This paper considers a problem of bioreactor control, which is formulated in Anderson and Miller (1990) and Ungar (1990) as a benchmark problem for application of neural network-based adaptive control algorithms. A completely adaptive control of this strongly nonlinear system is achieved with no a priori knowledge of its dynamics. This becomes possible thanks to a novel architecture of the controller, which is based on an affine Radial Basis Function network approximation of the sampled-data system mapping. Approximation with such net-work could be considered as a generalization of a standard practice to linearize a nonlinear system about the working regime. As the network is affine in the control components, it can be inverted with respect to the control vector by using fast matrix computations. The considered approach includes several features, recently introduced in some advanced process control algorithms. These features—multirate sampling, on-line adaptation, and Radial Basis Function approximation of the system nonlinearity—are crucial for the achieved high performance of the controller.

1.
Anderson, C. W., and Miller, W. T. Ill, 1990, “Challenging Control Problems,” Sutton, R. S., Miller, W. T. Ill, and Werbos, P. J., eds., Neural Networks for Control, The MIT Press, London, pp. 475–511.
2.
Chen
S.
, and
Billings
S. A.
,
1992
, “
Neural Networks for Non-Linear Dynamic System Modelling and Identifications
,”
Int. J. Control
, Vol.
56
, No.
2
, pp.
319
346
.
3.
Chen
S.
,
Billings
S. A.
, and
Grant
P. M.
,
1992
, “
Recursive Hybrid Algorithm for Non-Linear Systems Identification Using Radial Basis Function Networks
,”
Int. J. Control
, Vol.
55
, No.
5
, pp.
1051
1070
.
4.
Goodwin, G. C., and Sin, K. S., 1984, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, NJ.
5.
Gorinevsky, D. M., 1993, “Adaptive Learning Control Using Radial Basis Function Network Approximation Over Task Parameter Domain,” 1993 IEEE Int. Symp. on Intelligent Control, Chicago, IL, Aug.
6.
Gorinevsky, D. M., 1994a, “Periodic Adaptive Stabilization of the Unstable Nonminimum Phase System,” American Control Conf., Baltimore, MD, June.
7.
Gorinevsky, D. M., 1994b, “An Algorithm for On-Line Parametric Nonlinear Least Square Optimization,” 33rd IEEE CDC, Lake Buena Vista, FL, Dec.
8.
Gorinevsky
D. M.
,
1995
, “
On the Persistency of Excitation in Radial Basis Function—Network Identification of Nonlinear Systems
,”
IEEE Tran. on Neural Networks
, Vol.
6
, No.
5
, pp.
1237
1244
.
9.
Kansa
E. J.
,
1990
, “
Multiquadrics—A Scattered Data Approximation Scheme with Applications to Computational Fluid Dynamics—I
,”
Computers Math. Applic.
, Vol.
19
, No.
8
, pp.
127
145
.
10.
Lozano-Leal
R.
,
1989
, “
Robust Adaptive Regulation Without Persistent Excitation
,”
IEEE Trans. on Automat. Contr.
, Vol.
34
, pp.
1260
1267
.
11.
Sadeh
N.
,
1993
, “
A Perceptron Network for Functional Identification and Control of Nonlinear System
,”
IEEE Trans. on Neural Networks
, Vol.
4
, No.
6
, pp.
982
988
.
12.
Ortega
R.
,
1991
, “
On Periodic Adaptive Stabilization of Nonminimum Phase Systems
,”
Contr. Theory and Adv. Techn.
, Vol.
7
, No.
4
, pp.
675
681
.
13.
Poggio
T.
, and
Girosi
P.
,
1990
, “
Networks for Approximation and Learning
,”
Proceeding of the IEEE
, Vol.
7
, No.
9
, pp.
1481
1497
.
14.
Puskoris
G. v.
, and
Feldkamp
L. A.
,
1994
, “
Neurocontrol of Nonlinear Dynamical Systems with Kalman Filter-Trained Recurrent Networks
,”
IEEE Tr. on Neural Networks
, Vol.
5
, No.
2
, pp.
279
297
.
15.
Sanner
R. M.
, and
Slotine
J.-J. E.
,
1992
, “
Gaussian Networks for Direct Adaptive Control
,”
IEEE Trans. on Neural Networks
, Vol.
3
, No.
6
, pp.
837
863
.
16.
Ungar, L. H., 1990, “A Bioreactor Benchmark for Adaptive Network-Based Process Control,” Sutton, R. S., Miller, W. T. Ill, and Werbos, P. J., eds., Neural Networks for Control, The MIT Press, London, pp. 388–399.
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