Promotional Information

Springer Book Archives

Table of Contents

1 Probability Theory Preliminaries.- 1.1 Random Variables.- 1.2 Expectation.- 1.3 Conditional Expectation.- 1.4 Independence, Characteristic Functions.- 1.5 Random Processes.- 1.6 Stochastic Integral.- 1.7 Stochastic Differential Equations.- 2 Limit Theorems on Martingales.- 2.1 Martingale Convergence Theorems.- 2.2 Local Convergence Theorems.- 2.3 Estimation for Weighted Sums of a Martingale Difference Sequence.- 2.4 Estimation for Double Array Martingales.- 3 Filtering and Control for Linear Systems.- 3.1 Controllability and Observability.- 3.2 Kalman Filtering for Systems with Random Coefficients.- 3.3 Discrete-Time Riccati Equations.- 3.4 Optimal Control for Quadratic Costs.- 3.5 Optimal Tracking.- 3.6 Model Reference Control.- 3.7 Control for CARIMA Models.- 4 Coefficient Estimation for ARMAX Models.- 4.1 Estimation Algorithms.- 4.2 Convergence of ELS Without the PE Condition.- 4.3 Local Convergence of SG.- 4.4 Convergence of SG Without the PE Condition.- 4.5 Convergence Rate of SG.- 4.6 Removing the SPR Condition By An Overparameterization Technique.- 4.7 Removing the SPR Condition By Using Increasing Lag Least Squares.- 5 Stochastic Adaptive Tracking.- 5.1 SG-Based Adaptive Tracker With d = 1.- 5.2 SG-Based Adaptive Tracker With d ?1.- 5.3 Stability and Optimality of Åström-Wittenmark Self-Tuning Tracker.- 5.4 Stability and Optimality of ELS-Based Adaptive Trackers.- 5.5 Model Reference Adaptive Control.- 6 Coefficient Estimation in Adaptive Control Systems.- 6.1 Necessity of Excitation for Consistency of Estimates.- 6.2 Reference Signal With Decaying Richness.- 6.3 Diminishingly Excited Control.- 7 Order Estimation.- 7.1 Order Estimation by Use of a Priori Information.- 7.2 Order Estimation by not Using Upper Bounds for Orders.- 7.3 Time-Delay Estimation.-7.4 Connections of CIC and BIC.- 8 Optimal Adaptive Control with Consistent Parameter Estimate.- 8.1 Simultaneously Gaining Optimality and Consistency in Tracking Systems.- 8.2 Adaptive Control for Quadratic Cost.- 8.3 Connection Between Adaptive Controls for Tracking and Quadratic Cost.- 8.4 Model Reference Adaptive Control With Consistent Estimate.- 8.5 Adaptive Control With Unknown Orders, Time-Delay and Coefficients.- 9 ARX(?) Model Approximation.- 9.1 Statement of Problem.- 9.2 Transfer Function Approximation.- 9.3 Estimation of Noise Process.- 10 Estimation for Time-Varying Parameters.- 10.1 Stability of Random Time-Varying Equations.- 10.2 Conditional Richness Condition.- 10.3 Analysis of Kalman Filter Based Algorithms.- 10.4 Analysis of LMS-Like Algorithms.- 11 Adaptive Control of Time-Varying Stochastic Systems.- 11.1 Preliminary Results.- 11.2 Systems with Random Parameters.- 11.3 Systems with Deterministic Parameters.- 12 Continuous-Time Stochastic Systems.- 12.1 The Model.- 12.2 Parameter Estimation.- 12.3 Adaptive Control.- References.