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9780898714111 Academic Inspection Copy

Indefinite Quadratic Estimation and Control

A Unified Approach to H2 and H? Theory
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This monograph presents a unified mathematical framework for a wide range of problems in estimation control. The authors discuss the two most commonly used methodologies: the stochastic "H2" approach and the deterministic (worst-case) "H*" approach. Despite the fundamental differences in the philosophies of these two approaches, the authors have discovered that, if indefinite metric spaces are considered, they can be treated in the same way, and are essentially the same. The benefits and consequences of this unification are pursued in detail, with discussions of how to generalize well-known results from "H2" theory to the "H*" setting, as well as new results and insight, the development of new algorithms, and applications to adaptive signal processing. The book focuses primarily on discrete-time dynamical systems, since these are the systems most important in current applications.
Preface Chapter 1: Introduction and Motivation Chapter 2: Linear Estimation in Krein Spaces Chapter 3: State-Space Models in Krein Space Chapter 4: Finite-Horizon H-Infinity Filtering Chapter 5: Array Algorithms Chapter 6: Several Related Problems Chapter 7: H-Infinity Optimality of the LMS Algorithm Chapter 8: Duality Chapter 9: Finite-Horizon Control Problems Chapter 10: Input-Output Approach to H 2 and H-Infinity Estimation Chapter 11: Input-Output Approach to H 2 and H-Infinity Control Chapter 12: The Discrete-Time Algebraic Riccati Equation Chapter 13: Infinite-Horizon Results for State-Space Models Chapter 14: Asymptotic Behavior Chapter 15: Optimal H-Infinity Solutions Chapter 16: Continuous-Time Results and Final Remarks Bibliography Index.
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