Optimal Control and Estimation

by Stengel, Robert F.

• ISBN13: 9780486682006
• ISBN10: 0486682005
• eBook ISBN(s): 9780486134819
• Edition: Revised
• Format: Paperback
• Copyright: 1994-09-20
• Publisher: Dover Publications
• More Book Details
• Purchase Benefits

Summary

Graduate-level text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems.

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