Adaptive control of infinite-dimensional systems without parameter estimation: An overview

IMA Journal of Mathematical Control and Information

Volumn 14, Issue 2, 1997, Pages 175-206

  Logemann, Hartmut ^a   Townley, Stuart ^b  

^a UNIVERSITY OF BATH   (United Kingdom)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Adaptive control; Frequency domain methods; Infinite dimensional systems; Nonlinear controllers; Stabilization; State space methods; Tracking

Indexed keywords

CONTROL EQUIPMENT; FREQUENCY DOMAIN ANALYSIS; NONLINEAR CONTROL SYSTEMS; PROBLEM SOLVING; STATE SPACE METHODS;

INFINITE DIMENSIONAL SYSTEMS;

ADAPTIVE CONTROL SYSTEMS;

EID: 0030647566     PISSN: 02650754     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamci/14.2.175     Document Type: Review

References (84)

1. BYRNES, C. I., 1987. Adaptive stabilization of infinite-dimensional linear systems, pp. 1435-1440 in Proc. 26th IEEE Conference on Decision and Control, Los Angeles.
2. BYRNES, C. I., GILLIAM, D. S. & HE, J., 1994. Root-locus and boundary feedback design for a class of distributed parameter systems, SIAM J. Control & Opt. 32, 1364-427.
3. BYRNES, C. I., & WILLEMS, J. C., 1984. Adaptive stabilization of multivariable linear systems, pp. 1574-1577 in Proc. 23rd IEEE Conference on Decision and Control, Las Vegas.
4. CALLIER, F. M., & DESOER, C. A., 1980. Stabilization, tracking and disturbance rejection in multivariable convolution systems, Annales de la Société Scientifique de Bruxelles 94, 7-51.
5. COOK, P. A. 1992. Controllers with universal tracking properties, in Proc. of Int. IMA Conf. on Control: Modelling, Computation, Information, Manchester.
6. COPPUS, G. W. M., SHA, S. L., & WOOD, R. K., 1983. Robust multivariable control of a binary distillation column, IEE Proceedings, Pt. D 130, 201-8.
7. CURTAIN, R. F., 1983. Tracking and regulation for distributed parameter systems, Matematica Aplicada e Computacional 2, 199-218.
8. CURTAIN, R. F., LOGEMANN, H., TOWNLEY, S., & ZWART, H., 1994. Well-posedness, stabilizability and admissibility for Pritchard-Salamon systems, Math. Systems, Estimation and Control 4 (summary pp. 493-496; full electronic manuscript = 38pp; retrieval code 85404 Full paper is available by anonymous ftp from trick.ntp.springer.de in the directory/jmsec.; full hardcopy to appear).
9. DAHLEH, M., 1988. Sufficient information for the adaptive stabilization of delay systems, Systems & Control Letters 11, 357-63.
10. DAHLEH, M., 1989. Generalizations of Tychonov's theorem, with applications to adaptive control of SISO delay systems, Systems & Control Letters 13, 421-7.
11. DAHLEH, M., & HOPKINS, JR. W. E., 1986. Adaptive stabilization of single-input single-output delay systems, IEEE Trans. Auto. Control 31, 577-9.
12. DAVISON, E. J., 1976. Multivariable tuning regulators: the feedforward and robust control of a general servomechanism problem, IEEE Trans. Auto. Control 21, 35-47.
13. DUNCAN, T. E., & PASIK-DUNCAN, B., 1988. Adaptive control of linear delay time systems, Stochastics 24, 45-74.
14. DUNCAN, T. E., & PASIK-DUNCAN, B., 1991. Adaptive control of linear stochastic evolution systems, Stochastics and Stochastics Reports 36, 71-90.
15. EMIRSAJLOW, Z., PRITCHARD, A. J., & TOWNLEY, S., to appear. On structured perturbations for two classes of linear infinite-dimensional systems, Dynamics and Control.
16. FERNÁNDEZ, G., ORTEGA, R., & BEGOVICH, O., 1988. Conditions for preservation of stability of adaptive controllers for systems with unmodeled delay, IEEE Trans. Auto. Control 33, 601-3.
17. FRANCIS, B. A., 1977. The multivariable servomechanism problem from the input-output viewpoint, IEEE Trans. Auto. Control 22, 322-8.
18. GRIPENBERG, G., LONDEN, S.-O., & STAFFANS, O., 1990. Volterra Integral and Functional Equations, Cambridge University Press, Cambridge.
19. GROSDIDIER, P., MORARI, M., & HOLT, B. R., 1985. Closed-loop properties from steady-state gain information, Ind. Eng. Chem. Fundam. 24, 221-35.
20. HINRICHSEN, D., & PRITCHARD, A. J., 1992. Destabilization by output feedback, Differential and Integral Equations 5, 357-86.
21. HONG, K. S., & BENTSMAN, J., 1994. Direct adaptive control of parabolic systems: algorithm synthesis and convergence and stability analysis, IEEE Trans. Auto. Control 39, 2018-33.
22. ILCHMANN, A., 1991. Non-identifier-based adaptive control of dynamical systems: a survey, IMA J. of Math. Control & Information 8, 321-66.
23. ILCHMANN, A., 1993. Non-Identifier-Based High-Gain Adaptive Control, Springer-Verlag, London.
24. ILCHMANN, A., & LOGEMANN, H., 1992. High-gain adaptive stabilization of multivariable systems, Systems & Control Letters 18, 355-364.
25. ILCHMANN, A., & RYAN, E. P., 1994. Universal λ-tracking for nonlinearly perturbed systems in the presence of noise, Automatica 30, 337-346.
26. JOHANSSON, R., 1986. Estimation and direct adaptive control of delay-differential systems, Automatica 22, 555-560.
27. JUSSILA, T. T., & KOIVO, H. N., 1987. Tuning of multivariable PI-controllers for unknown delay-differential systems, IEEE Trans. Auto. Control 32, 364-368.
28. ∞-Control for Distributed Parameter Systems, Birkhäuser Verlag, Boston.
29. KOBAYASHI, T., 1984. A digital adaptive control law for a parabolic distributed parameter system, Systems & Control Letters 4, 175-179.
30. KOBAYASHI, T., 1986. Design of robust multivariable tuning regulators for infinite-dimensional systems by discrete-time input-output data, Int. J. Control 44, 83-90.
31. KOBAYASHI, T., 1987a. Global adaptive stabilization of infinite-dimensional systems, Systems & Control Letters 9, 215-223.
32. KOBAYASHI, T., 1987b. Model reference adaptive control for spectral systems, Int. J. Control 46, 1511-1523.
33. KOBAYASHI, T., 1988. A digital PI-controller for distributed parameter systems, SIAM J. Control & Opt. 26, 1399-1414.
34. LOGEMANN, H., 1990. Adaptive exponential stabilization for a class of nonlinear retarded processes, Math. Control, Signals, and Systems 3, 255-269.
35. LOGEMANN, H., 1991. Circle criteria, small-gain conditions and internal stability for infinite-dimensional systems, Automatica 27, 677-690.
36. LOGEMANN, H., 1993. Stabilization and regulation of infinite-dimensional systems using coprime factorizations, pp. 102-139 in Analysis and Optimization of Systems: State and Frequency-Domain Approaches to Infinite-Dimensional Systems, edited by R.F. Curtain, A. Bensoussan and J.L. Lions, Springer-Verlag, Berlin.
37. LOGEMANN, H., BONTSEMA, J., & OWENS, D. H., 1988. Low-gain control of distributed parameter systems with unbounded control and observation, Control Theory and Advanced Technology 4, 429-446.
38. LOGEMANN, H., & ILCHMANN, A., 1994. An adaptive servomechanism for a class of infinite-dimensional systems, SIAM J. Control & Opt. 32, 917-936.
39. LOGEMANN, H., & MÅRTENSSON, B., 1992. Adaptive stabilization of infinite-dimensional systems, IEEE Trans. Auto. Control 37, 1869-1883.
40. LOGEMANN, H., & MÅRTENSSON, B., 1994. Adaptive stabilization of discrete-time infinite-dimensional systems, pp. 767-768 in Systems and Networks: Mathematical Theory and Applications, vol. II, edited by U. Helmke, R. Mennicken and J. Saurer, Akademie Verlag, Berlin.
41. LOGEMANN, H., & OWENS, D. H., 1987. Robust high-gain feedback control of infinite-dimensional minimum-phase systems, IMA J. Math. Control & Information 4, 195-220
42. LOGEMANN, H., & OWENS, D. H., 1988. Input-output theory of high-gain adaptive stabilization of infinite-dimensional systems with nonlinearities, Int. J. Adaptive Control and Signal Processing 2, 193-216.
43. LOGEMANN, H., & OWENS, D. H., 1989. Low-gain control of unknown infinite-dimensional systems: a frequency-domain approach, Dynamics and Stability of Systems 4, 13-29.
44. LOGEMANN, H., & OWENS, D. H., 1992. On high-gain adaptive stabilization of infinite-dimensional systems with nonlinearities, pp. 303-317 in The Mathematics of Control Theory, edited by D.H.Owens and N.K. Nichols, Oxford University Press, Oxford.
45. † SIAM J. Control & Opt. 35, 78-116.
46. LOGEMANN, H., & TOWNLEY, S., 1997. Discrete-time low-gain control of uncertain infinite-dimensional systems, Mathematics Preprint 95/06, University of Bath, 1995 Preprints in this series are available by anonymous ftp from ftp.maths.bath.ac.uk in the directory /pub/preprints. IEEE Trans. Auto. Control 42, 22-37.
47. LOGEMANN, H., & ZWART, H., 1991. Some remarks on adaptive stabilization of infinite-dimensional systems, Systems & Control Letters 16, 199-207.
48. LOGEMANN, H., & ZWART, H., 1992. On robust PI-control of infinite-dimensional systems, SIAM J. Control & Opt. 30, 573-593.
49. LUNZE, J., 1985. Determination of robust multivariable I-controllers by means of experiments and simulation, Syst. Anal. Model. Simul. 2, 227-249.
50. LUNZE, J., 1987. Experimentelle Erprobung einer Einstellregel für PI-Mehrgrößenregler bei der Herstellung von Ammoniumnitrat-Harnstoff-Lösung, Messen Steuern Regeln 30, 2-6.
51. MÅRTENSSON, B., 1985. The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization, Systems & Control Letters 6, 87-91.
52. MÅRTENSSON, B., 1986. Adaptive Stabilization, PhD thesis, Lund Institute of Technology, Dept. of Automatic Control.
53. MÅRTENSSON, B., 1987. Adaptive stabilization of multivariable linear systems, Contemporary Mathematics 68, 191-225.
54. MÅRTENSSON, B., 1991. The unmixing problem, IMA J. Math. Control & Information 8, 367-377.
55. MÅRTENSSON, B., & POLDERMAN, J. W., 1993. Correction and simplification to "The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization", Systems & Control Letters 20, 465-470.
56. MILLER, D. E., & DAVISON, E. J., 1989. The self-tuning robust servomechanism problem, IEEE Trans. Auto. Control 34, 511-523.
57. MILLER, D. E., & DAVISON, E. J., 1993. An adaptive tracking problem with a control input constraint, Automatica 29, 877-887.
58. MORARI, M., 1985. Robust stability of systems with integral control, IEEE Trans. Auto. Control 30, 574-577.
59. MUSTAFA, D., 1994. How much integral action can a control system tolerate?, Linear Algebra and its Applications 205/206, 965-970.
60. NUSSBAUM, R. D., 1983. Some remarks on a conjecture in parameter adaptive control, Systems & Control Letters 3, 243-246.
61. ORTEGA, R., & LOZANO, R., 1988. Globally stable adaptive controller for systems with delay, Int. J. Control 47, 17-23.
62. POHJOLAINEN, S., 1982. Robust multivariable PI-controllers for infinite-dimensional systems, IEEE Trans. Auto. Control 27, 17-30.
63. POHJOLAINEN, S., 1985. Robust controller for systems with exponentially stable strongly continuous semigroups, J. Math. Analysis and Applications 111, 622-636.
64. PRITCHARD, A. J., & SALAMON, D., 1987. The linear-quadratic control problem for infinite-dimensional systems with unbounded input and output operators, SIAM J. Control & Opt. 25, 121-144.
65. REBARBER, R., & TOWNLEY, S., 1995. Robustness and continuity of the spectrum for uncertain distributed parameter systems, Automatica 31, 1533-1546.
66. RYAN, E. P., (Guest Editor). 1991. Special Issue on Universal Stabilizers and High-Gain Adaptive Control, IMA J. of Math. Control & Information 8, 321-439.
67. RYAN, E. P., 1993. Adaptive stabilization of multi-input nonlinear systems, Int. J. Robust and Nonlinear Control 3, 169-181.
68. RYAN, E. P., 1994. A nonlinear universal servomechanism, IEEE Trans. Auto. Control 39, 753-761.
69. SALAMON, D., 1987. Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach, Trans. Amer. Math. Soc. 300, 383-431.
70. SALAMON, D., 1989. Realization theory in Hilbert space, Math. Systems Theory 21, 147-164.
71. TOWNLEY, S., 1995. Simple adaptive stabilization of output feedback stabilizable distributed parameter systems, Dynamics and Control, 5, 107-123.
72. TOWNLEY, S., 1996. Topological aspects of universal adaptive stabilization, SIAM J. Control & Opt. 34, 1044-70.
73. VIDYASAGAR, M., 1983. A note on time-invariance and causality, IEEE Trans. Auto. Control 28, 929-931.
74. VIDYASAGAR, M., 1985. Control systems synthesis: a factorization approach, MIT Press, Cambridge, MA. operators,
75. WEISS, G., 1989a. Admissible observation operators for linear semigroups, Israel J. Math. 65, 17-43.
76. WEISS, G., 1989b. The representation of regular linear systems on Hilbert spaces, pp. 401-416 in Distributed Parameter Systems, edited by F. Kappel, K. Kunisch & W. Schappacher, Birkhäuser Verlag, Basel.
77. WEISS, G., 1994a. Transfer functions of regular linear systems, part I: characterization of regularity, Trans. Amer. Math. Soc. 342, 827-854.
78. WEISS, G., 1994b. Regular linear systems with feedback, Math. Control, Signals, and Systems 7, 23-57.
79. WEISS, G., & CURTAIN, R. F., 1997. Dynamic stabilization of regular linear systems, IEEE Trans. Auto. Control 42, 4-21.
80. WEN, J. T.-Y., & BALAS, M. J., 1986. Direct model reference adaptive control in infinite-dimensional Hilbert space, pp. 309-327 in Adaptive and Learning Systems, edited by K.S. Narendra, Plenum Press, New York.
81. WEN, J. T.-Y., & BALAS, M. J., 1989. Robust adaptive control in Hilbert space, J. Math. Analysis and Applications 143, 1-26.
82. WILLEMS, J. C., & BYRNES, C. I., 1984. Global adaptive stabilization in the absence of information on the sign of the high frequency gain, pp. 49-57 in Proc. INRIA Conf. on Analysis and Optimization of Systems, Springer-Verlag, Berlin.
83. WONHAM, W. M., 1979. Linear multivariable control: a geometric approach, 2nd ed., Springer-Verlag, New York.
84. ZHU, X.-J., 1989. A finite spectrum unmixing set for GL(3, ℝ), pp. 403-410 in Computation and Control edited by K. Bowers & J. Lund, Birkhäuser Verlag, Boston.