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E-grāmata: Robust Controllability of Linear Systems

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  • Formāts: 206 pages
  • Izdošanas datums: 01-Jun-2013
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-13: 9781621001959
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Robust Controllability of Linear SystemsPalielināt
  • Formāts: 206 pages
  • Izdošanas datums: 01-Jun-2013
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-13: 9781621001959
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Controllability, i.e. the ability of a dynamic system to be transferred from a given set of initial positions to a given target set by a proper choice of the control function, is one of the basic system properties. Controllability has been well studied for systems without uncertainties by using an open-loop control. Unfortunately, this elegant theory is not applicable to real-life systems which are affected by unmeasurable components. For such systems, the controllability should be augmented by a robustness property with respect to any admissible uncertainty realization. As a rule, the robust controllability is realized by a feedback control. This book presents current research in the study of robust controllability of linear systems.
Introduction xi
1 Robust Controllability for Non-Uniformly Bounded Controls and Disturbances
1(26)
1.1 Introduction
1(1)
1.2 Main Notions
1(6)
1.2.1 Definition
1(2)
1.2.2 Scalarization
3(4)
1.3 Linear Robust Transferring Strategies
7(13)
1.3.1 Necessary and Sufficien Conditions
7(6)
1.3.2 Class of Linear Robust Transferring Strategies
13(3)
1.3.3 Robust Controllability in a Pursuit Problem
16(4)
1.4 Concluding Remarks and Literature Review
20(1)
1.5 Exercises
21(1)
1.6 Appendix: Proofs
22(5)
1.6.1 Proof of Lemma 1.4
22(2)
1.6.2 Proof of Lemma 1.5
24(1)
1.6.3 Proof of Lemma 1.6
25(2)
2 Robust Controllability for Uniformly Bounded Controls and Disturbances
27(56)
2.1 Introduction
27(1)
2.2 Preliminary Discussion and Problem Statement
27(3)
2.3 Robust Controllability Set of Linear Transferring Strategy
30(41)
2.3.1 Definition
30(7)
2.3.2 Existence and General Analytical Description
37(3)
2.3.3 Set-Theoretical Properties
40(2)
2.3.4 Boundary Structure
42(29)
2.3.5 Boundary Smoothness Properties
71(1)
2.4 Pursuit Problem
71(2)
2.5 Concluding Remarks and Literature Review
73(2)
2.6 Exercises
75(1)
2.7 Appendix: Proofs
76(7)
2.7.1 Proof of Lemma 2.4
76(1)
2.7.2 Proof of Lemma 2.5
77(1)
2.7.3 Proof of Lemma 2.6
78(1)
2.7.4 Proof of Theorem 2.7
78(1)
2.7.5 Proof of Theorem 2.8
79(1)
2.7.6 Proof of Theorem 2.9
80(3)
3 Saturated Linear Transferring Strategies
83(56)
3.1 Introduction
83(1)
3.2 Defnition and Examples
83(8)
3.3 Analysis and Construction of Czsat
91(36)
3.3.1 Set-theoretical Properties of Czsat
91(1)
3.3.2 Boundary Structure
91(5)
3.3.3 One Important Inclusion
96(10)
3.3.4 Limit Cases
106(5)
3.3.5 Non-Emptiness of Czsat(K(.))
111(8)
3.3.6 Procedure of Constructing Czsat
119(8)
3.4 Pursuit Problem
127(2)
3.5 Concluding Remarks and Literature Review
129(1)
3.6 Exercises
130(1)
3.7 Appendix: Proofs
131(8)
3.7.1 Proof of Theorem 3.1
131(3)
3.7.2 Proof of Theorem 3.2
134(1)
3.7.3 Proof of Lemma 3.1 (by contradiction)
135(1)
3.7.4 Proof of Theorem 3.6
136(3)
4 Inverse Problem for Robust Controllability Set Construction
139(44)
4.1 Introduction
139(1)
4.2 Inverse Problem Formulation and Examples
140(9)
4.2.1 Problem Formulation
140(2)
4.2.2 Examples
142(7)
4.3 Necessary Conditions for the Controllability Set Boundary
149(3)
4.4 Algorithm of the Strong Inverse Problem Solution
152(8)
4.5 Solution of the Weak Inverse Problem
160(6)
4.6 Inverse Pursuit Problem
166(6)
4.6.1 Using Algorithm 4.1
166(5)
4.6.2 Using Algorithm 4.2
171(1)
4.7 Concluding Remarks and Literature Review
172(1)
4.8 Exercises
173(1)
4.9 Appendix: Proofs
174(9)
4.9.1 Proof of Lemma 4.2
174(2)
4.9.2 Proof of Lemma 4.3
176(1)
4.9.3 Proof of Lemma 4.4
177(2)
4.9.4 Proof of Lemma 4.5
179(2)
4.9.5 Proof of Lemma 4.6
181(2)
5 Answers and Hints to Exercises
183(4)
5.1
Chapter I
183(1)
5.2
Chapter II
184(1)
5.3
Chapter III
185(1)
5.4
Chapter IV
185(2)
Main Notations 187(2)
References 189(4)
Index 193
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