System theory for system identification

Journal of Econometrics

Volumn 118, Issue 1-2, 2004, Pages 313-339

  Van Schuppen, Jan H ^a  

^a CWI   (Netherlands)

Author keywords

Computation and complexity; Control; Realization; System identification; System theory

Indexed keywords

ABSTRACTING; COMPUTATIONAL COMPLEXITY; HIERARCHICAL SYSTEMS; LINEAR ALGEBRA; MATHEMATICAL MODELS; PREDICTIVE CONTROL SYSTEMS; PROBLEM SOLVING; SYSTEM THEORY;

DYNAMIC SYSTEMS;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 0346724429     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(03)00145-3     Document Type: Article

References (68)

1. Alur R., Dill D.L. A theory of timed automata. Theoretical Computer Science. 126:1994;183-235.
2. Antoulas A.C., Willems J.C. A behavioral approach to linear exact modeling. IEEE Transactions on Automatic Control. 38:1993;1776-1802.
3. Berman A., Plemmons R.J. Nonnegative Matrices in the Mathematical Sciences. 1979;Academic Press, New York.
4. Berman, A., Neumann M., Stern R.J. Nonnegative Matrices in Dynamic Systems. 1989;Wiley, New York.
5. Birkhoff G., MacLane A. A Survey of Modern Algebra. 4th Edition:1977;MacMillan Publ. Co. Inc. New York.
6. Blondel V., Tsitsiklis J.N. NP-Hardness of some linear control design problems. SIAM Journal on Control and Optimization. 35:1997;2118-2127.
7. Blondel V.D., Tsitsiklis J.N. Complexity of stability and controllability of elementary hybrid systems. Automatica. 35:1999;479-489.
8. Blum L., Cucker F., Shub M., Smale S. Complexity and Real Computation. 1997;Springer, New York.
9. Brockett, R.W., 1980. Remarks on finite dimensional nonlinear estimation. In: Lobry, C. (Ed.), Analyse des systèmes, in Astérisque 75-76 (Société Mathématique de France, pp. 47-55).
10. Cheng A., Nielsen M. Open maps, behavioural equivalences, and congruences. Theoretical Computer Sciences. 190:1998;87-112.
11. Cox D.A., Little J.B., O'Shea D.B. Using Algebraic Geometry. 1998;Springer, Berlin.
12. Dasgupta, B., Sontag, E.D., 1998. A polynomial-time algorithm for an equivalence problem which arises in hybrid systems theory. Report, Department of Mathematics, Rutgers University, New Brunswick, NJ, USA.
13. Davey B.A., Priestley H.A. Introduction to Lattices and Order. 1990;Cambridge University Press, Cambridge.
14. Davis P.J. Circulant Matrices. 1979;Wiley, New York.
15. Fuhrmann P.A. A Polynomial Approach to Linear Algebra. 1996;Springer, Berlin.
16. Gantmacher, F.R., 1959. The Theory of Matrices, Vol. 1, 2. Chelsea Publ. Co., New York.
17. Garey M.R., Johnson D.S. Computers and intractability: a Guide to the Theory of NP-Completeness. 1979;W.H. Freeman and Company, New York.
18. Goldstein L.J. Abstract Algebra: A First Course. 1973;Prentice-Hall Inc. Englewood Cliffs, NJ.
19. Goldreich D. Computational complexity. Engquist B., Schmid W. Mathematics Unlimited - 2001 and beyond. 2001;507-524 Springer, Berlin.
20. Gondran M., Minoux M. Linear algebra in dioids. a survey of recent results Annals of Discrete Mathematics. 19:1984;147-164.
21. Habets, L.C.G.J.M., Van Schuppen, J.H., 2000. A control problem for affine dynamical systems on a full-dimensional simplex. Report PNA-R0017, CWI, Amsterdam.
22. Habets L.C.G.J.M., Van Schuppen J.H. Control of piecewise-linear hybrid system on simplices and rectangles. Di Benedetto M.D., Sangiovanni-Vincentelli A. Hybrid Systems; Computation and Control. 2001;261-274 Springer, Berlin.
23. Habets, L.C.G.J.M., Van Schuppen, J.H., 2002. Reduction of affine systems on polytopes. In Proceedings of the International Symposium MTNS.
24. Halmos P.R. Finite-Dimensional Vector Spaces. 1993;Springer, New York.
25. Heinrich R., Schuster S. The Regulation of Cellular Systems. 1996;Chapman and Hall, New York.
26. Hopcroft J.E., Ullman J.D. Introduction to Automata Theory, Languages, and Computation. 1979;Addison-Wesley Publishing Company, Reading, MA.
27. Inan K. On a class of timer hybrid systems reducible to finite state automata. Discrete Event Dynamics Systems. 4:1995;83-96.
28. Jacobson, N., 1980. Basic Algebra, Vol. 2. W.H. Freeman and Company, New York.
29. Jacobson, N., 1985. Basic Algebra, Vol. 1, 2nd Edition. W.H. Freeman and Company, New York.
30. Jacobs B. Categorical Logic and Type Theory. 1999;Elsevier, Amsterdam.
31. Kalman R.E. Mathematical description of linear dynamical systems. SIAM Journal on Control. 1:1963;152-192.
32. Kalman R.E. When is a linear control system optimal? Journal of Basic Engineering. 86:1964;51-60.
33. Kalman R.E., Falb P.L., Arbib M.A. Topics in Mathematical Systems Theory. 1969;McGraw-Hill Book Co. New York.
34. Kreuzer, M., Robbiano, L., 2000. Computational Commutative Algebra, Vol. 1. Springer, Berlin.
35. Lam T.-Y. Lectures on Modules and Rings. 1999;Springer, Berlin.
36. Lamouchi, H., Thistle, J., 2000. Effective control synthesis for des under partial observations. In Proceedings of the 40th IEEE Conference on Decision and Control. IEEE Press, New York.
37. Liu R., Suen L.-C. Minimal dimension realization and identifiability of input-output sequences. IEEE Transactions Automatic Control. 22:1997;227-232.
38. Luenberger D.G. Introduction to Dynamic Systems - Theory, Models and Applications. 1979;Wiley, New York.
39. Milner R. Communication and Concurrency. 1989;Prentice-Hall, Englewood Cliffs, NJ.
40. Murota K. Systems Analysis by Graphs and Matroids - Structural Solvability and Controllability. 1987;Springer, Berlin.
41. Murota K. Matrices and Matroids for Systems Analysis. 1999;Springer, Berlin.
42. Nielsen M., Joyal A., Winskel G. Bisimulation from open maps. Information and Computation. 127:1997;164-185.
43. Polderman J.W., Willems J.C. Introduction to Mathematical System Theory - A Behavioral Approach. 1997;Springer, New York.
44. Ramadge, P.J.G., Wonham, W.M., 1989. The control of discrete event systems. Proceedings of the IEEE 77, 81-98.
45. Ricker, S.L., Van Schuppen, J.H., 2001. Decentralized failure diagnosis with asynchronous communication between supervisors. In Proceedings of the European Control Conference (ECC2001), pp. 1002-1006.
46. Rutten, J.J.M.M., 1996. Universal coalgebra: a theory of systems. Report CS-R9652, CWI, Amsterdam.
47. Rutten, J.J.M.M., 1999. Coalgebra, concurrency, and control. Report SEN-R9921, CWI, Amsterdam.
48. Sipser M. Introduction to the Theory of Computation. 1997;PWS Publishing Company, Boston.
49. Sampath M., Sengupta R., Lafortune S., Sinnamohideen K., Teneketzis D. Diagnosability of discrete event systems. IEEE Transactions on Automatic Control. 40:1995;1555-1575.
50. Sampath, M., Lafortune, S., Teneketzis, D., 1996. A language-based approach to failure diagnosis of discrete event systems. In Proceedings International Workshop on Discrete Event Systems (WODES'96). The Institution of Electrical Engineers, London, pp. 261-271.
51. Schrijver A. Theory of Linear and Integer Programming. 1986;Wiley, New York.
52. Sontag E.D. Nonlinear regulation. the piecewise linear approach IEEE Transactions on Automatic Control. 26:1981;346-358.
53. Sontag E.D. Remarks on piecewise-linear algebra. Pacific Journal of Mathematics. 98:1982;183-201.
54. Sontag E.D. Mathematical Control Theory: Deterministic Finite Dimensional Systems. 2nd Edition:1998;Springer, New York.
55. Tanaka, R., Murato, K., 2000. Symmetric failures in symmetric control systems. In Proceedings of the International Symposium MTNS, Université de Perpignan, Perpignan, France.
56. Tsitsiklis J.N. On the control of discrete-event systems. Mathematics of Control, Signals, and Systems. 2:1989;95-107.
57. Van den Hof, J.M., 1996. System theory and system identification of compartmental systems. Ph.D. Thesis, University of Groningen, Groningen.
58. Van den Hof J.M. Structural identifiability of linear compartmental systems. IEEE Transactions on Automatic Control. 43:1998;800-818.
59. Van der Woude J.W. A graph-theoretic characterization for the rank of a transfer matrix of a structured system. Mathematics of Control, Signals, and Systems. 4:1991;33-40.
60. Van der Woude J.W. The generic number of invariant zeros of a structured linear system. SIAM Journal on Control and Optimization. 38:1999;1-21.
61. Van der Woude J.M., Murota K. Disturbance decoupling with pole placement for structured systems. SIAM Journal of Matrix Analysis and Applications. 162:1995;922-942.
62. Wechler W. Universal Algebra for Computer Scientists. 1992;Springer, Berlin.
63. Willems J.C. From time series to linear systems - Part I. finite dimensional linear time invariant systems. Automatica. 22:1986;561-580.
64. Willems J.C. From time series to linear systems - Part II. exact modelling. Automatica. 22:1986;675-694.
65. Willems J.C. From time series to linear systems - Part III. approximate modelling. Automatica. 23:1987;87-115.
66. Wong, K.C., 1998. On the complexity of projections of discrete-event systems. In Proceedings of the International Workshop on Discrete-Event Systems (WODES'98). IEE, London, pp. 201-206.
67. Wong K.C., Wonham W.M. Hierarchical control of discrete-event systems. Discrete Event Dynamic Systems. 6:1996;241-273.
68. Wong, K.C., Wonham, W.M., 2000. On the computation of observers in discrete-event systems. Conference on Information Sciences and Systems.