Time-Lag Control Systems

Name: Time-Lag Control Systems
Brand: Academic Press
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Oguztoreli(Autor*in)

Og?uzto?reli(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

337 Seiten

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Front Cover
Time-Lag Control Systems
Copyright Page
Contents
Preface
PART I: Ordinary Delay-Differential Equations
Chapter I. Introduction
1.1. DYNAMIC CHARACTERIZATION OF A PHYSICAL SYSTEM INVOLVING TIME DELAY
1.2. EXAMPLES OF DELAY-DIFFERENTIAL EQUATIONS
1.3. HISTORICAL SKETCH
Chapter II. Delay-Differential Equations
2.1. INTRODUCTION
2.2. NOTATION AND DEFINITIONS
2.3. ADVANCE IN INITIAL INSTANT
2.4. e-APPROXIMATE SOLUTIONS
2.5. UNIQUENESS OF SOLUTIONS OF A DELAY-DIFFERENTIAL EQUATION
2.6. EXISTENCE THEOREMS
2.7. CONSTRUCTION OF SOLUTIONS: I. EULER'S POLYGONAL METHOD
2.8. CONSTRUCTION OF SOLUTIONS: II. PICARD'S SUCCESSIVE APPROXIMATIONS
2.9. DEPENDENCE OF SOLUTIONS ON THE INITIAL DATA
2.10. DEPENDENCE OF SOLUTIONS UPON PARAMETERS
2.11. DEPENDENCE OF SOLUTIONS ON THE RIGHT-HAND SIDE OF THE EQUATION
2.12. GRONWALL'S LEMMA
2.13. DIFFERENTIABILITY PROPERTIES OF FUNCTIONALS
2.14. DIFFERENTIABILITY PROPERTIES OF SOLUTIONS WITH RESPECT TO PARAMETERS
2.15. ANALYTICITY PROPERTIES OF SOLUTIONS
2.16. FIRST VARIATION OF A SOLUTION WITH RESPECT TO AN INITIAL FUNCTION
2.17. DIFFERENTIATION WITH RESPECT TO THE INITIAL MOMENT
2.18. DELAY-DIFFERENTIAL EQUATIONS WITH MEASURABLE RIGHT-HAND SIDES
2.19. BOUNDEDNFSS AND STABILITY: I. AUXILIARY THEOREMS
2.20. BOUNDEDNESS AND STABILITY: II. DEFINITIONS
2.21. BOUNDEDNESS AND STABILITY: III. THEOREMS
2.22. PERTURBED SYSTEMS
2.23. SYSTEMS WITH FINITE HEREDITY
2.24. FINAL REMARKS
Chapter III. Linear Delay-Differential Equations
3.1. GENERAL FORM OF A LINEAR DELAY-DIFFERENTIAL EQUATION
3.2. PRINCIPLE OF CLOSED CYCLES
3.3. EXISTENCE AND UNIQUENESS OF SOLUTIONS
3.4. GENERAL FORM OF SOLUTIONS
3.5. ADJOINT EQUATIONS OF THE FIRST AND SECOND KIND
3.6. CONSTRUCTION OF KERNEL MATRICES OF THE FIRST AND SECOND KIND
3.7. DEPENDENCE UPON PARAMETERS AND INITIAL DATA
3.8. EQUATIONS OF CLOSED-CYCLE TYPE WITH CONSTANT COEFFICIENTS
3.9. KERNEL MATRIX OF THE FIRST KIND FOR EQUATIONS OF CLOSED-CYCLE TYPE WITH CONSTANT COEFFICIENTS
3.10. KERNEL MATRIX OF THE SECOND KIND FOR EQUATIONS OF CLOSED-CYCLE TYPE WITH CONSTANT COEFFICIENTS
3.11. INTEGRAL EQUATION SATISFIED BY THE KERNEL MATRICES M AND, N
3.12. STABILITY AND BOUNDEDNESS
Chapter IV. Nonlinear Delay-Differential Equations
4.1. APPROXIMATION OF CONTINUOUS FUNCTIONALS BY FUNCTIONAL POLYNOMIALS: THEOREM OF M . FRÉCHET
4.2. APPROXIMATIONS OF SOLUTIONS
4.3. EQUATIONS WHOSE RIGHT-HAND SIDES ARE FUNCTIONAL POLYNOMIALS OF SECOND ORDER
4.4. EQUATIONS WHOSE RIGHT-HAND SIDES ARE FUNCTIONAL POWER SERIES
4.5. SEPARABLE KERNELS: I. EQUATIONS OF SECOND DEGREE
4.6. SEPARABLE KERNELS: II. EQUATIONS WITH ANALYTIC RIGHT-HAND SIDE
4.7. APPROXIMATION OF CONTINUOUS KERNELS BY SEPARABLE KERNELS
4.8. EXTENSION
4.9. BOUNDEDNESS AND STABILITY
Chapter V. Piecewise Continuous Delay-Differential Equations
5.1. INTRODUCTION
5.2. CONTINUATION OF A SOLUTION
5.3. BOUNDEDNESS AND STABILITY
5.4. LIMITS OF THE SOLUTIONS OF (5.1.3) AS THE RETARDATIONS AND THE SWITCHING DELAY APPROACH ZERO
5.5. EXTENSION
Chapter VI. Delay-Differential Equations Depending on Arbitrary Functions
6.1. NOTATION AND DEFINITIONS
6.2. DELAY-DIFFERENTIAL EQUATIONS ON Lp SPACES
6.3. LINEAR EQUATIONS: I. THE FUNCTIONAL V Is LINEAR IN x AND u
6.4. LINEAR EQUATIONS: II. THE FUNCTIONAL V Is LINEAR IN x ONLY
6.5. NONLINEAR EQUATIONS: I. THE FUNCTIONAL V Is QUADRATIC IN x
6.6. NONLINEAR EQUATIONS: II. THE FUNCTIONAL V Is A FUNCTIONAL POWER SERIES IN x
6.7. REMARK
PART II: Optimal Processes with Time Delay
Chapter VII. Formulation of Optimal Problems Involving Time Delay
7.1. DYNAMIC CHARACTERIZATION OF A CONTROL SYSTEM INVOLVING TIME DELAY
7.2. CONSTRAINTS
7.3. PERFORMANCE CRITERIA
7.4. TARGET SETS
7.5. FORMULATION OF AN OPTIMUM PROBLEM INVOLVING TIME DELAY
7.6. REDUCTION OF INTEGRAL CONSTRAINTS
7.7. TERMINAL AND AVERAGING CONTROL PROBLEMS
7.8. THE "BANG-BANG" CONTROLS
7.9. THE TIME-OPTIMAL PROBLEM
7.10. MINIMUM OF MAXIMUM DEVIATION
7.11. PERFORMANCE CRITERIA EXPRESSED BY LEBESGUE-STIELTJES INTEGRALS
7.12. DETERMINISTIC, STOCHASTIC, AND ADAPTIVE CONTROLS
7.13. QUESTIONS RELATED TO THE OPTIMIZATION PROBLEM
7.14. CONVEX SETS
Chapter VIII. Existence of Optimal Pairs
8.1. REDUCTION OF THE ORIGINAL PROBLEM INTO A TERMINAL CONTROL PROBLEM
8.2. ATTAINABLE SETS. NOTATION AND DEFINITIONS
8.3. PROPERTIES OF THE SETS A. THEOREM OF ROXIN
8.4. EXISTENCE OF OPTIMAL PAIRS. THEOREM OF NEUSTADT
8.5. EXTENDED FILIPPOV LEMMA
8.6. THE RANGE OF A VECTOR MEASURE
8.7. EXTENDED "BANG-BANG" PRINCIPLE OF LASALLE
8.8. UNIFORM APPROXIMATION OF SOLUTIONS. THEOREM OF WARGA
8.9. RELAXED PROBLEM. THEOREM OF WARGA
8.10. LINEAR SYSTEMS. THEOREM OF NEUSTADT
Chapter IX. Optimization of Control Systems Involving Time Delay Using Dynamic Programming
9.1. REFORMULATION OF THE OPTIMIZATION PROBLEM
9.2. PRINCIPLE OF OPTIMALITY
9.3. APPLICATION OF FUNCTIONAL EQUATION TECHNIQUE
9.4. FIRST VARIATIONS OF THE FUNCTIONALS G(t, t), Gt'(t, t), AND Ht'(T, t)
9.5. NECFSARY CONDITIONS FOR OPTIMALITY
9.6. THE MATRIX ?(t, t)
9.7. TERMINAL CONTROL: 1
9.8. AVERAGING CONTROLS
9.9. TERMINAL CONTROLS: 2
9.10. PROCESSES WITH QUADRATIC PERFORMANCE INDICES
9.11. OPTIMAL COST
Chapter X. Time Optimal Problem
10.1. FORMULATION OF THE PROBLEM
10.2. REDUCTION OF THE PROBLEM TO AN INTEGRAL EQUATION
10.3. THE FUNCTIONAL O( t, f, u) AND THE SETS ?(t) AND ?0(t)
10.4. PROPERTIES OF O, ?, AND ?0. THEOREMS OF LASALLE
10.5. EXISTENCE OF AN OPTIMAL PAIR
10.6. CONTINUITY OF THE FUNCTIONAL T(f, u)
10.7. FURTHER PROPERTIES OF ?(t) AND OPTIMAL PAIRS
10.8. OPTIMAL CONTROLS. THEOREMS OF LASALLE
10.9. OPTIMAL INITIAL FUNCTIONS
10.10. A NECESSARY CONDITION FOR OPTIMALITY. THEOREM OF NEUSTADT
Chapter XI. Optimal Pursuit Strategy
11.1. FORMULATION OF THE PURSUIT PROBLEM
11.2. THE FUNCTIONALS O(t, f, u), Ø(t, ?, v), AND THE SETS C(t), D(t)
11.3. EXISTENCE OF OPTIMAL STRATEGIES
11.4. PROPERTIES OF OPTIMAL STRATEGIES
11.5. OPTIMAL CONTROLS IN A PARTICULARE
Bibliography
Author Index
Subject Index

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