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E-raamat: Zhang Functions and Various Models

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-May-2015
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662473344
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Zhang Functions and Various ModelsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 29-May-2015
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662473344
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This book focuses on solving different types of time-varying problems. It presents various Zhang dynamics (ZD) models by defining various Zhang functions (ZFs) in real and complex domains. It then provides theoretical analyses of such ZD models and illustrates their results. It also uses simulations to substantiate their efficacy and show the feasibility of the presented ZD approach (i.e., different ZFs leading to different ZD models), which is further applied to the repetitive motion planning (RMP) of redundant robots, showing its application potential.

Part I Scalar-Valued ZF in Real Domain.-Time-Varying Reciprocal.- Time-Varying Inverse Square Root.- Time-Varying Square Root.-Part II Vector-Valued ZF in Real Domain.-System of Time-Varying Linear Equations.- Over-Determined and Under-Determined Systems of Time-Varying Linear Equations.- Time-Varying Linear Matrix-Vector Inequality.-Part III Matrix-Valued ZF in Real Domain.-Time-VaryingMatrix Inverse.- Time-VaryingMatrix Left Pseudoinverse.- Time-VaryingMatrix Right Pseudoinverse.- Time-VaryingMatrix Square Root.-Part IV ZF in Complex Domain.-Time-Varying Complex Reciprocal.- Time-Varying Complex Matrix Inverse.- Time-Varying Complex Matrix Generalized Inverse.-Part V ZF Application to Robot Control.-Application to Fixed-Base Robot RMP.- Application to Mobile Robot RMP.

Arvustused

This detailed, yet concise book of 236 pages contains 5 parts and 18 chapters on Zhang functions (ZF) and Zhang neural dynamics (ZD). This book on neural computing may serve as a revelation to numerical analysts as it alters the whole field of computing. (Frank Uhlig, zbMATH 1339.65002, 2016)

Part I Scalar-Valued ZF in Real Domain
1 Time-Varying Reciprocal
3(14)
1.1 Introduction and Preliminaries
3(2)
1.2 ZFs and ZD Models
5(3)
1.3 Theoretical Results and Analyses
8(2)
1.4 Simulink Modeling
10(1)
1.5 Illustrative Examples
11(4)
1.6 Summary
15(1)
References
16(1)
2 Time-Varying Inverse Square Root
17(16)
2.1 Introduction
17(1)
2.2 ZFs and ZD Models
18(4)
2.2.1 The First ZF and ZD Model
18(1)
2.2.2 The Second ZF and ZD Model
19(1)
2.2.3 The Third ZF and ZD Model
20(1)
2.2.4 The Fourth ZF and ZD Model
20(1)
2.2.5 The Fifth ZF and ZD Model
21(1)
2.2.6 The Sixth ZF and ZD Model
21(1)
2.3 Theoretical Results and Analyses
22(2)
2.4 Simulink Modeling
24(3)
2.5 Illustrative Examples
27(3)
2.6 Summary
30(1)
References
30(3)
3 Time-Varying Square Root
33(16)
3.1 Introduction
33(1)
3.2 ZFs and ZD Models
34(4)
3.3 Simulink Modeling
38(1)
3.4 Illustrative Examples
39(5)
3.5 Summary
44(1)
References
45(4)
Part II Vector-Valued ZF in Real Domain
4 System of Time-Varying Linear Equations
49(12)
4.1 Introduction
49(1)
4.2 ZFs and ZD Models
50(3)
4.2.1 The First ZF and ZD Model
51(1)
4.2.2 The Second ZF and ZD Model
51(2)
4.3 Theoretical Results and Analyses
53(2)
4.4 Illustrative Examples
55(4)
4.5 Summary
59(1)
References
59(2)
5 Over-Determined and Under-Determined Systems of Time-Varying Linear Equations
61(14)
5.1 Introduction
61(1)
5.2 ZFs and ZD Models
62(4)
5.2.1 With m > n (Over-Determined System)
62(1)
5.2.2 With m > n (Under-Determined System)
63(3)
5.3 Illustrative Examples
66(6)
5.4 Summary
72(1)
References
73(2)
6 Time-Varying Linear Matrix-Vector Inequality
75(16)
6.1 Introduction
75(1)
6.2 ZFs and ZD Models
76(6)
6.2.1 The First ZF and ZD Model
76(1)
6.2.2 The Second ZF and ZD Model
77(1)
6.2.3 The Third ZF and ZD Model
78(4)
6.3 Illustrative Examples
82(5)
6.4 Summary
87(1)
References
87(4)
Part III Matrix-Valued ZF in Real Domain
7 Time-Varying Matrix Inverse
91(14)
7.1 Introduction
91(1)
7.2 ZFs and ZD Models
92(3)
7.3 Theoretical Results and Analyses
95(2)
7.4 Simulink Modeling
97(3)
7.5 Illustrative Examples
100(3)
7.6 Summary
103(1)
References
103(2)
8 Time-Varying Matrix Left Pseudoinverse
105(16)
8.1 Introduction
105(2)
8.2 ZFs and ZD Models
107(5)
8.2.1 The First ZF and ZD Model
107(2)
8.2.2 The Second ZF and ZD Model
109(1)
8.2.3 The Third ZF and ZD Model
109(1)
8.2.4 The Fourth ZF and ZD Model
110(1)
8.2.5 The Fifth ZF and ZD Model
111(1)
8.3 Illustrative Examples
112(6)
8.4 Summary
118(1)
References
118(3)
9 Time-Varying Matrix Right Pseudoinverse
121(8)
9.1 Introduction
121(1)
9.2 ZFs and ZD Models
122(2)
9.3 Theoretical Results
124(1)
9.4 Illustrative Examples
125(2)
9.5 Summary
127(1)
References
127(2)
10 Time-Varying Matrix Square Root
129(22)
10.1 Introduction
129(1)
10.2 ZFs and ZD Models
130(7)
10.3 Theoretical Results and Analyses
137(2)
10.4 MATLAB Simulink Modeling
139(3)
10.4.1 Simulink Blocks
139(1)
10.4.2 Parameter Settings
140(2)
10.5 Illustrative Examples
142(5)
10.6 Summary
147(1)
References
147(4)
Part IV ZF in Complex Domain
11 Time-Varying Complex Reciprocal
151(12)
11.1 Introduction
151(1)
11.2 Complex ZFs and ZD Models
152(4)
11.3 Illustrative Examples
156(4)
11.4 Summary
160(1)
References
160(3)
12 Time-Varying Complex Matrix Inverse
163(10)
12.1 Introduction
163(1)
12.2 Complex ZFs and ZD Models
164(2)
12.3 Illustrative Examples
166(5)
12.4 Summary
171(1)
References
171(2)
13 Time-Varying Complex Matrix Generalized Inverse
173(22)
13.1 Introduction
173(2)
13.2 Complex ZFs and ZD Models
175(9)
13.2.1 The First Complex ZD Model
176(3)
13.2.2 The Second Complex ZD Model
179(1)
13.2.3 The Third Complex ZD Model
180(1)
13.2.4 The Fourth Complex ZD Model
181(1)
13.2.5 The Fifth Complex ZD Model
182(2)
13.3 Illustrative Examples
184(7)
13.4 Summary
191(1)
References
191(4)
Part V ZF Application to Robot Control
14 Application to Fixed-Base Robot RMP
195(20)
14.1 Introduction
195(2)
14.2 RMP Performance Index Derived via Different ZFs
197(1)
14.3 Scheme and QP Formulations
198(3)
14.3.1 Acceleration-Level RMP Scheme
199(1)
14.3.2 Bound Constraint Transformation Technique
199(1)
14.3.3 QP Reformulation
200(1)
14.3.4 QP Solver
200(1)
14.4 Illustrative Examples
201(11)
14.4.1 Pentagram-Path Tracking
202(5)
14.4.2 East-Asian Character Writing
207(2)
14.4.3 "V" Path Path Tracking
209(1)
14.4.4 Comparisons with Velocity-Level RMP Scheme
210(2)
14.5 Summary
212(1)
References
212(3)
15 Application to Mobile Robot RMP
215
15.1 Introduction
215(2)
15.2 RMP Performance Index Derived via Different ZFs
217(3)
15.2.1 Kinematics Modeling of Mobile Robot Manipulators
217(1)
15.2.2 Velocity-Level RMP Performance Index
218(2)
15.3 Scheme and QP Formulations
220(4)
15.3.1 Velocity-Level RMP Scheme
220(2)
15.3.2 QP Reformulation
222(1)
15.3.3 QP Solver
223(1)
15.4 Illustrative Examples
224(10)
15.4.1 Circular Path Tracking
224(6)
15.4.2 Lissajous-Figure Path Tracking
230(4)
15.5 Summary
234(1)
References
235
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