EKF Based Generalized Predictive Control of Nonlinear Systems

Abstract

In this paper, Autoregressive with exogenous input (ARX) and dynamic neural network (DNN) based generalized predictive control (GPC) methods are designed to control of nonlinear systems. ARX and DNN models adaptively approximate the plant dynamics and predict the future behavior of the nonlinear system. While control process goes on, the poles of the ARX and DNN models are constrained in a stable region using a projection operator for structural stability. Simulation results are given to compare the tracking performances of the methods. ARX-GPC and DNN-GPC both yield good tracking performances while keeping the changes in control signal as low as possible. The simulation results show that even though ARX is a linear model, it provides acceptable tracking results as well as DNN model.

Keywords

• Generalized predictive control,ARX,dynamic neural network,Kalman filter and extended Kalman filter, nonlinear systems and adaptive learning rate

References

1. [1] K.J. Astrom. Theory and applications of adaptive control-a survey. Automatica, 19(5):471 – 486, 1983.
2. [2] Selami Beyhan and Musa Alc. Extended fuzzy function model with stable learning methods for online system identification. International Journal of Adaptive Control and Signal Processing, 25(2):168–182, 2011.
3. [3] D.W. Clarke, C. Mohtadi, and P.S. Tuffs. Generalized predictive control part i. the basic algorithm. Automatica, 23(2):137 – 148, 1987.
4. [4] D W Clarke, C Mohtadi, and P S Tuffs. Generalized predictive control part ii. extensions and interpretations. Automatica, 23(2):149–160, March 1987.
5. [5] Kaynak O Efe M O, Abadoglu E. A novel analysis and design of a neural network assisted nonlinear controller for a bioreactor. International Journal of Robust and Nonlinear Control, 9:799–815, 1999.
6. [6] M. Ghiassi, H. Saidane, and D.K. Zimbra. A dynamic artificial neural network model for forecasting time series events. International Journal of Forecasting, 21(2):341 – 362, 2005.
7. [7] Sanqing Hu and Jun Wang. Global stability of a class of discrete-time recurrent neural networks. Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 49(8):1104–1117, Aug 2002.
8. [8] Petros A. Ioannou and Jing Sun. Robust Adaptive Control. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1995.

9. [9] Serdar Iplikci. A support vector machine based control application to the experimental three-tank system. ISA Transactions, 49(3):376 – 386, 2010.
10. [10] Liang Jin, Peter N. Nikiforuk, and Madan M. Gupta. Absolute stability conditions for discrete-time recurrent neural networks. IEEE Transactions on Neural Networks, 5(6):954–964, 1994.