The problem of viability of hybrid systems is considered in this work. A model for a hybrid system is developed including a means of including three forms of uncertainty: transition dynamics, structural uncertainty, and parametric uncertainty. A computational basis for viability of hybrid systems is developed and applied to three control law classes. An approach is developed for robust viability based on two extensions of the controllability operator. The three-tank example is examined for both the viability problem and robust viability problem. The theory is applied through simulation to an active magnetic bearing system and to a batch polymerization process showing that viability can be satisfied in practice. The problem of viable attainability is examined based on the controllability operator approach introduced by Nerode and colleagues. Lastly, properties of the controllability operator are presented.

This volume contains the proceedings of the Fourth Workshop on Hybrid - stems: Computation and Control (HSCC 2001) held in Rome, Italy on March 28-30, 2001. The Workshop on Hybrid Systems attracts researchers from in- stry and academia interested in modeling, analysis, synthesis, and implemen- tion of dynamic and reactive systems involving both discrete (integer, logical, symbolic) and continuous behaviors. It is a forum for the discussion of the - test developments in all aspects of hybrid systems, including formal models and computational representations, algorithms and heuristics, computational tools, and new challenging applications. The Fourth HSCC International Workshop continues the series of workshops held in Grenoble, France (HART’97), Berkeley, California, USA (HSCC’98), N- megen, The Netherlands (HSCC’99), and Pittsburgh, Pennsylvania, USA (HSCC 2000). Proceedings of these workshops have been published in the Lecture Notes in Computer Science (LNCS) series by Springer-Verlag. In line with the beautiful work that led to the design of the palace in which the workshop was held, Palazzo Lancellotti in Rome, resulting from the col- boration of many artists and architects of di erent backgrounds, the challenge faced by the hybrid system community is to harmonize and extract the best from two main research areas: computer science and control theory.

This book constitutes the refereed proceedings of the Third International Workshop on Hybrid Systems: Computation and Control, HSCC 2000, held in Pittsburgh, PA, USA in March 2000.; The 32 revised full papers presented together with abstracts of four invited talks were carefully reviewed and selected from a total of 71 papers submitted.; The focus of the works presented is on modeling, control, synthesis, design and verification of hybrid systems.; Among the application areas covered are control of electromechanical systems, air traffic control, control of automated freeways, and chemical process control.

This book constitutes the refereed proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control, HSCC 2002, held in Stanford, California, USA, in March 2002. The 33 revised full papers presented were carefully reviewed and selected from 73 submissions. All current issues in hybrid systems are addressed including formal models and methods and computational representations, algorithms and heuristics, computational tools, and innovative applications.

This book documents the scientific outcome of the Third International Workshop on Hybrid Systems, held in Ithaca, NY, USA, in October 1994. It presents a selection of carefully reviewed and revised full papers chosen from the workshop contribution and is the successor to LNCS 736, the seminal "Hybrid Systems" volume edited by Grossman, Nerode, Ravn, and Rischel. Hybrid systems are models for networks of digital and continuous devices, in which digital control programs sense and supervise continuous and discrete plants governed by differential or difference equations. The investigation of hybrid systems is creating a new and fascinating discipline bridging mathematics, computer science, and control engineering.

Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.