مدل‌های تصادفی، برآورد و کنترل جلد ۲ (ریاضیات در علم و مهندسی)

This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws. Front Page......Page 1 Stochastic Models, Estimation, and Control......Page 4 Copyright Page......Page 5 Contents......Page 8 Preface......Page 12 Notation......Page 14 8.1 Introduction......Page 18 8.2 Basic Structure......Page 19 8.3 Three Classes of Smoothing Problems......Page 20 8.4 Fixed-Interval Smoothing......Page 22 8.5 Fixed-Point Smoothing......Page 32 8.6 Fixed-Lag Smoothing......Page 33 8.7 Summary......Page 34 References......Page 35 Problems......Page 36 9.1 Introduction......Page 40 9.2 Pseudonoise Addition and Artificial Lower Bounding of P......Page 41 9.3 Limiting Effective Filter Memory and Overweighting Most Recent Data......Page 45 9.4 Finite Memory Filtering......Page 50 9.5 Linearized and Extended Kalman Filters......Page 56 References......Page 76 Problems......Page 79 10.1 Introduction......Page 85 10.2 Problem Formulation......Page 87 10.3 Uncertainties in Φ and Bd: Lkelihood Equations......Page 91 10.4 Uncertainties in Φ and Bd : Full-Scale Estimator......Page 97 10.5 Uncertainties in Φ and Bd : Performance Analysis......Page 113 10.6 Uncertainties in Φ and Bd : Attaining Online Applicability......Page 118 10.7 Uncertainties in Qd and R......Page 137 10.8 Bayesian and Multiple Model Filtering Algorithms......Page 146 10.9 Correlation Methods for Self-Tuning: Residual "Whitening"......Page 153 10.10 Covariance Matching and Other Techniques......Page 158 10.11 Summary......Page 160 References......Page 161 Problems......Page 168 11.1 Introduction......Page 176 11.2 Extensions of Linear System Modeling......Page 177 11.3 Markov Process Fundamentals......Page 184 11.4 Itô Stochastic Integrals and Differentials......Page 192 11.5 Itô Stochastic Differential Equations......Page 198 11.6 Forward Kolmogorov Equation......Page 209 References......Page 219 Problems......Page 222 12.1 Introduction......Page 229 12.2 Nonlinear Filtering with Discrete-Time Measurements: Conceptually......Page 230 12.3 Conditional Moment Estimators......Page 232 12.4 Conditional Quasi-Moments and Hermite Polynomial Series......Page 256 12.5 Conditional Mode Estimators......Page 258 12.6 Statistically Linearized Filter......Page 260 12.7 Nonlinear Filtering with Continuous-Time Measurements......Page 262 12.8 Summary......Page 274 References......Page 276 Problems......Page 282 Index......Page 290