Viability of Hybrid Systems

<p>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</p><p>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 Fixed Point Approximation.-  4.4 Computation of TIC{COFPAA{I for Three Admissible Control Law Classes.-  4.4.1 Piecewise Constant Control.-  4.4.2 Piecewise Constant with Finite Switching.-  4.4.3 Piecewise Constant with Polynomial Control.-  4.5 Time{Dependent Viability Set.-  4.5.1 Piecewise Constant Control.-  4.6 Examples.-  4.6.1 Time{Independent Constraints.-  4.6.2 Time{Dependent Constraints.-  4.7 Conclusion.-  5 Robust Viability.-  5.1 Uncertainty and Robustness.-  5.2 Ordering of the Controllability Operator under Uncertainty.-  5.3 The Uncertain Controllability Operator and the Uncertainty Operator.-  5.4 Robust Viability.-  5.5 Robust Viability Control Design.-  5.6 Examples.-  5.7 Conclusion.-  6 Viability in Practice.-  6.1 Reachable Set Computation of the Controllability Operator.-  6.2 Viable Cascade Control and Application to a Batch Polymerization Process [55][56].-  6.2.1 Batch Polymerization Process Model.-  6.2.2 Hybrid Model.-  6.2.3 Viable Cascade Control.-  6.2.4 Batch Polymerization Control.-  6.2.5 Discussion and Conclusions.-  6.2.6 Appendix.-  6.3 Conclusion.-  7 An Operator Approach to Viable Attainability of Hybrid Systems [60].-  7.1 Introduction.-  7.2 Attainability and the Attainability Operator.-  7.3 Viable Attainability and the Viable Attainability Operator.-  7.4 Simulation Examples.-  7.5 Conclusion.-  8 Some Topics Related to the Controllability Operator.-  8.1 Topological Continuity Arising from Fixed Point Approximation Algorithm.-  8.2 The Lattice over Control Laws of the Controllability Operator.-  8.3 Homotopic Approximation under PWC_.- k.-  PWCPC_.- k.-  8.4 Conclusion.-  9 Conclusions.-  References.</p>