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Estimators for Uncertain Dynamic Systems
When solving the control and design problems in aerospace and naval engi­ neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from measurement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti­ mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple­ mentation. For example, the dimension of these algorithms can be very high.
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Estimators for Uncertain Dynamic Systems
When solving the control and design problems in aerospace and naval engi­ neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from measurement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti­ mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple­ mentation. For example, the dimension of these algorithms can be very high.
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Estimators for Uncertain Dynamic Systems

Estimators for Uncertain Dynamic Systems

by A.I. Matasov
Estimators for Uncertain Dynamic Systems

Estimators for Uncertain Dynamic Systems

by A.I. Matasov

Overview

When solving the control and design problems in aerospace and naval engi­ neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from measurement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The type and complexity of these variational problems depend on the process model, the model of uncertainties, and the estimation performance criterion. A solution of variational problem determines an optimal estimator. Howerever, there exist at least two reasons why we use nonoptimal esti­ mators. The first reason is that the numerical algorithms for solving the corresponding variational problems can be very difficult for numerical imple­ mentation. For example, the dimension of these algorithms can be very high.

Product Details

ISBN-13: 9789401062367
Publisher: Springer Netherlands
Publication date: 10/06/2012
Series: Mathematics and Its Applications , #458
Edition description: Softcover reprint of the original 1st ed. 1998
Pages: 420
Product dimensions: 6.30(w) x 9.45(h) x 0.04(d)

Table of Contents

1. Guaranteed Parameter Estimation.- 1. Simplest Guaranteed Estimation Problem.- 2. Continuous Measurement Case.- 3. Linear Programming.- 4. Necessary and Sufficient Conditions for Optimality.- 5. Dual Problem and Chebyshev Approximation.- 6. Combined Model for Measurement Noise.- 7. Least-Squares Method in Guaranteed Parameter Estimation.- 8. Guaranteed Estimation with Anomalous Measurement Errors.- 9. Comments to Chapter 1.- 10. Excercises to Chapter 1.- 2. Guaranteed Estimation in Dynamic Systems.- 1. Lagrange Principle and Duality.- 2. Uncertain Deterministic Disturbances.- 3. Conditions for Optimality of Estimator.- 4. Computation of Estimators.- 5. Optimality of Linear Estimators.- 6. Phase Constraints in Guaranteed Estimation Problem.- 7. Comments to Chapter 2.- 8. Excercises to Chapter 2.- 3. Kalman Filter in Guaranteed Estimation Problem.- 1. Level of Nonoptimality for Kaiman Filter.- 2. Bound for the Level of Nonoptimality.- 3. Derivation of Main Result.- 4. Kaiman Filter with Discrete Measurements.- 5. Proofs for the Case of Discrete Measurements.- 6. Examples for the Bounds of Nonoptimality Levels.- 7. Comments to Chapter 3.- 8. Excercises to Chapter 3.- 4. Shastic Guaranteed Estimation Problem.- 1. Optimal Shastic Guaranteed Estimation Problem.- 2. Approximating Problem. Bound for the Level of Nonoptimality.- 3. Derivation of Main Result for Shastic Problem.- 4. Discrete Measurements in Shastic Estimation Problem.- 5. Examples for Shastic Problems.- 6. Kaiman Filter under Uncertainty in Intensities of Noises.- 7. Comments to Chapter 4.- 8. Excercises to Chapter 4.- 5. Estimation Problems in Systems with Aftereffect.- 1. Pseudo-Fundamental Matrix and Cauchy Formula.- 2. Guaranteed Estimation in Dynamic Systems with Delay.- 3. Level of Nonoptimality in Shastic Problem.- 4. Simplified Algorithms for Mean-Square Filtering Problem.- 5. Control Algorithms for Systems with Aftereffect.- 6. Reduced Algorithms for Systems with Weakly Connected Blocks.- 7. Comments to Chapter 5.- 8. Excercises to Chapter 5.
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