Theory of Optimal SearchElsevier, 20 janv. 1976 - 322 pages 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; andmethods 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 particularbranches, 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 |
Table des matières
1 | |
17 | |
Chapter II Uniformly Optimal Search Plans | 35 |
Chapter III Properties of Optimal Search Plans | 84 |
Chapter IV Search with Discrete Effort | 101 |
Chapter V Optimal Search and Stop | 118 |
Chapter VI Search in the Presence of False Targets | 136 |
Chapter VII Approximation of Optimal Plans | 179 |
Chapter IX Markovian Target Motion | 221 |
Reference Theorems | 235 |
Necessary Conditions for Constrained Optimization of Separable Functionals | 237 |
245 | |
Author Index | 251 |
255 | |
259 | |
Chapter VIII Conditionally Deterministic Target Motion | 197 |
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Expressions et termes fréquents
addition allocation f applied approximation assumed assumption Borel bounded broad-search calculate called Chapter considered constraint contact investigation continuous decreasing defined definition depend detecting the target detection function discrete discussed effort Example exists expected false targets fe F(X find the target finite fixed follows given gives holds increasing increment independent Lemma locally optimal looks in cell maximum mean measure method minimizes motion necessary Note Observe obtained optimal for cost optimal nonadaptive optimal search plan placed pointwise Lagrangian position posterior presented probability of detecting problem Proof proved region remaining respect result satisfy search and stop search space Section semiadaptive plan sensor shown situation Suppose sweep width target distribution Theorem track uniformly optimal plan x e X yields