Domain Of Attraction

Domain Of Attraction Addresses The Estimation And Control Of The Domain Of Attraction Of Equilibrium Points Via Sos Programming. The Volume Offers A Unified Framework To Address These Issues In Various Cases, Which Are Tailored To The Nature Of The Nonlinear Systems Involved.

Titel:	Domain Of Attraction
Auteur:	Chesi, Graziano
Mediatype:	Boek
Bindwijze:	Paperback
Taal:	Engels
Aantal pagina's:	306
Uitgever:	Springer London Ltd
Plaats van publicatie:	03
NUR:	Bedrijfsinformatietechnologie
Afmetingen:	234 x 156 x 16
Gewicht:	432 gr
ISBN/ISBN13:	9780857299581
Intern nummer:	18167442

Notation

xv

Abbreviations

xvii

Part I SOS Programming

1

(86)

1 SOS Polynomials

3

(42)

1.1 Polynomials and Power Vectors

3

(5)

1.1.1 General Case

4

(2)

1.1.2 Special Cases

6

(2)

1.2 SMR

8

(6)

1.2.1 General Case

8

(4)

1.2.2 Special Cases

12

(2)

1.3 SOS Polynomials

14

(8)

1.3.1 General Case

14

(5)

1.3.2 Special Cases

19

(3)

1.4 SOS Parameter-Dependent Polynomials and SOS Matrix Polynomials

22

(8)

1.4.1 SOS Parameter-Dependent Polynomials: General Case

22

(3)

1.4.2 SOS Parameter-Dependent Polynomials: Special Cases

25

(2)

1.4.3 SOS Matrix Polynomials

27

(3)

1.5 Extracting Power Vectors from Linear Subspaces

30

(11)

1.5.1 General Case

30

(6)

1.5.2 Special Cases

36

(5)

1.6 Gap between Positive Polynomials and SOS Polynomials

41

(2)

1.7 Notes and References

43

(2)

2 Optimization with SOS Polynomials

45

(42)

2.1 Unconstrained Optimization

46

(15)

2.1.1 Positivity and Non-positivity: General Case

46

(6)

2.1.2 Positivity and Non-positivity: Special Cases

52

(5)

2.1.3 Minimum of Rational Functions

57

(4)

2.2 Constrained Optimization

61

(15)

2.2.1 Positivstellensatz

62

(1)

2.2.2 Minimum of Rational Functions

63

(3)

2.2.3 Solving Systems of Polynomial Equations and Inequalities

66

(7)

2.2.4 Positivity of Matrix Polynomials

73

(3)

2.3 Optimization over Special Sets

76

(7)

2.3.1 Positivity over Ellipoids

76

(4)

2.3.2 Positivity over the Simplex

80

(3)

2.4 Rank Constrained SMR Matrices of SOS Polynomials

83

(1)

2.5 Notes and References

84

(3)

Part II Domain of Attraction

87

(178)

3 Dynamical Systems Background

89

(16)

3.1 Equilibrium Points of Nonlinear Systems

89

(2)

3.2 Stability

91

(2)

3.3 DA

93

(2)

3.4 Controlled Systems

95

(1)

3.5 Common Equilibrium Points of Uncertain Nonlinear Systems

96

(1)

3.6 Robust Stability

97

(3)

3.7 RDA

100

(2)

3.8 Robustly Controlled Systems

102

(1)

3.9 Notes and References

103

(2)

4 DA in Polynomial Systems

105

(46)

4.1 Polynomial Systems

105

(3)

4.2 Estimates via LFs

108

(15)

4.2.1 Establishing Estimates

108

(3)

4.2.2 Choice of the LF

111

(1)

4.2.3 LEDA

112

(7)

4.2.4 Estimate Tightness

119

(4)

4.3 Estimates via Quadratic LFs

123

(10)

4.3.1 Establishing Estimates

123

(3)

4.3.2 LEDA

126

(4)

4.3.3 Estimate Tightness

130

(3)

4.4 Optimal Estimates

133

(11)

4.4.1 Maximizing the Volume of the Estimate

133

(2)

4.4.2 Enlarging the Estimate with Fixed Shape Sets

135

(5)

4.4.3 Establishing Global Asymptotical Stability

140

(4)

4.5 Controller Design

144

(5)

4.6 Notes and References

149

(2)

5 RDA in Uncertain Polynomial Systems

151

(46)

5.1 Uncertain Polynomial Systems

151

(3)

5.2 Estimates via Common LFs

154

(15)

5.2.1 Establishing Estimates

154

(4)

5.2.2 Choice of the LF

158

(2)

5.2.3 Parameter-Dependent LEDA and LERDA

160

(7)

5.2.4 Estimate Tightness

167

(2)

5.3 Estimates via Parameter-Dependent LFs

169

(19)

5.3.1 Establishing Parameter-Dependent Estimates

170

(3)

5.3.2 Choice of the LF

173

(2)

5.3.3 Parameter-Dependent LEDA

175

(5)

5.3.4 LERDA

180

(8)

5.4 Optimal Estimates

188

(5)

5.4.1 Maximizing the Volume of the Estimate

189

(1)

5.4.2 Enlarging the Estimate with Fixed Shape Sets

190

(1)

5.4.3 Establishing Robust Global Asymptotical Stability

191

(2)

5.5 Controller Design

193

(3)

5.6 Notes and References

196

(1)

6 DA and RDA in Non-polynomial Systems

197

(38)

6.1 Non-polynomial Systems

197

(3)

6.2 Estimates via LFs

200

(15)

6.2.1 Establishing Estimates

200

(5)

6.2.2 Bounding the Remainders

205

(2)

6.2.3 Choice of the LF

207

(1)

6.2.4 LEDA

208

(4)

6.2.5 Estimate Tightness

212

(3)

6.3 Optimal Estimates

215

(6)

6.3.1 Maximizing the Volume of the Estimate

216

(1)

6.3.2 Enlarging the Estimate with Fixed Shape Sets

217

(3)

6.3.3 Establishing Global Asymptotical Stability

220

(1)

6.4 Controller Design

221

(3)

6.5 Uncertain Non-polynomial Systems

224

(1)

6.6 Estimates for Uncertain Non-polynomial Systems

225

(9)

6.6.1 Establishing Estimates

226

(3)

6.6.2 Choice of the LF

229

(1)

6.6.3 LERDA

230

(4)

6.6.4 Extensions

234

(1)

6.7 Notes and References

234

(1)

7 Miscellaneous

235

(30)

7.1 Union of Estimates

236

(2)

7.2 Equilibrium Points in Uncertain Systems

238

(12)

7.2.1 Estimate Computation

240

(1)

7.2.2 Estimate Tightness

241

(2)

7.2.3 Variable Shape Estimates

243

(7)

7.3 Trajectory Bounds for Given Sets of Initial Conditions

250

(9)

7.3.1 Analysis

253

(1)

7.3.2 Synthesis and Tightness

254

(5)

7.4 A Note on Degenerate Polynomial Systems

259

(3)

7.5 Notes and References

262

(3)

A LMI Problems

265

(2)

B Determinant and Rank Constraints via LMIs

267

(2)

C MATLAB Code: SMRSOFT

269

(4)

References

273

(6)

Author Biography

279

(2)

Index

281

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Prijs:	€ 97,00
Levertijd:	3 tot 5 werkdagen
Bindwijze:	Boek, Paperback
Genre:	Bedrijfsinformatietechnologie

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