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Optimal Control and Estimation


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Table of Contents

1. INTRODUCTION 1.1 Framework for Optimal Control 1.2 Modeling Dynamic Systems 1.3 Optimal Control Objectives 1.4 Overview of the Book Problems References 2. THE MATHEMATICS OF CONTROL AND ESTIMATION 2.1 "Scalars, Vectors, and Matrices " Scalars Vectors Matrices Inner and Outer Products "Vector Lengths, Norms, and Weighted Norms " "Stationary, Minimum, and Maximum Points of a Scalar Variable (Ordinary Maxima and Minima) " Constrained Minima and Lagrange Multipliers 2.2 Matrix Properties and Operations Inverse Vector Relationship Matrix Determinant Adjoint Matrix Matrix Inverse Generalized Inverses Transformations Differentiation and Integration Some Matrix Identities Eigenvalues and Eigenvectors Singular Value Decomposition Some Determinant Identities 2.3 Dynamic System Models and Solutions Nonlinear System Equations Local Linearization Numerical Integration of Nonlinear Equasions Numerical Integration of Linear Equations Representation of Data 2.4 "Random Variables, Sequences, and Processes " Scalar Random Variables Groups of Random Variables Scalar Random Sequences and Processes Correlation and Covariance Functions Fourier Series and Integrals Special Density Functions of Random Processes Spectral Functions of Random Sequences Multivariate Statistics 2.5 Properties of Dynamic Systems Static and Quasistatic Equilibrium Stability "Modes of Motion for Linear, Time-Invariant Systems " "Reachability, Controllability, and Stabilizability " "Constructability, Observability, and Detectability " Discrete-Time Systems 2.6 Frequency Domain Modeling and Analysis Root Locus Frequency-Response Function and Bode Plot Nyquist Plot and Stability Criterion Effects of Sampling Problems References 3. OPTIMAL TRAJECTORIES AND NEIGHBORING-OPTIMAL SOLUTIONS 3.1 Statement of the Problem 3.2 Cost Functions 3.3 Parametric Optimization 3.4 Conditions for Optimality Necessary Conditions for Optimality Sufficient Conditions for Optimality The Minimum Principle The Hamiltonn-Jacobi-Bellman Equation 3.5 Constraints and Singular Control Terminal State Equality Constraints Equality Constraints on the State and Control Inequality Constraints on the State and Control Singular Control 3.6 Numerical Optimization Penalty Function Method Dynamic Programming Neighboring Extremal Method Quasilinearization Method Gradient Methods 3.7 Neighboring-Optimal Solutions Continuous Neighboring-Optimal Control Dynamic Programming Solution for Continuous Linear-Quadratic Control Small Disturbances and Parameter Variations Problems References 4. OPTIMAL STATE ESTIMATION 4.1 Least-Squares Estimates of Constant Vectors Least-Squares Estimator Weighted Least-Squares Estimator Recursive Least-Squares Estimator 4.2 Propagation of the State Estimate and Its Uncertainty Discrete- Time Systems Sampled-Data Representation of Continuous-Time Systems Continuous-Time Systems Simulating Cross-Correlated White Noise 4.3 Discrete-Time Optimal Filters and Predictors Kalman Filter Linear-Optimal Predictor Alternative Forms of the Linear-Optimal filter 4.4 Correlated Disturbance Inputs and Measurement Noise Cross-Correlation of Disturbance Input and Measurement Noise Time-Correlated Measurement Noise 4.5 Continuous-Time Optimal Filters and Predictors Kalman-Bucy Filter Duality Linear-Optimal Predictor Alternative Forms of the Linear-Optimal Filter Correlation in Disturbance Inputs and Measurement Noise 4.6 Optimal Nonlinear Estimation Neighboring-Optimal Linear Estimator Extended Kalman-Bucy Filter Quasilinear Filter 4.7 Adaptive Filtering Parameter-Adaptive Filtering Noise-Adaptive Filtering Multiple-Model Estimation Problems References 5. STOCHASTIC OPTIMAL CONTROL 5.1 Nonlinear Systems with Random Inputs and Perfect Measurements Stochastic Principle of Optimality for Nonlinear Systems Stochastic Principle of Optimality for Linear-Quadratic Problems Neighboring-Optimal Control Evaluation of the Variational Cost Function 5.2 Nonlinear Systems with Random Inputs and Imperfect Measurements Stochastic Principle of Optimality Dual Control Neigbboring-Optimal Control 5.3 The Certainty-Equivalence Property of Linear-Quadratic-Gaussian Controllers The Continuous-Time Case The Discrete-Time Case Additional Cases Exhibiting Certainty Equivalence 5.4 "Linear, Time-Invariant Systems with Random Inputs and Imperfect Measurements " Asymptotic Stability of the Linear-Quadratic Regulator Asymptotic Stability of the Kalman-Bucy Filter Asymptotic Stability of the Stochastic Regulator Steady-State Performance of the Stochastic Regulator The Discrete-Time Case Problems References 6. LINEAR MULTIVARIABLE CONTROL 6.1 Solution of the Algeb

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