Control of piecewise-linear hybrid systems on simplices and rectangles

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2034, Issue , 2001, Pages 261-274

  Habets, Luc C G J M ^a,b   van Schuppen, Jan H ^a  

^a CWI   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Control law; Facet; Multi dimensional rectangle; Piecewise linear hybrid systems; Polyhedral set; Reachability; Simplex

Indexed keywords

DISCRETE EVENT SIMULATION; GEOMETRY; HYBRID SYSTEMS; LINEAR SYSTEMS; STATE FEEDBACK;

CONTROL LAWS; FACET; MULTI DIMENSIONAL; PIECEWISE LINEAR; POLYHEDRAL SET; REACHABILITY; SIMPLEX;

PIECEWISE LINEAR TECHNIQUES;

EID: 84944201228     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45351-2_23     Document Type: Conference Paper

References (21)

1. E. Asarin, O. Bournez, T. Dang, and O. Maler. Approximate reachability analysis of piecewise-linear hybrid systems. In N. Lynch and B.H. Krogh, editors, Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science, pages 20-31, Berlin, 2000. Springer-Verlag.
2. A. Bemporad, G. Ferrari-Trecate, and M. Morari. Observability and controllability of piecewise affine and hybrid systems. In Proceedings of the 38th IEEE Conference on Decision and Control, pages 3966-3971, New York, 1999. IEEE Press.
3. A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints. Automatica, 35:407-427, 1999.
4. L. Berardi, E. De Santis, and M.D. Di Benedetto. Control of switching systems under state and input constraints. In Proc. European Control Conference (ECC99), 1999.
5. M.S. Branicky. Studies in hybrid systems: Modeling, analysis, and control. PhD thesis, M.I.T., Cambridge, MA, 1995.
6. E.B. Castelan and J.C. Hennet. On invariant polyhedra of continuous-time linear systems. IEEE Trans. Automatic Control, 38:1680-1685, 1993.
7. L.C.G.J.M. Habets and J.H. van Schuppen: A control problem for affine dynamical systems on a full-dimensional simplex. Report PNA-R0017, CWI, Amsterdam, 2000. www.cwi.nl/ftp/CWIreports/PNA/PNA-R0017.ps.Z
8. B. Jeannet. Convex polyhedra library. Report, Verimag, Université Joseph Fourier, Grenoble, 1999.
9. G. Lafferriere, G.J. Pappas, and S. Sastry. Subanalytic stratifications and bisimulations. In T.A. Henzinger and S. Sastry, editors, Hybrid systems: Computation and control, volume 1386 of Lecture Notes in Computer Science, pages 205-220, Berlin, 1998. Springer-Verlag.
10. G. Lafferriere, G. Pappas, and S. Sastry: O-minimal hybrid systems. Math. Control Signals Systems, 13:1-21, 2000.
11. C.W. Lee. Subdivisions and triangulations of polytopes. In J.E. Goodman and J. O'Rourke, editors, Handbook of discrete and computational geometry, pages 271-290. CRC Press, Boca Raton, NY, U.S.A., 1997.
12. N. Lynch and B.H. Krogh: Hybrid Systems: Computation and Control. Volume 1790 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2000.
13. R.T. Rockafellar. Convex analysis. Princeton University Press, Princeton, 1970.
14. E.D. Sontag. Nonlinear regulation: The piecewise linear approach. IEEE Trans. Automatic Control, 26:346-358, 1981.
15. E.D. Sontag. Remarks on piecewise-linear algebra. Pacific J. Math., 98:183-201, 1982.
16. E.D. Sontag: Interconnected automata and linear systems: A theoretical framework in discrete-time. In R. Alur, T.A. Henzinger, and E.D. Sontag, editors, Hybrid Systems III: Verification and Control, volume 1066 of Lecture Notes in Computer Science, pages 436-448, Berlin, 1996. Springer-Verlag.
17. F.W. Vaandrager and J.H. van Schuppen, editors. Hybrid systems: Computation and control (HSCC'99). Volume 1569 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1999.
18. J.H. van Schuppen. Control for a class of hybrid systems. Report PNA-R9716, CWI, Amsterdam, 1997. www.cwi.nl/ftp/CWIreports/PNA/PNA-R9716.ps.Z
19. J.H. van Schuppen. A sufficient condition for controllability of a class of hybrid systems. In T.A. Henzinger and S. Sastry, editors, Hybrid systems: Computation and control, volume 1386 of Lecture Notes in Computer Science, pages 374-383, Berlin, 1998. Springer-Verlag.
20. M. Vassilaki and G. Bitsoris. Constrained regulation of linear continuous-time dynamical systems. Systems & Control Lett., 13:247-252, 1989.
21. G.M. Ziegler. Lectures on polytopes. Volume 152 of Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1995.