Control and Dynamic Systems
Advances in Theory and Applications
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Control and Dynamic Systems: Advances in Theory and Applications reviews progress in the field of control and dynamic systems theory and applications, with emphasis on filtering and stochastic control in dynamic systems. Topics include linear and nonlinear filtering techniques; concepts and methods in stochastic control; and discrete-time optical stochastic observers. The theory of disturbance-accommodating controllers is also presented. Comprised of nine chapters, this volume begins with an overview of filtering and stochastic control in dynamic systems, followed by a discussion on linear and nonlinear filtering techniques. The reader is then introduced to concepts and methods in stochastic control, as well as the innovations process and its applications to sensitivity analysis and system identification. Subsequent chapters focus on the status of observer theory and its major results as applied to discrete-time linear systems; the properties of the class of discrete-time Riccati equations that arise in the filtering problem; and the theory of disturbance-accommodating controllers. The identification of noise characteristics in a Kalman filter and estimation of adaptive minimum variance in discrete-time linear systems round out the book. This monograph will be useful to practicing technologists and research workers interested in filtering and stochastic control in dynamic systems.
Table of Contents
Contributors
Preface
Contents of Previous Volume
An Overview of Filtering and Stochastic Control in Dynamic Systems
I. General Stochastic Control Problem
A. Definition of the Basic Problem
B. Some Types of Control Policies
II. General Solution of the Optimal Stochastic Control Problem
A. A Recursive Solution of the Control Problem
B. Solving the Nonlinear Filtering Problem
C. Practical Considerations in Determining a Stochastic Control Policy
III. Linear Quadratic Systems and Extensions
A. The linear Recursive FilteringProblem
B. The Optimal,Closed-Loop, Stochastic Control Policy
IV. Summary of Proposed Algorithms
A. Nonlinear Filtering Algorithms
B. Stochastic Control Algorithms
References
Linear and Nonlinear Filtering Techniques
I. Introduction
II. Linear Filtering
III. System Modeling
IV. Suboptimal Filter Design and Sensitivity Analysis
V. Partitioned Filter Approach
VI. Data Prefiltering
VII. Square Root Techniques
VIII. Divergence of the Filter
IX. Nonlinear Filtering
X. Concluding Remarks
References
Concepts and Methods in Stochastic Control
I. Introduction
II. Classes of Stochastic Control Policies and Some Properties of the Control
A. Formulation of the Stochastic Control Problem
B. Classes of Stochastic Control Policies
C. The Dual Effect of the Control, Probing, and Caution
III. Optimal Stochastic Control
IV. The Optimal Control for a Class of Systems
A. The Certainty Equivalence Result and Its Connection with the Dual Effect
B. Discussion and Examples
V. A Stochastic Closed-Loop Control Method for Nonlinear Systems
A. Formulation of the Problem
B. The Algoritiun
C. Simulation Results
VI. A Stochastic Resource Allocation Problem
A. Formulation of the Problem
B. The Algorithm
C. Simulation Results
VII. Conclusions
Appendix A. Proof of the Connection Between the Certainty Equivalence and the Dual Effect
Appendix B. The Closed-Loop Optimization of the Cost-To-Go
References
The Innovations Process with Applications to Identifications
I. Introduction
A. Problem Definition
B. Solution Overview
II. Mathematical Specifications and Background
A. Objectives and Restrictions
B. Method of Approach
III. Sensitivity Analysis
A. The Error Model
B. Behavior of the Error Mean
C. Behavior of the Error Covariance
D. Error Correlation
E. Behavior of the Innovations
F. Summary
IV. System Identification
A. Introduction and Assumptions
B. Limiting Behavior
C. Some Necessary and Sufficient Conditions
D. Some Steady State Considerations
E. Variance and Correlation of Residuals
F. Stochastic Approximation
G. The Partial Derivatives
V. Simulation Results
A. The Boozer Example
B. The Ohap Example
C. Summary
References
Discrete-Time Optical Stochastic Observer
I. Introduction
II. Definition of Discrete Observer for StochasticSystems
III. Construction of a Reduced-Order Observer
IV. An Alternate Reduced-Order Observer Algorithm
V. limiting Cases of the Reduced-Order Observer Solution
A. Minimal-Order Observer
B. Kalman Filter
C. Some Perfect Measurements
VI. Computational Advantages of Reduced Order Observers
VII. An Optimal Continuous-Time Observer Solution
VIII. Concluding Remarks
References
Discrete Riccati Equations: Alternative Algorithms,Asymptotic Properties,and System Theory Interpretations
I. Introduction
II. Square Root Algorithms and the Riccati Equation
A. The Time-Invariant, Zero Terminal, Cost Problem
B. The General Time-Variable Problem
C. Square Root Algorithms 33
D. Structure Algorithms
E. Equivalent Optimization Problems
III. System Structure
A. Observability
B. Invertibility and Detectability
C. Matrix Characterizations
IV. Singular Riccati Equations
A. Asymptotic Properties
B. Reduced Order Riccati Equations
References
Theory of Disturbance-Accommodating Controllers
I. Introduction
II. The Waveform-Mode Description of Realistic Disturbances
III. The Waveform-Mode Characterization Versus the Statistical Characterization
IV. State Models for Disturbances with Waveform Structure
A. Some Examples of State Models for Common Disturbances
B. Waveform Description of Unfamiliar Disturbances
C. "Unfamiliar Disturbances" Arising from Modeling Errors in System Parameters
D. Waveform Description of State-Dependent Disturbances
E. Waveform Description with Linear State Models
F. Experimental Determination of Linear State Models for Disturbances
G. Noise Combined with Disturbances Having Waveform Structure
H. Disturbance Waveform Models Equations (39) and (40) Versus Coloring Filters for White Noise
V. Design of Disturbance-Accommodating Controllers for Stabilization, Regulation, and Servo Tracking Control Problems
A. The Class of Systems and Disturbances to Be Considered
B. Practical Constraints on the Structure of Disturbance-Accommodating Controllers
C. Description of the Stabilization, Regulation and Servo-Tracking Control Problems
D. Philosophies of Disturbance Accommodation in Control Problems
E. The Notion of State Constructors (Observers) for Signals with Waveform Structure
F. Design of Disturbance-Absorbing Controllers
G. Design of Disturbance-Minimization Controllers
H. Design of Disturbance-Utilization Controllers
I. Design of Multimode Disturbance-Accommodating Controllers
J. Transfer Function Interpretation of Disturbance-Accommodating Controllers
VI. Conclusions
References
Appendix
Identification of the Noise Characteristics in a Kaiman Filter
I. Introduction
A. Background
B. Outline
II. System Description
III. Moment System Formulation
A. Mean State Model
B. Mean Measurement Model
C. Mean System Statistics
D. Covariance State Model
E. Covariance Measurement Model
F. Covariance System Statistics
IV. Estimates of the Moments
A. Estimates of the Means
B. Estimates of the Covariance Parameters
C. Adaptive Estimates of Both Moments
D. Comparison of Adaptive Techniques
V. Correlated Moment System Measurement Noise
A. Nonwhite Moment System Measurement Noise
B. Weighted Least Squares Estimates for No System State Noise
C. Linear Minimum Variance Estimates for No System State Noise
D. Weighted Leasted Squares Estimates for the General Case
VI. Conclusions
References
Appendix A
Appendix B
Appendix C
Adaptive Minimum VarianceEstimationin Discrete-Time LinearSystems
I. Introduction
II. Adaptive Filter Algorithm
III. Hypothesis Test for Time Correlation of Residuals
IV. Summary of the Adaptive Algorithm
V. Convergence of Algorithm
VI. Example
A. Description of System
B. Determination of Adaptive Filter Parameters
C. Step Size Control
D. Practical Considerations
E. Results of ComputerSimulation
VII. Conclusions
Appendix
References
Subject Index
Product details
- No. of pages: 648
- Language: English
- Copyright: © Academic Press 1976
- Published: March 28, 1976
- Imprint: Academic Press
- eBook ISBN: 9781483191249