Control Of Stochastic Hybrid Systems Based On Probabilistic Reachable Set Computation

This thesis proposes an algorithmic controller synthesis based on the computation of probabilistic reachable sets for stochastic hybrid systems. Hybrid systems consist in general of a composition of discrete and continuous valued dynamics, and are able to capture a wide range of physical phenomena. The stochasticity is considered in form of normally distributed initial continuous states and normally distributed disturbances, resulting in stochastic hybrid systems. The reachable sets describe all states, which are reachable by a system for a given initialization of the system state, inputs, disturbances, and time horizon. For stochastic hybrid systems, these sets are probabilistic, since the system state and disturbance are random variables. This thesis introduces probabilistic reachable sets with a predefined confidence, which are used in an optimization based procedure for the determination of stabilizing control inputs. Besides the stabilizing property, the controlled dynamics also observes input constraints, as well as, so-called chance constraints for the continuous state. The main contribution of this thesis is the formulation of an algorithmic control procedure for each considerd type of stochastic hybrid systems, where different discrete dynamics are considered. First, a control procedure for a deterministic system with bounded disturbances is introduced, and thereafter a probabilistic distribution of the system state and the disturbance is assumed. The formulation of probabilistic reachable sets with a predefined confidence is subsequently used in a control procedure for a stochastic hybrid system, in which the switch of the continuous dynamics is externally induced. Finally, the control procedure based on reachable set computation is extended to a type of stochastic hybrid systems with autonomously switching of the continuous dynamics.

Stochastic reachability analysis (SRA) is a method of analyzing the behavior of control systems which mix discrete and continuous dynamics. For probabilistic discrete systems it has been shown to be a practical verification method but for stochastic hybrid systems it can be rather more. As a verification technique SRA can assess the safety and performance of, for example, autonomous systems, robot and aircraft path planning and multi-agent coordination but it can also be used for the adaptive control of such systems. Stochastic Reachability Analysis of Hybrid Systems is a self-contained and accessible introduction to this novel topic in the analysis and development of stochastic hybrid systems. Beginning with the relevant aspects of Markov models and introducing stochastic hybrid systems, the book then moves on to coverage of reachability analysis for stochastic hybrid systems. Following this build up, the core of the text first formally defines the concept of reachability in the stochastic framework and then treats issues representing the different faces of SRA: • stochastic reachability based on Markov process theory; • martingale methods; • stochastic reachability as an optimal stopping problem; and • dynamic programming. The book is rounded off by an appendix providing mathematical underpinning on subjects such as ordinary differential equations, probabilistic measure theory and stochastic modeling, which will help the non-expert-mathematician to appreciate the text. Stochastic Reachability Analysis of Hybrid Systems characterizes a highly interdisciplinary area of research and is consequently of significant interest to academic researchers and graduate students from a variety of backgrounds in control engineering, applied mathematics and computer science. The Communications and Control Engineering series reports major technological advances which have potential for great impact in the fields of communication and control. It reflects research in industrial and academic institutions around the world so that the readership can exploit new possibilities as they become available.

This book constitutes the refereed proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control, HSCC 2006, held in Santa Barbara, CA, USA in March 2006. The 39 revised full papers presented together with the abstracts of 3 invited talks were carefully reviewed and selected from 79 submissions. Among the topics addressed are tools for analysis and verification, control and optimization, modeling, engineering applications, and emerging directions in programming language support and implementation. The papers focus on modeling, analysis, and implementation of dynamic and reactive systems involving both discrete and continuous behaviors.

This volume contains the proceedings of the Sixth Workshop on Hybrid Systems: Computation and Control (HSCC 2003), which was held in Prague, during April 3–5, 2003. The Hybrid Systems workshops attract researchers interested in the modeling, analysis, control, and implementation of systems which involve the interaction of both discrete and continuous state dynamics. The newest results and latest developments in hybrid system models, formal methods for analysis and control, computational tools, as well as new applications and examples are presented at these annual meetings. The Sixth Workshop continued the series of workshops held in Grenoble, France (HART’97), Berkeley, California, USA (HSCC’98), Nijmegen, The Neth- lands (HSCC’99), Pittsburgh, Pennsylvania, USA (HSCC 2000), Rome, Italy (HSCC 2001), and Stanford, California, USA (HSCC 2002). Proceedings of these workshops have been published by Springer-Verlag in the Lecture Notes in C- puter Science (LNCS) series. This year we assembled a technical program committee with a broad expertise in formal methods in computer science, control theory, applied mathematics, and arti?cial intelligence. We received a set of 75 high-quality submitted papers. After detailed review and discussion of these papers by the program committee, 36 papers were accepted for presentation at the workshop, and the ?nal versions of these papers appear in this volume.

This book constitues the refereed proceedings of the 6th International Workshop on Hybrid Systems: Computation and Control, HSCC 2003, held in Prague, Czech Republic, in April 2003. The 36 revised full papers presented were carefully reviewed and selected from 75 submissions. All current issues in hybrid systems are addressed including formal methods for analysis and control, computational tools, as well as innovative applications in various fields such as automotive control, the immune system, electrical circuits, operating systems, and human brains.

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.

These are the proceedings of the 9th International Workshop on Hybrid Systems: Computation and Control, HSCC 2006, March 2006. 39 revised papers are presented together with the abstracts of 3 invited talks. The focus is on modeling, analysis, and implementation of dynamic and reactive systems involving both discrete and continuous behaviors. Topics addressed include tools for analysis and verification, control and optimization, modeling, engineering applications, and new directions in language support and implementation.