Author | Davis, Jon H. author |
---|---|
Title | Foundations of Deterministic and Stochastic Control [electronic resource] / by Jon H. Davis |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0071-0 |
Descript | XIV, 426 p. online resource |
1 State Space Realizations -- 1.1 Linear Models -- 1.2 Realizations -- 1.3 Constructing Time Invariant Realizations -- 1.4 An Active Suspension Model -- 1.5 A Model Identification Problem -- 1.6 Simulating Recursive Identification -- 1.7 Discrete Time Models -- Problems -- 2 Least Squares Control -- 2.1 Minimum Energy Transfers -- 2.2 The Output Regulator -- 2.3 Linear Regulator Tracking Problems -- 2.4 Dynamic Programming -- Problems -- 3 Stability Theory -- 3.1 Introduction -- 3.2 Introduction to Lyapunov Theory -- 3.3 Definitions -- 3.4 Classical Lyapunov Theorems -- 3.5 The Invariance Approach -- 3.6 Input-Output Stability -- Problems -- 4 Random Variables and Processes -- 4.1 Introduction -- 4.2 Random Variables -- 4.3 Sample Spaces and Probabilities -- 4.4 Densities -- 4.5 Expectations, Inner Products and Variances -- 4.6 Linear Minimum Variance Estimates -- 4.7 Gramians and Covariance Matrices -- 4.8 Random Processes -- 4.9 Gaussian Variables -- Problems -- 5 Kalman-Bucy Filters -- 5.1 The Model -- 5.2 Estimation Criterion -- 5.3 The One Step Predictor -- Problems -- 6 Continuous Time Models -- 6.1 Introduction -- 6.2 Stochastic Integrals -- 6.3 Stochastic Differential Equations -- 6.4 Linear Models -- 6.5 Second Order Results -- 6.6 Continuous White Noise -- 6.7 Continuous Time Kalman-Bucy Filters -- Problems -- 7 The Separation Theorem -- 7.1 Stochastic Dynamic Programming -- 7.2 Dynamic Programming Algorithm -- 7.3 Discrete Time Stochastic Regulator -- 7.4 Continuous Time -- 7.5 The Time Invariant Case -- 7.6 Active Suspension -- Problems -- 8 Luenberger Observers -- 8.1 Full State Observers -- 8.2 Reduced Order Observers -- Problems -- 9 Nonlinear and Finite State Problems -- 9.1 Introduction -- 9.2 Finite State Machines -- 9.3 Finite Markov Processes -- 9.4 Hidden Markov Models -- Problems -- 10 Wiener-Hopf Methods -- 10.1 Wiener Filters -- 10.2 Spectral Factorization -- 10.3 The Scalar Case - Spectral Factorization -- 10.4 Discrete Time Factorization -- 10.5 Factorization in The Vector Case -- 10.6 Finite Dimensional Symmetric Problems -- 10.7 Spectral Factors and Optimal Gains -- 10.8 Linear Regulators and The Projection Theorem -- Problems -- 11 Distributed System Regulators -- 11.1 Open Loop Unstable Distributed Regulators -- 11.2 The โWiener-Hopfโ Condition -- 11.3 Optimal Feedback Gains -- 11.4 Matched Filter Evasion -- Problems -- 12 Filters Without Riccati Equations -- 12.1 Introduction -- 12.2 Basic Problem Formulation -- 12.3 Spectral Factors -- 12.4 Closed Loop Stability -- 12.5 Realizing The Optimal Filter -- Problems -- 13 Newtonโs Method for Riccati Equations -- 13.1 Newtonโs Method -- 13.2 Continuous Time Riccati Equations -- 13.3 Discrete Time Riccati Equations -- 13.4 Convergence of Newtonโs Method -- 14 Numerical Spectral Factorization -- 14.1 Introduction -- 14.2 An Intuitive Algorithm Derivation -- 14.3 A Convergence Proof for the Continuous Time Algorithm -- 14.4 Implementation -- 14.5 The Discrete Case -- 14.6 Numerical Comments -- A Hilbert and Banach Spaces and Operators -- A.1 Banach and Hilbert Spaces -- A.2 Quotient Spaces -- A.3 Dual Spaces -- A.4 Bounded Linear Operators -- A.5 Induced Norms -- A.6 The Banach Space G(X, Y) -- A.7 Adjoint Mappings -- A.8 Orthogonal Complements -- A.9 Projection Theorem -- A.10 Abstract Linear Equations -- A.11 Linear Equations and Adjoints -- A.12 Minimum Miss Distance Problems -- A.13 Minimum Norm Problems -- A.14 Fredholm Operators -- A.15 Banach Algebras -- A.15.1 Inverses and Spectra -- A.15.2 Ideals, Transforms, and Spectra -- A.15.3 Functional Calculus -- B Measure Theoretic Probability -- B.1 Measure Theory -- B.2 Random variables -- B.3 Integrals and Expectation -- B.4 Derivatives and Densities -- B.5 Conditional Probabilities and Expectations -- B.5.1 Conditional Probability -- B.5.2 Conditional Expectations -- References