Symbolic verification of hybrid systems: An algebraic approach

European Journal of Control

Volumn 7, Issue 5, 2001, Pages 541-556

  Mohrenschildt, Martin V ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Computer algebra; Differential equations; Hybrid system design; Hybrid systems; Symbolic solutions; System verification

Indexed keywords

EID: 0005581379     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.7.541-556     Document Type: Article

References (21)

1. Alur R, Coucoubetis C, Halbwachs N, Henzinger TA, Ho PH, Nicolin X, Olivero A, Sifakis J, Yovine S. "The Algorithmic Analysis of Hybrid Systems", Theor Comput Sci 1995; 138: 3-34
2. Alur R, Henzinger TA, Ho PH. Automatic symbolic verification of embedded systems. In: Proceedings of the 14th Annual IEEE real-time systems symposium (RTSS) 1993, pp 2-11
3. Bronstein M. The transcendental risch differential equation. J Symbol Computation, 1990; 9: 49-60
4. Henzinger TA. The theory of hybrid automata. In: 11th Annual IEEE symposium on logic in computer science (LICS) 96, 278-292
5. Filipoph P. Differential equations with discontinuous right-hand side. Mathematics and its Applications. Kluwer, ISBN 90-277-2699-X
6. Branicky MS. A unified framework for hybrid control: model and optimal control theory. IEEE Trans Auto Control 1998; 43(1)
7. Nicollin X, Olivero A, Sifakis J, Yovine S. An approach to the description and analysis of hybrid systems, Lecture Notes in Computer Science 1993; 736: 149-178
8. Mohrenschildt Mv. A normal form for rings of piecewise functions. J Symbolic Computation 1998; 26: 607-619
9. Mohrenschildt Mv. Using piecewise to solve classes of control theory problems. MapleTech 1997; 4(3): 33-37
10. Mohrenschildt Mv. Solving discontinuous differential equations. In: (eds). The Combinatory Program, Engeler E, Birkhauser, pp 98-116
11. Mohrenschildt Mv. Solving discontinuous ordinary differential equations with a computer algebra system, submitted to J Symbolic Computation
12. Hybrid Systems, Lecture Notes in Computer Science (736)
13. Clarke FH. et al. Non-smooth analysis and control theory. Springer, ISBN 0-387-98336-8
14. Kesten Y, Pnueli A, Sifakis J, Yovine S. Decidable integration graphs: a class of decidable hybrid systems. Information and Computation, 1999; 150: 209-243
15. Kurki-Suonio R. Hybrid models with fairness and distributed clocks, Lecture Notes in Computer Science 1993, 736, pp 103-120
16. Nicollin X, Sifakis J, Yovine S. Compiling real-time specifications into extended automata. IEEE TSE Real-Time Systems 1992; 18(9): 794-804
17. Singer MF. Formal solutions of differential equations. J Symbolic Computation 1990; 10: 59-94
18. Kapur D, Shyamasundar RK. Synthesizing controllers for hybrid systems. Hybrid and Real Time Systems, HART'97, Lecture Notes in Computer Science 1201, Springer-Verlag, 1997; 361-375
19. Pappas G, Lafferriere G, Yovine S. A new class of decidable hybrid systems, Hybrid Systems: Computation and Control, Lecture Notes in Computer Science 1569, HS'99, Nijmegen, The Netherlands, March 1999, 137-152
20. Manna Z, Sipma H. Deductive verification of hybrid systems using STeP, HSCC 98, Lecture Notes in Computer Science 1386, 1998; 305-318
21. Alur R, Henzinger A, Lafferriere G, Pappas GJ. Discrete Abstraction of Hybrid Systems. Proceedings of the IEEE, 2000; 88(2): 971-984