نظریه سیستم‌های عمومی: بنیادهای ریاضی (ریاضیات در علم و مهندسی)

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering Content: Edited by Page iii copyright page Page iv Dedication Page v Preface Pages xi-xii Chapter I Introduction Pages 1-9 Chapter II Basic Concepts Pages 10-39 Chapter III General Realization Theory Pages 40-66 Chapter IV Linearity Pages 67-85 Chapter V Past-Determinacy Pages 86-96 Chapter VI Stationarity and Time Invariance Pages 97-113 Chapter VII Controllability Pages 114-138 Chapter VIII Minimal Realization Pages 139-158 Chapter IX Stability Pages 159-169 Chapter X Interconnections of Subsystems, Decompositi0N, and Decoupling Pages 170-209 Chapter XI Computability, Consistency, and Completeness Pages 210-216 Chapter XII Categories of Systems and Associated Functors Pages 217-245 Appendix I References and Historical Account Pages 246-250 Appendix II Alternative Basis for Mathematical General Systems Theory Pages 251-254 Appendix III Open Systems and Goal-Seeking Systems Pages 255-261 Appendix IV Basic Notions in Category Theory Pages 262-264 Index Pages 265-268 Studies theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This title considers many computing techniques, such as methods of operator approximation with any given accuracy; methods of covariance matrix estimation; and, methods for low-rank matrix approximations. Textbook on the mathematics of general systems theory (cybernetics) and systems analysis - includes references