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E-raamat: Pedestrian Dynamics: Feedback Control of Crowd Evacuation

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  • Formaat: PDF+DRM
  • Sari: Understanding Complex Systems
  • Ilmumisaeg: 24-Jan-2008
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783540755616
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Pedestrian Dynamics: Feedback Control of Crowd EvacuationSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Understanding Complex Systems
  • Ilmumisaeg: 24-Jan-2008
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783540755616
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Effective evacuation of people from closed spaces is an extremely important topic, since it can save real lives in emergency situations that can be brought about by natural and human made disasters. Usually there are static maps posted at various places at buildings that illustrate routes that should be taken during emergencies. However, when disasters happen, some of these routes might not be valid because of structural problems due to the disaster itself and more importantly because of the distribution of congestion of people spread over the area. The average flow of traffic depends on the traffic density. Therefore, if all the people follow the same route, or follow a route without knowing the congestion situation, they can end up being part of the congestion which results in very low flow rate or worse a traffic jam. Hence it becomes extremely important to design evacuations that inform people how fast and in which direction to move based on real-time information obtained about the people distribution using various sensors. The sensors used can include cameras, infra red sensors etc., and the technology used to inform people about the desired movement can be communicated using light matrix, small speakers, and in the future using wireless PDAs. This book provides mathematical models of pedestrian movements that can be used specifically for designing feedback control laws for effective evacuation. The book also provides various feedback control laws to accomplish the effective evacuation. The book uses the hydrodynamic hyperbolic PDE macroscopic pedestrian models since they are amenable to feedback control design. The control designs are obtained through different nonlinear techniques including Lyapunov functional techniques, feedback linearization in the distributed model, and some discretized techniques.

Arvustused

From the reviews:

The book is intended for researchers, engineers, and graduate students in applied complexity and nonlinear dynamics as well as in pedestrian dynamics. (IEEE Control Systems Magazine, Vol. 29, October, 2009)

This book is dedicated the developing pedestrian dynamic models that can be used in the control and investigation of crowd behavior. This book is very interesting. It considered actual theme about evacuation strategy. The theory bases on the analogy with air dynamical processes and uses modern mathematical methods, as Lyapunovs theory for estimation stability of control processes. This book may be very useful for scientists, post graduate students who work in area of control strategy evacuation. (Yuri N. Sankin, Zentralblatt MATH, Vol. 1237, 2012)

1 Introduction
1
2 Traffic Flow Theory for 1-D
5
2.1 Introduction
5
2.2 Microscopic vs Macroscopic
6
2.3 Car-Following Model
7
2.4 Traffic Flow Theory
8
2.4.1 Flow
8
2.4.2 Conservation Law
9
2.4.3 Velocity–Density Relationship(s)
11
2.5 Traffic Flow Model 1-D
13
2.5.1 LWR Model
14
2.5.2 PW Model
15
2.5.3 AR Model
17
2.5.4 Zhang Model
19
2.5.5 Models Summary
22
2.6 Method of Characteristics
23
2.6.1 LWR Model Classification
23
2.6.2 Exact Solution
23
2.6.3 Blowup of Smooth Solutions
25
2.6.4 Weak Solution
27
3 Crowd Models for 2-D
33
3.1 Introduction
33
3.2 Traffic Flow Theory in 2-D
34
3.3 One Equation Crowd Model
35
3.4 First System Crowd Dynamic Model
36
3.4.1 Model Description
36
3.4.2 Conservation Form and Eigenvalues
38
3.5 Second Crowd Dynamic Model
40
3.5.1 Model Description
40
3.5.2 Conservation Form and Eigenvalues
41
3.6 Third Crowd Dynamic Model
44
3.6.1 Model Description
44
3.6.2 Derivation of a Macroscopic Model from a Microscopic Model in 2-D
45
3.6.3 Conservation Form and Eigenvalues
46
3.7 Comparison Between the Models
50
3.8 Linearization
53
3.8.1 One Equation Crowd Model
53
3.8.2 First System Model
55
3.8.3 Second System Model
56
3.8.4 Third System Model
58
4 Numerical Methods
61
4.1 Introduction
61
4.2 Fundamentals of FVM
62
4.2.1 Formulation of 2-D Numerical Schemes
63
4.3 Numerical Schemes
65
4.3.1 Lax-Friedrichs Scheme
65
4.3.2 FORCE Scheme
65
4.3.3 Roe's Scheme
66
4.4 Simulation
67
4.4.1 Initial and Boundary Conditions
67
4.4.2 Simulation Results
68
4.5 Matlab Program Code
78
4.5.1 One-equation Model
78
4.5.2 First System Model
81
4.5.3 Second System Model
87
4.5.4 Third System Model
91
5 Feedback Linearization (1-D Patches)
95
5.1 Introduction
95
5.2 Theory
96
5.2.1 Control Problem
96
5.2.2 Characteristic Index
97
5.2.3 State Feedback Control
97
5.2.4 Closed-Loop Stability
98
5.3 Application to the LWR (One patch)
98
5.4 Application to the LWR (n=5 patches)
101
5.5 Matlab Program Code
103
5.5.1 One-patch Control
103
5.5.2 Five-patch Control
104
6 Intelligent Evacuation Systems
107
6.1 Introduction
107
6.2 IPES Functions
109
6.3 IES Functions for Evacuation Scenarios
111
6.3.1 Subway Station
111
6.3.2 Airport
112
6.4 Four-Layer System Architecture
115
6.5 Four-Layer System: Scenarios
117
6.5.1 Subway Station
117
6.5.2 Airport
118
6.6 IT Issues and Requirements
118
6.7 Feedback Control and Dynamic Modeling
119
7 Discretized Feedback Control
121
7.1 Introduction
121
7.2 Pedestrian Flow Modeling
123
7.3 Feedback Linearization of State Equations
125
7.3.1 Stability Under Feedback Linearizing Control
126
7.3.2 Saturation of Control
128
7.4 Simulation Results
129
7.5 Code
133
7.6 Exercises
134
7.7 Computer Code
135
7.7.1 main.m
135
7.7.2 rhodot_nsec.m
138
7.7.3 vfcntrl_nsec_try.m
138
8 Discretized Optimal Control
141
8.1 Optimal Control
142
8.1.1 State Equations
142
8.1.2 Cost Function
143
8.1.3 Calculus of Variation
144
8.2 The Method of Steepest Descent
146
8.3 Numerical Results
147
8.4 Code
150
8.4.1 main.m
150
8.4.2 optimal_cntrl_calc_var_nsec_odesol.m
151
8.5 Exercises
152
8.6 Computer Code
152
8.6.1 optimal_corridor_evacuation/main
152
8.6.2 optimal_cntrl_calc_var_nsec_odesol
155
9 Distributed Feedback Control 1-D 161
9.1 Introduction
162
9.2 Modeling
163
9.2.1 One Equation Model
164
9.2.2 Two Equation Model
165
9.3 Feedback Control for One-Equation Model
166
9.3.1 Continuity Equation Control Model
166
9.3.2 State Feedback Control
167
9.3.3 Lyapunov Stability Analysis
168
9.3.4 Simulation Results
170
9.4 Control Saturation
172
9.5 Feedback Control for Two Equation Model
175
9.5.1 Two Equation Control Model
176
9.5.2 State Feedback Control Using Backstepping
176
9.5.3 Simulation
179
9.6 Exercises
182
9.7 Computer Code
182
9.7.1 feedback_1d_mass
182
9.7.2 feedback_1d_moment um
185
10 Distributed Feedback Control 2-D 189
10.1 Introduction
189
10.2 Feedback Control of One-Equation Model
191
10.2.1 One-Equation Model
191
10.2.2 Control Model
192
10.2.3 State Feedback Control
193
10.2.4 Lyapunov Stability Analysis
193
10.2.5 Simulation Results
195
10.3 Feedback Control for Two-Equation Model
197
10.3.1 Two Equation Model
197
10.4 Control Model
198
10.4.1 State Feedback Control Using Backstepping
199
10.4.2 Simulation Results
202
10.5 Exercises
204
10.6 Computer Code
204
10.6.1 feedback 2d
204
11 Robust Feedback Control 209
11.1 Introduction
209
11.2 Feedback Control for Continuity Equation Model
210
11.2.1 Input Uncertain Control Model
211
11.2.2 Robust Control by Lyapunov Redesign Method
212
11.2.3 Simulation Results
216
11.3 Robust Control for Two-Equation Model
220
11.3.1 Robust Backstepping: Unmatched Uncertainty
221
11.3.2 Robust Control: Matched Uncertainty
225
11.3.3 Robust Control: Both Matched and Unmatched Uncertainties
227
11.4 Computer Code
229
11.4.1 robust_1d
229
Bibliography 233
Index 243
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