Linear time logic control of discrete-time linear systems

IEEE Transactions on Automatic Control

Volumn 51, Issue 12, 2006, Pages 1862-1877

  Tabuada, Paulo ^a,b   Pappas, George J ^c  

^a University of Notre Dame   (United States)

^b University of California   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Automatic synthesis; Discrete time; Hybrid systems; Linear control systems; Linear time logic

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONTROL THEORY; DISCRETE TIME CONTROL SYSTEMS; LARGE SCALE SYSTEMS; LOGIC CIRCUITS;

AUTOMATIC SYNTHESIS; HYBRID SYSTEMS; LINEAR TIME LOGIC;

LINEAR SYSTEMS;

EID: 33745708511     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.886494     Document Type: Article

References (66)

1. B. Dutertre and V. Stavridou, "Formal requirements analysis of an avionics control system," IEEE Trans. Software Eng., vol. 23, no. 5, pp. 267-278, Oct. 1997.
2. M. Lansdaal and L. Lewis, "Boeing's 777 systems integration lab," IEEE Instrum. Meas. Mag., vol. 3, no. 3, pp. 13-18, Mar. 2000.
3. J. Teutsch and E. Hoffman, "Aircraft in the future ATM system - Exploiting the 4D aircraft trajectory," in Proc. 23rd Digital Avionics Syst. Conf., 2004, vol. 1, pp. 3.B.2.1-3.B.2.22.
4. J. Cook, S. Jing, and J. Grizzle, "Opportunities in automotive power-train control applications," in Proc. 2002 Int. Conf. Control Appl., 2002, pp. xlii-li.
5. Z. Sun and K. Hebbale, "Challenges and opportunities in automotive transmission control," in Proc. Amer. Control Conf., 2005, pp. 3284-3289.
6. J. Khurshid and H. Bing-Rong, "Military robots - A glimpse from today and tomorrow," in Proc. 8th Control, Automation, Robotics Vision Conf., 2004, pp. 771-777.
7. C. Morris, S. Stauth, and B. Parviz, "Self-assembly for microscale and nanoscale packaging: Steps toward self-packaging," IEEE Trans. Adv. Packag., vol. 28, no. 4, pp. 600-611, Nov. 2005.
8. P. Dario, M. Carrozza, E. Guglielmelli, C. Laschi, A. Menciassi, S. Micera, and F. Vecchi, "Robotics as a future and emerging technology: Biomimetics, cybernetics, and neuro-robotics in european project," IEEE Robot. Automat. Mag., vol. 12, no. 2, pp. 29-45, Feb. 2005.
9. T. A. Henzinger, P. W. Kopke, A. Puri, and P. Varaiya, "What's decidable about hybrid automata?," J. Comput. Syst. Sci., vol. 57, pp. 94-124, 1998.
10. Z. Manna and A. Pnueli, The Temporal Logic of Reactive and Concurrent Systems: Specification. Berlin, Germany: Springer-Verlag, 1992.
11. E. M. M. Clarke, D. Peled, and O. Grumberg, Model Checking. Cambridge, MA: MIT Press, 1999.
12. K. L. McMillan, Symbolic Model Checking. Norwell, MA: Kluwer, 1993.
13. S. Tripakis, "Undecidable problems in decentralized observation and control for regular languages," Inform. Process. Lett., vol. 90, no. 1, pp. 21-28, 2004.
14. R. Alur and D. Dill, "A theory of timed automata," Theoret. Comput. Sci., vol. 126, pp. 183-235, 1994.
15. R. Alur, C. Courcoubetis, N. Halbwachs, T. Henzinger, P. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine, "Hybrid automata: An algorithmic approach to specification and verification of hybrid systems," Theoret. Comput. Sci., vol. 138, pp. 3-34, 1995.
16. A. Puri and P. Varaiya, "Decidability of hybrid systems with rectangular inclusions," Comput. Aided Verif., pp. 95-104, 1994.
17. T. Henzinger and R. Majumdar, "Symbolic model checking for rectangular hybrid systems," in TACAS 2000: Tools and Algorithms for the Construction and Analysis of Systems, ser. Lecture Notes in Computer Science, S. Graf, Ed. New York: Springer-Verlag, 2000.
18. G. Lafferriere, G. J. Pappas, and S. Sastry, "O-minimal hybrid systems," Math. Control, Signals Syst., vol. 13, no. 1, pp. 1-21, Mar. 2000.
19. R. Alur, T. A. Henzinger, G. Lafferriere, and G. J. Pappas, "Discrete abstractions of hybrid systems," Proc. IEEE, vol. 88, no. 7, pp. 971-984, Jul. 2000.
20. M. Broucke, "A geometric approach to bisimulation and verification of hybrid systems," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, F. W. Vaandrager and J. H. van Schuppen, Eds. New York: Springer-Verlag, 1999, vol. 1569, pp. 61-75.
21. J. Stiver, X. Koutsoukos, and P. Antsaklis, "An invariant based approach to the design of hybrid control systems," Int. J. Robust Nonlinear Control, vol. 11, no. 5, pp. 453-478, 2001.
22. E. Asarin, G. Schneider, and S. Yovine, "On the decidability of the reachability problem for planar differential inclusions," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, M.D. D. Benedetto and A. Sangiovanni-Vincentelli, Eds. New York: Springer-Verlag, 2001, vol. 2034, pp. 89-104.
23. A. Chotinan and B. Krogh, "Verification of infinite state dynamical systems using approximate quotient transition systems," IEEE Trans. Autom. Control, vol. 46, no. 9, pp. 1401-1410, Sep. 2001.
24. J. Cury, B. Krogh, and T. Ninomi, "Synthesis of supervisory controllers for hybrid systems based on approximating automata," IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 564-568, Apr. 1998.
25. A. Tiwari and G. Khanna, "Series of abstractions for hybrid automata," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, C. Tomlin and M. R. Greenstreet, Eds. New York: Springer-Verlag, 2002, vol. 2289, pp. 465-478.
26. A. Bicchi, A. Marigo, and B. Piccoli, "On the reachability of quantized control systems," IEEE Trans. Autom. Control, vol. 47, no. 4, pp. 546-563, Apr. 2002.
27. S. Pancanti, L. Leonardi, L. Pallottino, and A. Bicchi, "Optimal control of quantized linear systems," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Sience, C. Tomlin and M. R. Greenstreet, Eds. New York: Springer-Verlag, 2002, pp. 351-363.
28. Y. Chitour and B. Piccoli, "Controllability for discrete systems with a finite control set," Math. Control, Signals Syst., vol. 14, no. 2, pp. 173-193,2001.
29. N. Elia and S. K. Mitter, "Stabilization of linear systems with limited information," IEEE Trans. Autom. Control, vol. 46, no. 9, pp. 1384-1400, Sep.2001.
30. R. W. Brockett and D. Liberzon, "Quantized feedback stabilization of linear systems," IEEE Trans. Autom. Control, vol. 45, no. 7, pp. 1279-1289, Jul. 2000.
31. M. Antoniotti and B. Mishra, "Discrete-event models + temporal logic = supervisory controller: Automatic synthesis of locomotion controllers," in Proc. IEEE Int. Conf. Robotics Automation, 1995, pp. 1441-1446.
32. T. Moor and J. M. Davoren, "Robust controller synthesis for hybrid systems using modal logic," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, M. D. D. Benedetto and A. Sangiovanni-Vincentelli, Eds. New York: Springer-Verlag, 2001, vol. 2034.
33. L. Habets and J. H. van Schuppen, "Control of piecewise-linear hybrid systems on simplices and rectangles," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Sience, M. D. D. Benedetto and A. Sangiovanni-Vincentelli, Eds. New York: Springer-Verlag, 2001, vol. 2034, pp. 261-274.
34. R. Vidal, S. Schaffert, O. Shakernia, J. Lygeros, and S. Sastry, "Decidable and semi-decidable controller synthesis for classes of discrete time hybrid systems," in Proc. 40th IEEE Conf. Decision Control, Orlando, FL, Dec. 2001, pp. 1243-1248.
35. P. J. Ramadage and W. M. Wonham, "The control of discrete event systems," Proc. IEEE, vol. 77, no. 1, pp. 81-98, Jan. 1989.
36. R. Kumar and V. Garg, Modeling and Control of Logical Discrete Event Systems. Norwell, MA: Kluwer, 1995.
37. C. Cassandras and S. Lafortune, Introduction to Discrete Event Systems. Norwell, MA: Kluwer, 1999.
38. S. Jiang and R. Kumar, "Supervisory control of discrete event systems with CTL* temporal logic specifications," in Proc. 40th IEEE Conf. Decision Control, Orlando, FL, Dec. 2001, vol. 5, pp. 4122-4127.
39. J. S. Ostroff, Temporal Logic for Real-Time Systems. New York: Wiley, 1989.
40. E. A. Emerson and E. M. Clarke, "Using branching time temporal logic to synthesize synchronization skeletons," Sci. Comput. Program., vol. 2, pp. 241-266, 1982.
41. Z. Manna and P. Wolper, "Synthesis of communication processes from temporal logic specifications," ACM Trans. Program. Lang. Syst., vol. 6, pp. 68-93, 1984.
42. P. Madhusudan and P. Thiagarajan, "Branching time controllers for discrete event systems," Theoret. Comput. Sci., vol. 274, pp. 117-149, Mar. 2002.
43. P. Madhusudan and P. Thiagarajan, "A decidable class of asynchronous distributed controllers," in Proc. 13th Int. Conf. Concurrency Theory, L. Brim, M. Kret'ýsk'y, and A. Kucera, Eds., 2002, vol. 2421, pp. 145-160.
44. I. Castellani, M. Mukund, and P. Thiagarajan, "Synthesizing distributed transition systems from global specifications," in Proc. Foundations Software Technology Theoretical Computer Science, 1999, vol. 1739, pp. 219-231.
45. L. de Alfaro, T. A. Henzinger, and F. Y. C. Mang, "The control of synchronous systems," in 11th Int. Conf. Concurrency Theory, C. Palamidessi, Ed., 2000, vol. 1877, pp. 458-473.
46. L. de Alfaro, T. A. Henzinger, and F. Y. C. Mang, "The control of synchronous systems, Part ii," in Proc. 12th Int. Conf. Concurrency Theory, K. G. Larsen and M. Nielsen, Eds., 2001, vol. 2154, pp. 566-582.
47. M. Faella, S. L. Torre, and A. Murano, "Dense real-time games," in Proc. 17th Annu. IEEE Symp. Logic Comput. Sci., Copenhagen, Denmark, Jul. 2002, pp. 167-176.
48. Y. Abdeddaim and O. Maler, "Preemptive job-shop scheduling using stopwatch automata," in Proc. Tools Algorithms Construction Analysis Syst., 2002, vol. 2280, pp. 113-126.
49. G. Behrmann, A. Fehnker, T. Hune, K. G. Larsen, P. Pettersson, J. Romijn, and F. W. Vaandrager, "Minimum-cost reachability for priced timed automata," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, M. D. D. Benedetto and A. Sangiovanni-Vincentelli, Eds. New York: Springer-Verlag, 2001, vol. 2034, pp. 147-161.
50. R. Alur, S. L. Torre, and G. Pappas, "Optimal paths in weighted timed automata," in Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, M. D. D. Benedetto and A. Sangiovanni-Vincentelli, Eds. New York: Springer-Verlag, 2001, vol. 2034, pp. 49-62.
51. D. D. Souza and P. Madhusudan, "Timed control synthesis for external specifications," in Proc. 19th Annu. Symp. Theoretical Aspects Computer Science, H. Alt and A. Ferreira, Eds., 2002, vol. 2285, pp. 571-582.
52. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages and Computation. Reading, MA: Addison-Wesley, 1979.
53. R. Milner, Communication and Concurrency. Upper Saddle River, NJ: Prentice-Hall, 1989.
54. M. Browne, E. Clarke, and O. Grumberg, "Characterizing finite Kripke structures in propositional temporal logic," Theoret. Comput. Sci., vol. 59, pp. 115-131, 1988.
55. P. Brunovsky, "A classification of linear controllable systems," Kybernetika, vol. 6, no. 3, pp. 173-188, 1970.
56. R. E. Kalman, "Kronecker invariants and feedback," in Ordinary Differential Equations, L. Weiss, Ed. New York: Academic, 1972, pp. 459-471.
57. A. Bouajjani, J. Fernandez, and N. Halbwachs, "Minimal model generation," in CAV90: Computer Aided Verification, ser. Lecture Notes in Computer Science, R. Kurshan and E. M. Clarke, Eds. New York: Springer-Verlag, 1990, vol. 531, pp. 197-203.
58. P. Kanellakis and S. Smolka, "CCS expressions, finite-state processes, and three problems of equivalence," Inform. Comput., vol. 86, pp. 43-68, 1990.
59. J. Bochnak, M. Coste, and M.-F. Roy, Real Algebraic Geometry. New York: Springer-Verlag, 1998.
60. J. R. Buchi, "On a decision method in restricted second order arithmetic," in Proc. Internat. Congr. Logic, Method and Philos. Sci., Stanford, CA, 1962, pp. 1-12, Stanford Univ. Press.
61. P. Wolper, "Constructing automata from temporal logic formulas: A tutorial," in Lectures on Formal Methods and Performance Analysis, ser. Lecture Notes in Computer Science, E. Brinksma, H. Hermanns, and J. P. Katoen, Eds. New York: Springer-Verlag, 2000, vol. 2090.
62. F. Somenzi and R. Bloem, "Efficient buchi automata from ltl formulae," in Proc. 12th Int. Conf. Computer Aided Verification, E. A. Emerson and A. P. Sistla, Eds., 2000, vol. 1855, pp. 248-263.
63. R. Gerth, D. Peled, M. Y. Vardi, and P. Wolper, "Simple on-the-fly automatic verification of linear temporal logic," in Proc. 15th IFIP Workshop Protocol Specification, Testing and Verification, P. Dembinski and M. Sredniawa, Eds., Warsaw, Poland, Jun. 1996, pp. 3-18.
64. P. Ramadge, "Some tractable supervisory control problems for discrete event systems modeled by Buchi automata," IEEE Trans. Autom. Control, vol. 34, no. 1, pp. 10-19, Jan. 1989.
65. R. Kumar, V. Garg, and S. Markus, "On supervisory control of sequential behaviors," IEEE Trans. Autom. Control, vol. 37, no. 12, pp. 1978-1985, Dec. 1992.
66. J. Thistle and W. M. Wonham, "Supervision of infinite behavior of discrete-event systems," SIAM J. Control Optim., vol. 32, no. 4, pp. 1098-1113, Jul. 1994.