDIX;287
11.4.5;C0NSLUSI0N;288
11.4.6;REFERENCES;288
11.5;CHAPTER 50. RECOGNITION OF A FLOW OF RANDOM EVENTS. MAIN MODELS AND TECHNIQUES;290
11.5.1;INTRODUCTION;290
11.5.2;THE MODEL OF REACTION TO AN EVENT;291
11.5.3;THE PROBABILISTIC MODELS OF EVENT CLASSES AND EVENT FLOW;291
11.5.4;THE PROBABILISTIC LEARNING AND RECOGNITION TECHNIQUES;292
11.5.5;THE MODEL OF NON-OVERLAPPING CLASSES IN THE SPACE OF REACTIONS TO AN EVENT;293
11.5.6;THE LEARNING AND RECOGNITIONTECHNIQUES IN CASE OF NON-OVERLAPPING CLASSES IN THE SPACE OF REACTIONS TO AN EVENT;294
11.5.7;CONCLUSION;295
11.5.8;REFERENCES;296
11.6;CHAPTER 51. NONPARAMETRIC ALGORITHMS OF STATISTICAL DIAGNOSTICS;298
11.6.1;INTRODUCTION;298
11.6.2;APOSTERIORI DISORDER PROBLEMS;298
11.6.3;THE PROBLEM OF SEQUENTIAL DISORDER DETECTION;300
11.6.4;DISORDER PROBLEMS IN A GENERAL SITUATION;301
11.6.5;CONCLUSIONS;301
11.6.6;REFERENCES;302
11.7;CHAPTER 52. ESTIMATION OF MODEL PARAMETERS OF RANDOM PROCESSES WITH INSTANTLY CHANGING PROPERTIES;304
11.7.1;INTRODUCTION;304
11.7.2;STATEMENT OF THE PROBLEM;304
11.7.3;PROCEDURE OF LIKELIHOOD FUNCTION MAXIMIZING;305
11.7.4;PARTICULAR MODEIS OF RANDOM PROCESSES;306
11.7.5;Appendix·THE PROOF OF THEOREM;307
11.7.6;REFERENCES;308
11.8;CHAPTER 53. EFFICIENCY OF TESTING OF THE CHANGE IN THE POISSON FLOW INTENSITY;310
11.8.1;Introduction;310
11.8.2;Some properties of the logarithm of likelihood ratio functional;311
11.8.3;The efficiency of the intensity change detection;311
11.8.4;Characteristics of the moment and value estimations;313
11.8.5;The results of the statistical modelling;314
11.8.6;Conclusion;315
11.8.7;REFERENCES;315
11.9;CHAPTER 54. LINEAR SYSTEM ANALYSIS METHOD WHEN REGIME CHANGE PROCESS IS SEMI-MARKOVONE;316
11.9.1;INTRODUCTION;316
11.9.2;PROBLEM DESCRIPTION;316
11.9.3;THE EXPECTATION OF THE SYSTEM STATE VECTOR;316
11.9.4;SPECIAL CASES;318
11.9.5;CONCLUSION;319
11.9.6;REFERENCES;319
12;PART 6: CONTROL OF STOCHASTIC SYSTEMS;320
12.1;CHAPTER 55. ON CONTROLLABILITY OF INFINITE DIMENSIONAL LINEAR STOCHASTIC SYSTEMS;320
12.1.1;INTRODUCTION;320
12.1.2;THE CONTROLLABILITY PROBLEM;320
12.1.3;A DUAL EXTREMUM PROBLEM AND THE DUALITY PRINCIPLE;321
12.1.4;THE STOCHASTIC CONTROLLABILITY CRITERIA;322
12.1.5;CONTROLLABILITY AND STOCHASTIC LINEAR REGULATORS;323
12.1.6;CONCLUSION;323
12.1.7;REFERENCES;323
12.2;CHAPTER 56. CONTROL AND ESTIMATION IN STOCHASTIC HEREDITARY SYSTEMS;324
12.2.1;HEREDITARY SYSTEMS CONTROL OPTIMALITY CONDITIONS;324
12.2.2;LINEAR-QUADRATIC PROBLEM;324
12.2.3;ESTIMATION OF THE STATES FOR THE HEREDITARY SYSTEMS;325
12.2.4;EXACT SOLUTIONS OF LINEAR-QUADRAI;327
12.2.5;REFERENCES;328
12.3;CHAPTER 57. ONE OPTIMAL CONTROL METHOD IN CERTAIN CLASS OF PROBLEMS;330
12.3.1;INTRODUCTION;330
12.3.2;THE DETERMINATION OF OPTIMAL CONTROL IN THE MANY-STEP-TYPE GAME PROBLEM;330
12.3.3;THE DETERMINATION OF OPTIMAL CONTROL IN THE NON-GAME MULTI-DIMENTIONAL PROBLEM;333
12.3.4;CONCLUSION;334
12.3.5;REFERENCES;334
12.4;CHAPTER 58. STOCHASTIC MECHANISMS OF THE ACTIVE SYSTEMS FUNCTIONING;336
12.4.1;INTRODUCTION;336
12.4.2;STOCHASTIC MECHANISMS;337
12.4.3;LINEAR MODEL OP THE AE POTENTIAL;338
12.4.4;THE AIM OF THE CENTRE;338
12.4.5;ESTIMATING AND CONTROL ALGORITHMS IN THE ABSENCE OF THE ACTIVITY;338
12.4.6;GAME DECISION;338
12.4.7;PROBLEM OF THE OPTIMAL SYNTHESIS;338
12.4.8;CONCLUSIONS;339
12.4.9;REFERENCES;340
12.5;CHAPTER 59. STOCHASTIC CONTROL OF THE COMPUTATIONAL PROCESS IN MULTIPROCESSOR SYSTEMS;342
12.5.1;INTRODUCTION;342
12.5.2;CONFLICTS BETWEEN PARALLEL PROCESSES IN MULTIPROCESSOR SYSTEMS;342
12.5.3;A MATHEMATICAL MODEL OF CONFLICTS IN A MULTIPROCESSOR SYSTEM;343
12.5.4;OPTIMAL DECISION RULES FOR CONFLICT SETTLING;343
12.5.5;MULTICRITERIA CONFLICT SETTLING MODELS IN MULTIPROCESSOR SYSTEMS;344
12.5.6;MARKOV DECISION MAKING PROCESSES WITH VECTOR-VALUED PENALTIES;345
12.5.7;ADAPTIVE CONFLICT SETTLING ALGORITHM IN MULTIPROCESSOR SYSTEMS;345
12.5.8;CONCLUSION;346
12.5.9;REFERENCES;346
12.6;CHAPTER 60. DESIGN OF HEATING CONTROL ALGORITHMS BY SOLVING AN INVERSE DYNAMICS PROBLEM;348
12.6.1;1.INTRODUCTION;348
12.6.2;2. STATEMENT OF THE PROBLEM;348
12.6.3;3. SOLUTION OF THE PROBLEM BY USING THE CONCEPT OF AN INVERSE DYNAMICS PROBLEM;349
12.6.4;REFERENCES;349
12.7;CHAPTER 61. NONLINEAR DISTRIBUTED PARAMETER STOCHASTIC SYSTEM OPTIMAL CONTROL UNDER INCOMPLETE MEASUREMENT;352
12.7.1;INTRODUCTION;352
12.7.2;I. PROBLEM STATEMENT;352
12.7.3;2. OPTIMAL CONTROL STRUCTURE;353
12.7.4;3.APPROXIMATE SOLUTION METHOD;354
12.7.5;CONCLUSION;356
12.7.6;REFERENCES;356
13;PART 7: ADAPTIVE CONTROL OF STOCHASTICSYSTEMS;358
13.1;CHAPTER 62. ACTIVELY ADAPTIVE CONTROL FOR THE STOCHASTIC SYSTEMS;358
13.1.1;INTRODUCTION;358
13.1.2;PROBLEM STATEMENT;358
13.1.3;PROBLEM SOLUTION;359
13.1.4;NON-LINEAR STATIC SYSTEM CONTROL;359
13.1.5;CONTROL OF A LINEAR DYNAMIC SYSTEM;360
13.1.6;CONCLUSION;361
13.1.7;REFERENCES;361
13.2;CHAPTER 63. ON STOCHASTIC SYSTEM CONTROL WITH UNKNOWN PARAMETERS AND UNCERTAIN STATISTICAL CHARACTERISTICS OF DISTURBANCES;362
13.2.1;THE FORMULATION OF THE PROBLEM;362
13.2.2;THE SYNTHESIS OF UNIFORM STAVILIZING REGULATORS;363
13.2.3;THE STUDY ON ASYMPTOTIC CHARACTERISTICS OF PARAMETER ADJUSTING PROCES;363
13.2.4;EXAMPLE;364
13.2.5;APPENDIX;365
13.2.6;REFERENCES;366
13.3;CHAPTER 64. OPTIMAL STOCHASTIC CONTROL OF THE CUTTING MODES ON THE GRINDERS;368
13.4;CHAPTER 65. DEADBEAT SELF TUNING CONTROLLERS;372
13.4.1;INTRODUCTION;372
13.4.2;STATEMENT OF THE PROBLEM;372
13.4.3;PROCESS MODEL;373
13.4.4;ESTIMATION ALGORITHM;373
13.4.5;CONTROL ALGORITHM;374
13.4.6;EXPERIMENTAL RESULTS;375
13.4.7;CONCLUSION;376
13.4.8;REFERENCES;376
13.4.9;APPENDIX;376
13.5;CHAPTER 66. ADAPTIVE CONTROL OF FINITE MARKOV CHAINS EMPLOYING STOCHASTIC APPROXIMATION METHOD;378
13.5.1;INTRODUCTION;378
13.5.2;THESTRUCTURE OF THE FINITE CONTROLLED MARKOV CHAIN;379
13.5.3;THE PROPERTIES OF LIMIT MEAN LOSSES;380
13.5.4;STATEMENT OF THE PROBLEM DEATING WITH THE ADAPTIVE CONTROL OF THE FINITE MARKOV CHAIN;380
13.5.5;ADAPTIVE CONTROL ALGORITHM;380
13.5.6;CONCLUSION;382
13.5.7;REFERENCES;382
13.6;CHAPTER 67. SELF-ORGANIZING STOCHASTIC CONTROL SYSTEMS;384
13.6.1;INTRODUCTION;384
13.6.2;PROBLEM STATEMENT;384
13.6.3;JOINT DETECTION AND ESTIMATION IN SELF-ORGANIZING SYSTEMS;385
13.6.4;DESIGN OF SELF-ORGANIZING CONTROL ALGORYTHMS;386
13.6.5;CONCLUSION;389
13.6.6;REFERENCES;389
14;PART 8: OPTIMIZATION OF STOCHASTIC SYSTEMS;390
14.1;CHAPTER 68. PRINCIPLES OF THE CONSTRUCTION OF COMPLEX ALGORITHMS FOR INFORMATION PROCESSING AND CONTROL IN SYSTEMS WITH STOCHASTIC EXCHANGE STRUCTURE;390
14.1.1;DYNAMIC SYSTEMS WITH STOCHASTIC EXCHANGE STRUCTURE;390
14.1.2;COMPLEX ALGORITHM FOR THE INFORMATION PROCESSING AND CONTROL;391
14.1.3;CONCLUSIONS;393
14.1.4;REFERENCES;393
14.2;CHAPTER 69. AN OPTIMAL CONTROL FOR LINEAR STOCHASTIC SYSTEMS WITH PERIODIC COEFFICIENTS;394
14.2.1;INTRODUCTION;394
14.2.2;PROOF UP TEH THEOREMS;398
14.2.3;CONCLUSION;399
14.2.4;REFERENCES;399
14.3;CHAPTER 70. DESIGN OF STABLE STABILIZING REGULATORS IN LQ OPTIMAL CONTROL PROBLEM;400
14.3.1;INTRODUCTION;400
14.3.2;THE FEEDBACK SET;401
14.3.3;MINIMIZATION IN HARDY SPACE H2;402
14.3.4;VARIATION METHODS AND RIESZ-NEVANLINNA THEOREM;403
14.3.5;SPECIAL CASE;404
14.3.6;CONCLUSION;405
14.3.7;REFERENCES;405
14.4;CHAPTER 71. ON STOCHASTIC COORDINATION IN OPTIMIZATION ALGORITHMS;406
14.4.1;INTRODUCTION;406
14.4.2;EVOLUTIONARY METHOD;406
14.4.3;OPTIMIZATION TASK;407
14.4.4;EVOLUTIONARY ALGORITHM;408
14.4.5;CONCLUSIONS;411
14.4.6;REFERENCES;411
14.5;CHAPTER 72. NUMERICAL SYNTHESIS OF OPTIMAL CONTROL FOR SOME STOCHASTIC SYSTEMS;412
14.5.1;INTRODUCTION;412
14.5.2;STATEMENT OF THE PROBLEM;413
14.5.3;CHOICE OF THE BOUNDARY CONDITIONS;413
14.5.4;NUMERICAL SOLUTION OF A SPECIFIC PROBLEM;415
14.5.5;CONCLUSION;416
14.5.6;REFERENCES;417
14.6;CHAPTER 73. OPTIMAL CONTOL OF STOCHASTIC SYSTEMS WITH WIDE BAND NOISE DISTURBANCES;418
14.6.1;1. INTRODUCTION;418
14.6.2;2. THE BASIC CONVERGENCE THEOREMS FOR u = u(t,x);418
14.6.3;3. MAIN ASYMPTOTIC ESTIMATES;419
14.6.4;4, EXAMPLE;421
14.6.5;CONCLUSION;421
14.6.6;REFERENCES;422
14.7;CHAPTER 74. SOME ASYMPTOTIC PROPERTIES OF STOCHASTIC CONTROL PROBLEMS WITH PERFORMANCE INDICES AVERAGED ON INFINITE TIME INTERVAL;424
14.7.1;INTRODUCTION;424
14.7.2;LIMIT OUTPUTS SET;424
14.7.3;ASYMPTOTIC FORM OF LAGRANGE'S MULTIPLIERS METHOD;426
14.7.4;ESTIMATES OF OPTIMAL VALUE;427
14.7.5;REFERENCES;427
14.8;CHAPTER 75. ON A FUNCTIONAL EQUATION IN OPTIMAL STOCHASTIC CONTROL;428
14.8.1;INTRODUCTION;428
14.8.2;FIXED POINT OF MONOTONE INTEGRAL OPERATORS;428
14.8.3;SOLUTION - PROPERTIES OF THE FUNCTIONAL EQUATION;429
14.8.4;MARKOV GAMES;430
14.8.5;CONCLUSION;431
14.8.6;REFERENCES;431
14.9;CHAPTER 76. SIMULATION OF AN OPTIMAL REGULATOR FOR A PARTIALLY OBSERVED MARKOV CHAIN;432
14.9.1;INTRODUCTION;432
14.9.2;STATEMENT OF THE PROBLEM;432
14.9.3;CONCLUSIONS;436
14.9.4;REFERENCES;436
14.10;CHAPTER 77. THE OPTIMAL CONTROL OF DISCOUNTED MARKOV PROCESSES WITH INFINITE HORIZON;438
14.10.1;INTRODUCTION;438
14.10.2;FORMULATION OF A PROBLEM AND MAIN RESULTS;438
14.10.3;THE PROOF OF THE THEOREM;439
14.10.4;EXAMPLE;441
14.10.5;REFERENCES;441
14.11;CHAPTER 78. THE GENERALIZED MINIMAX APPROACH IN STOCHASTIC SYSTEM OPTIMIZATION PROBLEMS WITH PROBABILITY CONSTRAINTS;442
14.11.1;1. POSING OF STOCHASTIC OPTIMIZATION PROBLEM;442
14.11.2;2. THE GENERALIZED MINIMAX APPROACH;443
14.11.3;3. THE OPTIMAL ESTIMATION PROBLEM;443
14.11.4;4. THE OPTIMAL CONTROL PROBLEM;445
14.11.5;REFERENCES;446
14.12;CHAPTER 79. TWO-LEVEL CERTAINTY EQUIVALENCE PRINCIPLE FOR A LQ PROBLEM;448
14.12.1;INTRODUCTION;448
14.12.2;PROBLEM STATEMENT;448
14.12.3;SOLUTION TO TLLQS PROBLEM;449
14.12.4;DISCUSSION ON THE USEFULNESS OF LOCAL CONTROLLERS;450
14.12.5;DISCUSSION OF THE SOLUTION;451
14.12.6;CONCLUSIONS;452
14.12.7;REFERENCES;452
15;PART 9: STATISTICAL MODELLING INPROBLEMS OF QUEUEING, RELIABILITY AND DIAGNOSTICS;454
15.1;CHAPTER 80. ON ONE GENERALIZATION OF THE STOCHASTIC EXPERIMENT CONCEPT;454
15.1.1;REFERENCES;456
15.2;CHAPTER 81. QUASI-MARKOV PROCESSES AND DESCRIPTION OF SOME MODELS OF QUEUEING THEORY;458
15.2.1;INTRODUCTION;458
15.2.2;A NOTION OF QUASI-MARKOV PROCESS;458
15.2.3;SIMPLE PROPERTIES OF QUASIMARKOV PROCESSES;459
15.2.4;ASYMPTOTIC BEHAVIOUR FOR STATE PROBABILITIES OF QUASI-MARKOV PROCESSES;459
15.2.5;DESCRIPTION OF SOME QUEUEING MODELS;460
15.2.6;BIRTH-AND-DEATH PROCESSES;461
15.2.7;REFERENCES;462
15.3;CHAPTER 82. EVALUATION OF SYSTEM'S RELIABILITY WITH A FUZZY PRIOR INFORMATION;464
15.3.1;INTRODUCTION;464
15.3.2;GENERAL ASSUMPTIONS;464
15.3.3;PRIOR DISTRIBUTION OF THE SYSTEM'S HAZARD RATE;465
15.3.4;PRIOR DISTRIBUTION OF As FOR A CERTAIN· TYPE OF EXPERTS' OPINION;466
15.3.5;CONCLUSIONS;467
15.3.6;REFERENCES;467
15.4;CHAPTER 83. EFFECT OF PARTIAL AND POSTPONABLE OUTAGES OF GENERATING UNITS ON POWER SYSTEM RELIABILITY;468
15.4.1;INTRODUCTION;468
15.4.2;NOTATIONS AND ASSUMPTIONS;468
15.4.3;OUTAGE PROBABILITY FOR THE TWO AND THREE STATE MARKOV MODEL;469
15.4.4;DERIVATION OF THE MAXIMAL DEVIATIONS OF THE OUTAGE PROBABILITIES;469
15.4.5;EFFECT OF THE PARTIAL AND POSTPONABLE OUTAGES ON THE POWER RESERVE;470
15.4.6;REFERENCES;471
15.5;CHAPTER 84. STATISTIC MODELLING OF INTEGRATED CIRCUITS;474
15.5.1;INTRODUCTION;474
15.5.2;THE PRESENT-DAY TECHNIQUES;474
15.5.3;THE SUGGESTED TECHNIQUE;475
15.5.4;THE SOLUTION OF CONCRETE PROBLEMS;476
15.5.5;CONCLUSION;478
15.5.6;REFERENCES;479
15.6;CHAPTER 85. CONTROL, ACCURACY AND RELIABILITY OF A STATISTICAL SIMULATION OF NON STATIONARY SYSTEMS;480
15.6.1;INTRODUCTION;480
15.6.2;A RANDOM PROCESSES PARAMETERS CONTROL AND;480
15.6.3;MODELLING AND PROCESSING OF A RANDOM FIELDS;482
15.6.4;CONCLUSION;484
15.6.5;REFERENCES;484
15.7;CHAPTER 86. QUEUEING SYSTEM WITH INDEPENDENT QUEUES AND COMMON SERVER;486
15.7.1;INTRODUCTION;486
15.7.2;APPROACH TO THE PROBLEM SOLUTION;486
15.7.3;SOLUTION OF THE PROBLEM ABOUT THE QS OF THE FIRST TYPE;487
15.7.4;SOLUTION OF THE PROBLEM ABOUT THE QS OF THE SECOND TYPE;487
15.7.5;ITERATIVE ALGORITHM OF THE INITIAL PROBLEM SOLUTION;488
15.7.6;ABOUT CONVERGENCE OF ITERATIVE ALGORITHM;488
15.7.7;CONCLUSION;489
15.7.8;REFERENCES;489
15.8;CHAPTER 87. TWO-LEVEL SYSTEM OF VARIABLE STRUCTURE STOCHASTIC AUTOMATA FOR NONSTATIONARY ENVIRONMENTS;492
15.8.1;PROBLEM STATEMENT;492
15.8.2;ENVIRONMENT;492
15.8.3;QUALITY OF LEARNING;493
15.8.4;OPTIMAL ALGORITHMS;493
15.8.5;VARIABLE STRUCTURE STOCHASTIC AUTOMATA;493
15.8.6;PROBLEM OF CONVERGENCE;493
15.8.7;LINEAR REINFORCEMENT SCHEMES;493
15.8.8;TWO-LEVEL SYSTEM OF VSSA FOR NONSTATIONARY ENVIRONMENTS;494
15.8.9;AUTOMATA FOR QUICK-VARYING AND PERIODIC ENVIRONMENTS;494
15.8.10;"AN" AUTOMATA IN PERIODIC DETERMINISTIC ENVIRONMENT- AN EXAMPLE;494
15.8.11;AUTOMATA FOR SLOW-VARYING ENVIRONMENTS;494
15.8.12;HOW TO DESIGN AN AUTOMATON FOR -WIDE CLASS OF RANDOM ENVIRONMENTS;495
15.8.13;THE SYSTEM;496
15.8.14;THE GAME;496
15.8.15;RESULTS;496
15.8.16;CONCLUSION;497
15.8.17;REFERENCES;497
16;PART 10: POSTER DISPLAYS;498
16.1;CHAPTER 88. ADDITIVE DECOMPOSITION OF FINITE PROCESSES;498
16.1.1;INTRODUCTION;498
16.1.2;PERFECT TRIGONOMETRIC EXPANSIONS;498
16.1.3;PERFECT EXPANSION OPERATORS;500
16.1.4;HARMONIC KERNELS OF FINITE FUNCTIONS;501
16.1.5;SPECTRAL CHARACTERISTICS EVALUATION;502
16.1.6;SUMMARY;503
16.1.7;REFERENCES;503
16.2;CHAPTER 89. SIGNAL DETECTION AT A POISSON NOISE BACKGROUND;504
16.2.1;INTRODUCTION;504
16.2.2;PROBLEM STATEMENT;504
16.2.3;DETECTION METHODS;504
16.2.4;NUMERICAL MODELLING;506
16.2.5;REFERENCES;506
16.3;CHAPTER 90. ANALYTIC-STATISTICAL ANALYSIS OF MEASURING ERRORS IN TECHNOLOGICAL SYSTEMS;508
16.3.1;INTRODUCTION;508
16.3.2;ALGORITHM FOR DETERMING OF PERIPHERIAL DISPLACEMENT ERROR DISPERSION;508
16.3.3;SUMMARY ERROR DISPLACEMENT DISPERSION;509
16.3.4;CONCLUSIONS;509
16.3.5;REFERENCES;509
16.4;CHAPTER 91. LP-SEARCH WITH EXTREMAL PROBLEM STRUCTURE ANALYSIS;512
16.4.1;INTRODUCTION;512
16.4.2;MODIFICATION OF LP-SEARCH;512
16.4.3;THE METHOD OF ANALYSIS;512
16.4.4;THE METHODS OF INVESTIGATION AND TEST PROBLEMS;514
16.4.5;INVESTIGATION OF THE EFFICIENCY OF THE MODIFICATION OF LP-SEARCH;514
16.4.6;INVESTIGATION OF THE EFFICIENCY OF APPLICATION OF THE RESULTS OF ANALYSIS;514
16.4.7;CONCLUSION;514
16.4.8;REFERENCES;515
16.5;CHAPTER 92. THE SPECTRAL METHOD FOR SOLVING THE FOKKER-PLANCK-KOLMOGOROV EQUATION FOR STOCHASTIC CONTROL SYSTEM ANALYSIS;516
16.5.1;INTRODUCTION;516
16.5.2;SPECTRAL CHARACTERISTICS;516
16.5.3;PROPERTIES OF OPERATORS IN THE SPECTRAL DOMAIN;517
16.5.4;THE GENERALIZED CHARACTERISTIC FUNCTION EQUATION;518
16.5.5;CONCLUSION;521
16.5.6;REFERENCES;521
16.6;CHAPTER 93. METHOD TO DETERMINE DETECTING VECTOR FOR DIGITAL CIRCUITS RANDOM TESTING;522
16.6.1;INTRODUCTION;522
16.6.2;ANALYSIS OF THE RIP TESTING QUALITIES;522
16.6.3;SYNTHESIS OF THE RIP SEQUENCES;523
16.6.4;CONCLUSION;524
16.6.5;REFERENCES;525
17;AUTHOR INDEX;526