Preface |
|
xi | |
Glossary of Symbols |
|
xiii | |
|
|
1 | (30) |
|
1.1 Network-Based Distributed Control System |
|
|
1 | (3) |
|
1.2 Graph Theory and Interconnection Topology |
|
|
4 | (12) |
|
|
4 | (3) |
|
|
7 | (3) |
|
1.2.3 Algebraic Graph Theory |
|
|
10 | (6) |
|
1.3 Distributed Control Systems |
|
|
16 | (9) |
|
1.3.1 End-to-End Congestion Control Systems |
|
|
16 | (6) |
|
1.3.2 Consensus-Based Formation Control |
|
|
22 | (3) |
|
|
25 | (6) |
|
1.4.1 Graph Theory and Distributed Control Systems |
|
|
25 | (1) |
|
1.4.2 Delay in Control and Control by Delay |
|
|
26 | (1) |
|
|
26 | (5) |
|
2 Symmetry, Stability and Scalability |
|
|
31 | (36) |
|
|
31 | (5) |
|
2.1.1 Graph-Based Model of Distributed Control Systems |
|
|
31 | (3) |
|
2.1.2 Bipartite Distributed Control Systems |
|
|
34 | (2) |
|
2.2 Symmetry in the Frequency Domain |
|
|
36 | (3) |
|
|
36 | (2) |
|
2.2.2 Symmetry of Bipartite Systems |
|
|
38 | (1) |
|
2.3 Stability of Multivariable Systems |
|
|
39 | (4) |
|
2.3.1 Poles and Stability |
|
|
39 | (2) |
|
2.3.2 Zeros and Pole-Zero Cancelation |
|
|
41 | (2) |
|
2.4 Frequency-Domain Criteria of Stability |
|
|
43 | (10) |
|
2.4.1 Loop Transformation and Multiplier |
|
|
44 | (1) |
|
2.4.2 Multivariable Nyquist Stability Criterion |
|
|
45 | (5) |
|
2.4.3 Spectral Radius Theorem and Small-Gain Theorem |
|
|
50 | (3) |
|
2.4.4 Positive Realness Theorem |
|
|
53 | (1) |
|
2.5 Scalable Stability Criteria |
|
|
53 | (11) |
|
2.5.1 Estimation of Spectrum of Complex Matrices |
|
|
53 | (3) |
|
2.5.2 Scalable Stability Criteria for Asymmetric Systems |
|
|
56 | (4) |
|
2.5.3 Scalable Stability Criteria for Symmetric Systems |
|
|
60 | (1) |
|
2.5.4 Robust Stability in Deformity of Symmetry |
|
|
61 | (3) |
|
|
64 | (3) |
|
|
65 | (2) |
|
3 Scalability in the Frequency Domain |
|
|
67 | (44) |
|
3.1 How the Scalability Condition is Related with Frequency Responses |
|
|
67 | (4) |
|
3.2 Clockwise Property of Parameterized Curves |
|
|
71 | (5) |
|
3.3 Scalability of First-Order Systems |
|
|
76 | (9) |
|
3.3.1 Continuous-Time System |
|
|
76 | (3) |
|
3.3.2 Discrete-Time System |
|
|
79 | (6) |
|
3.4 Scalability of Second-Order Systems |
|
|
85 | (18) |
|
|
85 | (10) |
|
|
95 | (8) |
|
3.5 Frequency-Sweeping Condition |
|
|
103 | (5) |
|
3.5.1 Stable Quasi-Polynomials |
|
|
103 | (2) |
|
3.5.2 Frequency-Sweeping Test |
|
|
105 | (3) |
|
|
108 | (3) |
|
|
109 | (2) |
|
4 Congestion Control: Model and Algorithms |
|
|
111 | (18) |
|
4.1 An Introduction to Congestion Control |
|
|
111 | (5) |
|
4.1.1 Congestion Collapse |
|
|
112 | (2) |
|
4.1.2 Efficiency and Fairness |
|
|
114 | (1) |
|
4.1.3 Optimization-Based Resource Allocation |
|
|
114 | (2) |
|
4.2 Distributed Congestion Control Algorithms |
|
|
116 | (3) |
|
4.2.1 Penalty Function Approach and Primal Algorithm |
|
|
116 | (1) |
|
4.2.2 Dual Approach and Dual Algorithm |
|
|
117 | (1) |
|
4.2.3 Primal-Dual Algorithm |
|
|
118 | (1) |
|
4.2.4 REM: A Second-Order Dual Algorithm |
|
|
118 | (1) |
|
4.3 A General Model of Congestion Control Systems |
|
|
119 | (7) |
|
4.3.1 Framework of End-to-End Congestion Control under Diverse Round-Trip Delays |
|
|
119 | (3) |
|
4.3.2 General Primal-Dual Algorithm |
|
|
122 | (2) |
|
4.3.3 Frequency-Domain Symmetry of Congestion Control Systems |
|
|
124 | (2) |
|
|
126 | (3) |
|
|
127 | (2) |
|
5 Congestion Control: Stability and Scalability |
|
|
129 | (64) |
|
5.1 Stability of the Primal Algorithm |
|
|
129 | (9) |
|
5.1.1 Johari-Tan Conjecture |
|
|
129 | (2) |
|
5.1.2 Scalable Stability Criterion for Discrete-Time Systems |
|
|
131 | (4) |
|
5.1.3 Scalable Stability Criterion for Continuous-Time Systems |
|
|
135 | (3) |
|
|
138 | (14) |
|
5.2.1 Scalable Stability Criteria |
|
|
138 | (7) |
|
5.2.2 Dual Algorithm: the First-Order Limit Form of REM |
|
|
145 | (1) |
|
5.2.3 Design of Parameters of REM |
|
|
146 | (6) |
|
5.3 Stability of the Primal-Dual Algorithm |
|
|
152 | (11) |
|
5.3.1 Scalable Stability Criteria |
|
|
152 | (9) |
|
5.3.2 Proof of the Stability Criteria |
|
|
161 | (2) |
|
5.4 Time-Delayed Feedback Control |
|
|
163 | (7) |
|
5.4.1 Time-Delayed State as a Reference |
|
|
163 | (2) |
|
5.4.2 TDFC for Stabilization of an Unknown Equilibrium |
|
|
165 | (1) |
|
5.4.3 Limitation of TDFC in Stabilization |
|
|
166 | (4) |
|
5.5 Stabilization of Congestion Control Systems by Time-Delayed Feedback Control |
|
|
170 | (18) |
|
5.5.1 Introduction of TDFC into Distributed Congestion Control Systems |
|
|
170 | (1) |
|
5.5.2 Stabilizability under TDFC |
|
|
171 | (10) |
|
5.5.3 Design of TDFC with Commensurate Self-Delays |
|
|
181 | (7) |
|
|
188 | (5) |
|
5.6.1 Stability of Congestion Control with Propagation Delays |
|
|
188 | (1) |
|
5.6.2 Time-Delayed Feedback Control |
|
|
189 | (1) |
|
|
190 | (3) |
|
6 Consensus in Homogeneous Multi-Agent Systems |
|
|
193 | (26) |
|
6.1 Introduction to Consensus Problem |
|
|
193 | (3) |
|
6.1.1 Integrator Agent System |
|
|
193 | (1) |
|
6.1.2 Existence of Consensus Solution |
|
|
194 | (1) |
|
6.1.3 Consensus as a Stability Problem |
|
|
194 | (1) |
|
6.1.4 Discrete-Time Systems |
|
|
195 | (1) |
|
|
195 | (1) |
|
6.2 Second-Order Agent System |
|
|
196 | (10) |
|
6.2.1 Consensus and Stability |
|
|
196 | (3) |
|
6.2.2 Consensus and Consentability Condition |
|
|
199 | (4) |
|
6.2.3 Periodic Consensus Solutions |
|
|
203 | (1) |
|
|
204 | (2) |
|
6.3 High-Order Agent System |
|
|
206 | (10) |
|
|
206 | (2) |
|
6.3.2 Consensus Condition |
|
|
208 | (3) |
|
|
211 | (5) |
|
|
216 | (3) |
|
|
217 | (2) |
|
7 Consensus in Heterogeneous Multi-Agent Systems |
|
|
219 | (50) |
|
7.1 Integrator Agent System with Diverse Input and Communication Delays |
|
|
219 | (14) |
|
7.1.1 Consensus in Discrete-Time Systems |
|
|
220 | (1) |
|
7.1.2 Consensus under Diverse Input Delays |
|
|
221 | (3) |
|
7.1.3 Consensus under Diverse Communication Delays and Input Delays |
|
|
224 | (5) |
|
7.1.4 Continuous-Time System |
|
|
229 | (1) |
|
|
230 | (3) |
|
7.2 Double Integrator System with Diverse Input Delays and Interconnection Uncertainties |
|
|
233 | (10) |
|
7.2.1 Leader-Following Consensus Algorithm |
|
|
233 | (2) |
|
7.2.2 Consensus Condition under Symmetric Coupling Weights |
|
|
235 | (3) |
|
7.2.3 Robust Consensus under Asymmetric Perturbations |
|
|
238 | (2) |
|
|
240 | (3) |
|
7.3 High-Order Consensus in High-Order Systems |
|
|
243 | (12) |
|
|
243 | (2) |
|
7.3.2 Consensus Condition |
|
|
245 | (4) |
|
7.3.3 Existence of High-Order Consensus Solutions |
|
|
249 | (3) |
|
|
252 | (2) |
|
7.3.5 Consensus in Ideal Networks |
|
|
254 | (1) |
|
7.4 Integrator-Chain Systems with Diverse Communication Delays |
|
|
255 | (10) |
|
7.4.1 Matching Condition for Self-Delay |
|
|
255 | (1) |
|
7.4.2 Adaptive Adjustment of Self-Delay |
|
|
255 | (2) |
|
|
257 | (8) |
|
|
265 | (4) |
|
|
266 | (3) |
Index |
|
269 | |