Local linear PID controllers for nonlinear control

Control and Intelligent Systems

Volumn 33, Issue 1, 2005, Pages 26-34

  Lan, Jing ^a   Cho, Jeongho ^a   Erdogmus, Deniz ^b   Principe, J C ^a   Motter, M A ^c   Xu, J ^a  

^a UNIVERSITY OF FLORIDA   (United States)

^b Oregon Health and Science University Department of Biomedical Engineering   (United States)

^c NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

Gaussian mixture; Local linear model; PID controller; Self organizing maps

Indexed keywords

CONTROLLER DESIGN; GAUSSIAN MIXTURE; LINEAR CONTROLLERS; LOCAL LINEAR MODEL;

CONVERGENCE OF NUMERICAL METHODS; IDENTIFICATION (CONTROL SYSTEMS); MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; SELF ORGANIZING MAPS; TIME VARYING SYSTEMS;

THREE TERM CONTROL SYSTEMS;

EID: 19144365495     PISSN: 14801752     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. O. Nelles, Nonlinear system identification (New York: Springer, 2001).
2. I.J. Leontaritis & S.A. Billings, Input-output parametric models for nonlinear systems, Part 1: Deterministic nonlinear systems, International Journal of Control, 41(2), 1985, 303-328.
3. K.S. Narendra & K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Trans. on Neural Networks, 1(1), 1990, 4-27.
4. T.A. Johansen & B.A. Foss, Constructing NARMAX models using ARMAX models, International Journal of Control, 58(5), 1993, 1125-1153.
5. X. Ni, M. Verhaegen, A.J. Krijgsman, & H.B. Verbruggen, New method for identification and control of nonlinear dynamic systems, Engineering Applications of Artificial Intelligence, 9(3), 1996, 231-243.
6. D.M. Walker, N.B. Tufillaro, & P. Gross, Radial-basis models for feedback systems with fading memory, IEEE Trans. on Circuits and Systems, 48(9), 2001, 1147-1151.
7. B.S. Kim & A.J. Calise, Nonlinear flight control using neural networks, Journal of Guidance, Control, and Dynamics, 20(1), 1997, 26-33.
8. C.H. Lee & M.J. Chung, Gain-scheduled state feedback control design technique for flight vehicles, IEEE Trans. on Aerospace and Electronic Systems, 37(1), 2001, 173-182.
9. R.C. Dorf & R.H. Bishop, Modern control systems, 8th ed. (New York: Addison Wesley, 1998).
10. J.S.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Trans. on Systems, Man and Cybernetics, Part B, 23(3), 1993, 665-685.
11. J. Lan, J.C. Principe, & M.A. Motter, Identification of dynamical systems using GMM with VQ initialization, Proc. IJCNN'03, 1, 2003, 764-768.
12. J.C. Principe, L. Wang, & M.A. Motter, Local dynamic modeling with self-organizing maps and applications to nonlinear system identification and control, Proc. IEEE, 86(11), 1998, 2240-2258.
13. T. Kohonen, Self-organizing maps (New York: Springer, 1995).
14. G.J. Mclachlan & D. Peel, Finite mixture, models (New York: Wiley, 2001).
15. J. Stark, D.S. Broomhead, M.E. Davies, & J. Huke, Takens embedding theorems for forced and stochastic systems, Nonlinear Analysis, Theory Methods, and Applications, 30(8), 1997, 5303-5314.
16. M. Casdagli, Nonlinear prediction of chaotic time series, Physica D, 35(3), 1989, 335-356.
17. F. Takens, On numerical determination of the dimension of an attractor, in D. Rand & L.S. Young (Eds), Dynamical systems and turbulance, Warwick 1980, Lecture Notes in Mathematics, vol. 898, (Berlin: Springer-Verlag, 1981), 366-381.
18. D.T. Magill, Optimal adaptive estimations of sampled stochastic processes, IEEE Trans. on Automation and Control, AC-10, 1965, 434-439.
19. D.G. Lainiotis, Partitioning: A unifying framework for adaptive systems - I: Estimation - II: Control, Proc. IEEE, 64, 1976, 1126-1143, 1182-1197.
20. B. Martensson, Adaptive stabilization, doctoral diss., Lund Institute of Technology, Lund, Sweden, 1986.
21. K.S. Narendra & J. Balakrishnan, Adaptive control using multiple models, IEEE Trans. on Automatic Control, 4(2), 1997, 171-187.
22. R.A. Jacobs, M.I. Jordan, S.J. Nowlan, & G.E. Hinton, Adaptive mixtures of local experts, Neural Computation, 3, 1991, 79-87.
23. R. Murray-Smith & T.A. Johansen, Multiple model approaches to modeling and control (New York: Taylor & Francis, 1997).
24. K.S. Narendra & C. Xiang, Adaptive control of discrete-time systems using multiple models, IEEE Trans. on Automatic Control, 45(9), 2000, 1669-1686.
25. A.S. Morse, Supervisory control of families of linear set-point controller, Part 1: Exact matching, IEEE Trans. on Automatic Control, 42, 1996, 1413-1431.
26. M.A. Motter, Control of the NASA Langley 16-foot Transonic Tunne; with the Self-Organizing Feature Map, doctoral diss., University of Florida, Gainesville, FL, 1997.
27. G. Thampi, J.C. Principe, M.A. Motter, J. Cho, & J. Lan, Multiple model based flight control design, Proc. MWSCAS'02, vol. 3, Tulsa, OK, 2002, 133-136.
28. J. Cho, J. Lan, G. Thampi, J.C. Principe, & M.A. Motter, Identification of aircraft dynamics using a SOM and local linear models, Proc. MWSCAS'02, vol. 2, Tulsa, OK, 2002, 148-151.
29. S. Chen & S. Billings, Representations of non-linear systems: The NARMAX model, International Journal of Control, 49(3), 1989, 1013-1032.
30. R.E. Brown, G.N. Maliotis, & J.A. Gibby, PID self-tuning controller for aluminum rolling mill, IEEE Trans. on Industry Applications, 29(3), 1993, 578-583.
31. K.M. Vu, Optimal setting for discrete PID controllers, IEE Proc.-D, 139(1), 1992, 31-10.
32. J. Bao, J.F. Forbes, & P.J. McLellan, Robust Multiloop PID controller design: A successive semidefinite programming approach, Industrial and Engineering Chemistry Research, 38, 1999, 3407-3419.
33. X. He & H. Asada, A new method for identifying orders of input-output models for nonlinear dynamic systems, Proc. ACC, 1993, 2520-2524.
34. S. Haykin, Neural networks: A comprehensive foundation (Englewood Cliffs, NJ: Prentice Hall, 1998).