Stochastic Hybrid Systems,9780849390838

Stochastic Hybrid Systems

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ISBN13: 9780849390838
ISBN10: 0849390834
Format: Hardcover
Pub. Date: 2006-11-14
Publisher(s): CRC Press
List Price: $185.00

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Summary

Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems.Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems.Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.

Table of Contents

1 Stochastic Hybrid Systems: Research Issues and Areas 1(14)
Christos G. Cassandras and John Lygeros
1.1 Introduction
1(3)
1.1.1 The Origin of Hybrid Systems
1(2)
1.1.2 Deterministic and Non-deterministic Hybrid Systems
3(1)
1.1.3 Stochastic Hybrid Systems
3(1)
1.2 Modeling of Non-deterministic Hybrid Systems
4(3)
1.3 Modeling of Stochastic Hybrid Systems
7(2)
1.4 Overview of this Volume
9(6)
2 Stochastic Differential Equations on Hybrid State Spaces 15(32)
Jaroslav Krystul, Henk A.P. Blom, and Arunabha Bagchi
2.1 Introduction
15(3)
2.2 Semimartingales and Characteristics
18(4)
2.3 Semimartingale Strong Solution of SDE
22(5)
2.4 Stochastic Hybrid Processes as. Solutions of SDE
27(4)
2.5 Instantaneous Hybrid Jumps at a Boundary
31(2)
2.6 Related SDE Models on Hybrid State Spaces
33(7)
2.6.1 Stochastic Hybrid Model GB1 of Ghosh and Bagchi
34(2)
2.6.2 Stochastic Hybrid Model GB2 of Ghosh and Bagchi
36(2)
2.6.3 Hierarchy Between Stochastic Hybrid Models
38(2)
2.7 Markov and Strong Markov Properties
40(3)
2.8 Concluding Remarks
43(4)
3 Compositional Modelling of Stochastic Hybrid Systems 47(32)
Stefan Strubbe and Arjan van der Schaft
3.1 Introduction
47(1)
3.2 Semantical Models
48(7)
3.2.1 Transition Mechanism Structure
49(1)
3.2.2 Continuous Flow Spontaneous Jump System (CFSJS)
50(3)
3.2.3 Forced Transition Structure (FTS)
53(1)
3.2.4 CFSJS Combined with FTS
53(1)
3.2.5 Non-deterministic Transition System (NTS)
54(1)
3.3 Communicating PDPs
55(20)
3.3.1 Definition of the CPDP Model
56(4)
3.3.2 Semantics of CPDPs
60(1)
3.3.3 Composition of CPDPs
61(7)
3.3.4 Value Passing CPDPs
68(7)
3.4 Conclusions
75(4)
4 Stochastic Model Checking 79(28)
Joost-Pieter Katoen
4.1 Introduction
79(2)
4.1.1 Stochastic Model Checking
80(1)
4.1.2 Topic of this Survey
81(1)
4.2 The Discrete-time Setting
81(6)
4.2.1 Discrete-time Markov Chains
82(2)
4.2.2 Rewards
84(3)
4.3 The Continuous-time Setting
87(7)
4.3.1 Continuous-time Markov Chains
87(2)
4.3.2 Rewards
89(3)
4.3.3 Time-inhomogenity
92(2)
4.4 Bisimulation and Simulation Relations
94(6)
4.4.1 Strong Bisimulation
94(1)
4.4.2 Weak Bisimulation
95(2)
4.4.3 Strong Simulation
97(1)
4.4.4 Logical Characterization
98(2)
4.5 Epilogue
100(7)
4.5.1 Summary of Results
100(2)
4.5.2 Further Research Topics
102(5)
5 Stochastic Reachability: Theory and Numerical Approximation 107(32)
Maria Prandini and Jianghai Hu
5.1 Introduction
107(2)
5.2 Stochastic Hybrid System Model
109(5)
5.3 Reachability Problem Formulation
114(2)
5.4 Numerical Approximation Scheme
116(8)
5.4.1 Markov Chain Approximation
116(7)
5.4.2 Locally Consistent Transition Probability Functions
123(1)
5.5 Reachability Computations
124(4)
5.6 Possible Extensions
128(2)
5.6.1 Probabilistic Safety
128(1)
5.6.2 Regulation
129(1)
5.7 Some Examples
130(4)
5.7.1 Manufacturing System
131(2)
5.7.2 Temperature Regulation
133(1)
5.8 Conclusions
134(5)
6 Stochastic Flow Systems: Modeling and Sensitivity Analysis 139(30)
Christos G. Cassandras
6.1 Introduction
139(3)
6.2 Modeling Stochastic Flow Systems
142(4)
6.3 Sample Paths of Stochastic Flow Systems
146(2)
6.4 Optimization Problems in Stochastic Flow Systems
148(2)
6.5 Infinitesimal Perturbation Analysis (IPA)
150(14)
6.5.1 Single-Class Single-Node System
150(5)
6.5.2 Multi-node Tandem System
155(9)
6.6 Conclusions
164(5)
7 Perturbation Analysis for Stochastic Flow Systems with Feedback 169(22)
Yorai Wardi, George Riley, and Richelle Adams
7.1 Introduction
169(2)
7.2 SFM with Flow Control
171(7)
7.3 Retransmission-based Model
178(8)
7.4 Simulation Experiments
186(2)
7.5 Conclusions
188(3)
8 Stochastic Hybrid Modeling of On-Off TCP Flows 191(30)
João Hespanha
8.1 Related Work
193(6)
8.1.1 Models for Long-lived Flows
193(4)
8.1.2 Models for On-Off Flows
197(2)
8.2 A Stochastic Model for TCP
199(4)
8.3 Analysis of the TCP SHS Models
203(1)
8.4 Reduced-order Models
204(7)
8.4.1 Long-lived Flows
205(1)
8.4.2 Mixed-exponential Transfer-sizes
206(5)
8.5 Conclusions
211(10)
9 Stochastic Hybrid Modeling of Biochemical Processes 221(28)
Panagiotis Kouretas, Konstantinos Koutroumpas, John Lygeros, and Zoi Lygerou
9.1 Introduction
221(2)
9.2 Overview of PDMP
223(5)
9.2.1 Modeling Framework
223(3)
9.2.2 Simulation
226(2)
9.3 Subtilin Production by B. subtilis
228(7)
9.3.1 Qualitative Description
228(1)
9.3.2 An Initial Model
228(1)
9.3.3 A Formal PDMP Model
229(5)
9.3.4 Analysis and Simulation
234(1)
9.4 DNA Replication in the Cell Cycle
235(9)
9.4.1 Qualitative Description
235(2)
9.4.2 Stochastic Hybrid Features
237(2)
9.4.3 A PDMP Model
239(4)
9.4.4 Implementation in Simulation and Results
243(1)
9.5 Concluding Remarks
244(5)
10 Free Flight Collision Risk Estimation by Sequential MC Simulation 249(1)
Henk A.P. Blom, Jaroslav Krystul, G.J. (Bert) Bakker, Margriet B. Klompstra, and Bart Klein Obbink
10.1 Introduction
249(4)
10.1.1 Safety Verification of Free Flight Air Traffic
249(1)
10.1.2 Probabilistic Reachability Analysis
250(1)
10.1.3 Sequential Monte Carlo Simulation
251(1)
10.1.4 Development of MC Simulation Model
252(1)
10.2 Sequential MC Estimation of Collision Risk
253(6)
10.2.1 Stochastic Hybrid Process Considered
253(2)
10.2.2 Risk Factorisation Using Multiple Conflict Levels
255(1)
10.2.3 Characterisation of the Risk Factors
256(1)
10.2.4 Interacting Particle System Based Risk Estimation
257(1)
10.2.5 Modification of IPS Resampling Step 4
258(1)
10.3 Development of a Petri Net Model of Free Flight
259(12)
10.3.1 Specification of Petri Net Model
259(1)
10.3.2 High Level Interconnection Arcs
260(1)
10.3.3 Agents and LPNs to Represent AMFF Operations
261(3)
10.3.4 Interconnected LPNs of ASAS
264(1)
10.3.5 Interconnected LPNs of "Pilot Flying"
265(3)
10.3.6 Model Verification, Parameterisation, and Validation
268(1)
10.3.7 Dimensions of MC Simulation Model
269(2)
10.4 Simulated Scenarios and Collision Risk Estimates
271(5)
10.4.1 Parameterisation of the IPS Simulations
271(1)
10.4.2 Eight Aircraft on Collision Course
271(2)
10.4.3 Free Flight Through an Artificially Constructed Airspace
273(1)
10.4.4 Reduction of the Aircraft Density by a Factor Four
274(1)
10.4.5 Discussion of IPS Simulation Results
275(1)
10.5 Concluding Remarks
276(7)
Index 283

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