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.
STOCHASTIC HYBRID SYSTEMS: RESEARCH ISSUES AND AREAS Christos G. Cassandras and John Lygeros Introduction Modeling of Nondeterministic Hybrid Systems Modeling of Stochastic Hybrid Systems Overview of This Volume STOCHASTIC DIFFERENTIAL EQUATIONS ON HYBRID STATE SPACES Jaroslav Krystul, Henk A.P. Blom, and Arunabha Bagchi Introduction Semimartingales and Characteristics Semimartingale Strong Solution of SDE Stochastic Hybrid Processes as Solutions of SDE Instantaneous Hybrid Jumps at a Boundary Related SDE models on Hybrid State Spaces Markov and Strong Markov Properties Concluding Remarks COMPOSITIONAL MODELING OF STOCHASTIC HYBRID SYSTEMS Stefan Strubbe and Arjan van der Schaft Introduction Semantical Models Communicating PDPs Conclusions STOCHASTIC MODEL CHECKING Joost-Pieter Katoen Introduction The Discrete-Time Setting The Continuous-Time Setting Bisimulation and Simulation Relations Epilogue STOCHASTIC REACHABILITY: THEORY AND NUMERICAL APPROXIMATION Maria Prandini and Jianghai Hu Introduction Stochastic Hybrid System Model Reachability Problem Formulation Numerical Approximation Scheme Reachability Computations Possible Extensions Some Examples Conclusion STOCHASTIC FLOW SYSTEMS: MODELING AND SENSITIVITY ANALYSIS Christos G. Cassandras Introduction Modeling Stochastic Flow Systems Sample Paths of Stochastic Flow Systems Optimization Problems in Stochastic Flow Systems Infinitesimal Perturbation Analysis (IPA) Conclusions PERTURBATION ANALYSIS FOR STOCHASTIC FLOW SYSTEMS WITH FEEDBACK Yorai Wardi, George Riley, and Richelle Adams Introduction SFM with Flow Control Retransmission-Based Model Simulation Experiments Conclusions STOCHASTIC HYBRID MODELING OF ON-OFF TCP FLOWS Joao Hespanha Related Work A Stochastic Model for TCP Analysis of the TCP SHS Models Reduced-Order Models Conclusions STOCHASTIC HYBRID MODELING OF BIOCHEMICAL PROCESSES Panagiotis Kouretas, Konstantinos Koutroumpas, John Lygeros, and Zoi Lygerou Introduction Overview of PDMP Subtilin Production by B. subtilis DNA Replication in the Cell Cycle Concluding Remarks FREE FLIGHT COLLISION RISK ESTIMATION BY SEQUENTIAL MC SIMULATION Henk A.P. Blom, Jaroslav Krystul, G.J. (Bert) Bakker, Margriet B. Klompstra, and Bart Klein Obbink Introduction Sequential MC Estimation of Collision Risk Development of a Petri Net Model of Free Flight Simulated Scenarios and Collision Risk Estimates Concluding Remarks INDEX