Viability of Hybrid Systems: A Controllability Operator Approach

Viability of Hybrid Systems: A Controllability Operator Approach

by G. Labinaz, M. Guay


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Product Details

ISBN-13: 9789400737105
Publisher: Springer Netherlands
Publication date: 11/29/2013
Series: Intelligent Systems, Control and Automation: Science and Engineering , #55
Edition description: 2012
Pages: 246
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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 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.

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