Author | Bashirov, Agamirza E. author |
---|---|
Title | Partially Observable Linear Systems Under Dependent Noises [electronic resource] / by Agamirza E. Bashirov |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8022-0 |
Descript | XXVI, 338 p. online resource |
1 Basic Elements of Functional Analysis -- 1.1 Sets and Functions -- 1.2 Abstract Spaces -- 1.3 Linear Operators -- 1.4 Weak Convergence -- 2 Basic Concepts of Analysis in Abstract Spaces -- 2.1 Continuity -- 2.2 Differentiability -- 2.3 Measurability -- 2.4 Integrability -- 2.5 Integral and Differential Operators -- 3 Evolution Operators -- 3.1 Main Classes of Evolution Operators -- 3.2 Transformations of Evolution Operators -- 3.3 Operator Riccati Equations -- 3.4 Unbounded Perturbation -- 4 Partially Observable Linear Systems -- 4.1 Random Variables and Processes -- 4.2 Stochastic Modelling of Real Processes -- 4.3 Stochastic Integration in Hilbert Spaces -- 4.4 Partially Observable Linear Systems -- 4.5 Basic Estimation in Hilbert Spaces -- 4.6 Improving the Brownian Motion Model -- 5 Separation Principle -- 5.1 Setting of Control Problem -- 5.2 Separation Principle -- 5.3 Generalization to a Game Problem -- 5.4 Minimizing Sequence -- 5.5 Linear Regulator Problem -- 5.6 Existence of Optimal Control -- 5.7 Concluding Remarks -- 6 ntrol and Estimation under Correlated White Noises -- 6.1 Estimation: Preliminaries -- 6.2 Filtering -- 6.3 Prediction -- 6.4 Smoothing -- 6.5 Stochastic Regulator Problem -- 7 Control and Estimation under Colored Noises -- 7.1 Estimation -- 7.2 Stochastic Regulator Problem -- 8 Control and Estimation under Wide Band Noises -- 8.1 Estimation -- 8.2 More About the Optimal Filter -- 8.3 Stochastic Regulator Problem -- 9 Control and Estimation under Shifted White Noises -- 9.1 Preliminaries -- 9.2 State Noise Delaying Observation Noise: Filtering -- 9.3 State Noise Delaying Observation Noise: Prediction -- 9.4 State Noise Delaying Observation Noise: Smoothing -- 9.5 State Noise Delaying Observation Noise: Stochastic Regulator Prob-lem -- 9.6 Concluding Remarks -- 10 Control and Estimation under Shifted White Noises (Revised) -- 10.1 Preliminaries -- 10.2 Shifted White Noises and Boundary Noises -- 10.3 Convergence of Wide Band Noise Processes -- 10.4 State Noise Delaying Observation Noise -- 10.5 State Noise Anticipating Observation Noise -- 11 Duality -- 11.1 Classical Separation Principle and Duality -- 11.2 Extended Separation Principle and Duality -- 11.3 Innovation Process for Control Actions -- 12 Controllability -- 12.1 Preliminaries -- 12.2 Controllability: Deterministic Systems -- 12.3 Controllability: Stochastic Systems -- Comments -- Bibiography -- Index of Notation