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Dynamic Systems Models: New Methods of Parameter and State Estimation 1st ed. 2016 [Kõva köide]

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  • Formaat: Hardback, 201 pages, kõrgus x laius: 235x155 mm, kaal: 4616 g, XX, 201 p., 1 Hardback
  • Ilmumisaeg: 30-Mar-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319040359
  • ISBN-13: 9783319040356
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Dynamic Systems Models: New Methods of Parameter and State Estimation 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 201 pages, kõrgus x laius: 235x155 mm, kaal: 4616 g, XX, 201 p., 1 Hardback
  • Ilmumisaeg: 30-Mar-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319040359
  • ISBN-13: 9783319040356
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319040356.html
Märksõnad:
This book demonstrates the use of polynomial approximation from the mathematical fundamentals, through algorithm development to practical applications such as aeroplane flight dynamics or biological sequence analysis. Includes illustrative worked examples.

This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics.
Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated.
The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included.
Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.
1 Linear Estimators of a Random Parameter Vector
1(18)
1.1 Linear Estimator, Optimal in the Root-Mean-Square Sense
1(5)
1.2 Vector Measure of Nonlinearity of Vector Y1 in Relation to Vector θ
6(1)
1.3 Decomposition of Path of Observations to the Recurrence Algorithm
7(2)
1.4 Recurrent Form of Algorithm for Estimator Vector
9(4)
1.5 Problem of Optimal Linear Filtration
13(3)
1.6 Problem of Linear Optimal Recurrent Interpolation (Problem of Optimal Smoothing)
16(3)
References
18(1)
2 Basis of the Method of Polynomial Approximation
19(10)
2.1 Extension Sets of Observations: The Heuristic Path for Nonlinear Estimation
19(1)
2.2 The Statistical Basis
20(2)
2.3 Polynomial Approximation
22(2)
2.4 Calculating Statistical Moments and Choice of Stochastic Measure
24(3)
2.5 Fragment of Program of Modified Method of Trapezoids
27(2)
Reference
28(1)
3 Polynomial Approximation and Optimization of Control
29(16)
3.1 Introduction
29(1)
3.2 Problem of Polynomial Approximation of a Given Function
30(2)
3.3 Applied Examples
32(3)
3.3.1 Detection of a Polynomial Function
32(1)
3.3.2 Approximation Errors for a State Vector of Dynamic Systems
33(2)
3.4 Polynomial Approximation in Control Optimization Problems
35(3)
3.5 Optimization of Control by a Linear System: Linear and Quadratic Optimality Criteria
38(3)
3.6 Approximate Control Optimization for a Nonlinear Dynamic System
41(1)
3.7 Polynomial Approximation with Random Errors
42(1)
3.8 Identification of a "Black Box"
43(2)
References
44(1)
4 Polynomial Approximation Technique Applied to Inverse Vector-Function
45(26)
4.1 Introduction
45(3)
4.2 The Problem of Polynomial Approximation of an Inverse Vector-Function
48(5)
4.3 A Case Where Multiple Root Vectors Exist Along with Partitioning of the a Priori Domain
53(1)
4.4 Correctness of the Estimator Algorithm and a Way of Taking Random Observation Items into Account
54(2)
4.5 Implementations of the Polynomial Approximation Technique Applied to the Inverse Vector-Function
56(3)
4.6 Numerical Solutions of Underdetermined and Overdetermined Systems of Linear Algebraic Solutions
59(4)
4.7 Solving Simultaneous Equations with Nonlinearities Expressed by Integer Power Series
63(2)
4.8 Solving Simultaneous Equations with Nonlinearities Expressed by Trigonometric Functions, Exponentials, and Functions Including Modulus
65(1)
4.9 Solving a Two-Point Boundary Value Problem for a System of Nonlinear Differential Equations
66(2)
4.10 The System of Algebraic Equations with Complex-Valued Roots
68(3)
References
70(1)
5 Identification of Parameters of Nonlinear Dynamic Systems; Smoothing, Filtration, Forecasting of State Vectors
71(38)
5.1 Problem Statement
71(3)
5.2 Heuristic Schemes of a Simple Search and an Organized Search
74(1)
5.3 Mathematical Model to Test Algorithms
75(2)
5.4 Organized Search with the MATLAB Function ƒmins
77(2)
5.5 System of Implicit Algebraic Equations
79(1)
5.6 Contraction Operator
80(4)
5.7 Computational Scheme of Organized Search in Bayes Interpretation
84(4)
5.8 Smoothing, Filtration, and Forecasting (SFF) by Observations in Noise for a Nonlinear Dynamic System
88(14)
5.8.1 Mathematical Model of Dynamic System and Observations
89(1)
5.8.2 Conceptual Algorithm for Smoothing, Filtration, and Forecasting (SFF Algorithm)
90(2)
5.8.3 Qualitative Comparison of SFF Algorithm and PφK Algorithm
92(2)
5.8.4 Recurrent form of the SFF (RSFF) Algorithm
94(2)
5.8.5 About Computation of a Priori First and Second Statistical Moments
96(1)
5.8.6 Evaluation of the Initial Conditions and Parameter of the Van der Pol Equation
97(1)
5.8.7 Smoothing and Filtration for a Model of a Two-Level Integrator with Nonlinear Feedback
98(2)
5.8.8 The Solution of a Problem of a Filtration by the EKF Algorithm
100(1)
5.8.9 Identification of Velocity Characteristic of the Integrator and of the Nonlinearity of the Type "Backlash"
100(2)
5.9 A Servo-System with a Relay Drive and Hysteresis Loop
102(1)
5.10 Evaluation of Principal Moments of Inertia of a Solid
103(2)
5.11 Nonlinear Filtration at Bounded Memory of Algorithm
105(4)
References
108(1)
6 Estimating Status Vectors from Sight Angles
109(16)
6.1 Space Object Status Vector Evaluation
109(6)
6.1.1 Equations of Motion and Observation Data Model
110(1)
6.1.2 Scheme of Estimator
110(3)
6.1.3 Model Predictions
113(2)
6.2 Estimation of the Air- and Space-Craft Status Vector, Local Vertical Orientation Angles, and AC-Borne Sighting System Adjustment
115(10)
6.2.1 Primary Navigation Errors and Formulation of the Problem
117(2)
6.2.2 Navigation Parameters: The Nonlinear Estimation Problem
119(2)
6.2.3 Calculation Model and Estimation Results
121(2)
References
123(2)
7 Estimating the Parameters of Stochastic Models
125(44)
7.1 Introduction
125(3)
7.2 The Basic Structure of the Algorithm-Estimator
128(1)
7.3 Statistics and Empirical Frequencies
129(1)
7.4 The Law of Large Numbers
130(5)
7.5 A Bayesian Statistical Construction
135(1)
7.6 Estimating Hidden Markov Model Parameters by the Algorithm-Estimator
136(4)
7.7 Introduction
140(8)
7.7.1 Maximum Likelihood Method of Observing Instants of Direct Transitions
141(2)
7.7.2 Algorithm of Estimating Observation States in Instants of Indirect Transitions
143(2)
7.7.3 A Numerical Example
145(3)
7.8 Introduction and Statement of the Problem
148(8)
7.8.1 Basic Scheme of the Proposed Nonlinear Filtration Algorithm
150(4)
7.8.2 Effective Work of Nonlinear Filtration Algorithm at Estimating States of a Nominal Model Markov Random Process if Random Observation Errors are Large and Uniformly Distributed in [ --100, 100]
154(2)
7.9 Introduction
156(2)
7.10 Fundamentals of the Method
158(4)
7.11 Parameter Estimation for a Nonlinear STGARCH Model
162(2)
7.12 Parameter Estimation for a Multivariate MGARCH Model
164(2)
7.13 Conclusions
166(3)
References
167(2)
8 Designing Motion Control to a Target Point of Phase Space
169(18)
8.1 Introduction
169(1)
8.2 Setting Boundary Value Problems and Problem-Solving Procedures
170(3)
8.3 Necessary and Sufficient Conditions for Time-Optimal Control
173(3)
8.4 The Stages of the Calculation Process
176(1)
8.5 Near-Circular Orbit Correction in Minimum Practicable Time Using Micro-Thrust Operation of Two Engines
177(5)
8.6 Correcting the Near-Circular Orbit and Position of the Earth Satellite Vehicle in Minimum Practicable Time Using Micro-Thrust Operation of Two Engines
182(5)
References
186(1)
9 Inverse Problem of Dynamics: The Algorithm for Identifying the Parameters of an Aircraft
187(14)
9.1 Introduction
187(2)
9.2 Statement of the Problem and Basic Scheme of the Identification Algorithm
189(4)
9.3 Identification of Aerodynamic Coefficients of the Pitching Motion for a Pseudo F-16 Aircraft
193(7)
9.3.1 Pitching Motion Equations
194(4)
9.3.2 Parametric Model of Aerodynamic Forces and Moments
198(1)
9.3.3 Transient Processes of Characteristics of Nominal Motions
199(1)
9.3.4 Estimating Identification Accuracy of 48 Errors of Aerodynamic Parameters of the Aircraft
200(1)
9.4 Conclusions
200(1)
References 201