Viability of Hybrid Systems A Controllability Operator Approach [Hardcover]

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 book covers design and testing of hybrid systems. Includes a model incorporating transition dynamics, structural uncertainty, and parametric uncertainty; an approach for robust viability based on two extensions of the controllability operator, and more.

1 Introduction.- ?1.1 Motivation and History.- ?1.2 Summary and Organization.- ?1.3 Summary.- ?2 Literature Review.- ?2.1 Nerode et al Approach to Viability of Hybrid Systems [50],[71].- ?2.2 Aubin et al Approach to Viability of Hybrid

Systems [15].- ?2.3 Deshpande{Varaiya Approach to Viability of Hybrid Systems [35].- ?2.4 Related Literature.- ?2.5 Conclusion.- ?3 Hybrid Model.- ?3.1 Hybrid Phenomena and Hybrid Model.- ?3.2 Hybrid Trajectories and their Ordering.- ?3.3 Continuity, Fixed Points, and Correct Finite Control Automaton.- ?3.4 Uncertainty in Hybrid Systems.- ?3.5 The Three-Tank Problem.- ?3.6 Nerode{Kohn Formalism for Hybrid Systems.- ?3.7 Conclusion.- ?4 Viability.- ?4.1 Background.- ?4.2 Time{Independent Viability Set.- ?4.3 Fil³