Data-based intelligent modeling and control for nonlinear systems

Abstract

With the ever increasing complexity of industrial systems, model-based control has encountered difficulties and is facing problems, while the interest in data-based control has been booming. This paper gives an overview of data-based control, which divides it into two subfields, intelligent modeling and direct controller design. In the two subfields, some important methods concerning data-based control are intensively investigated. Within the framework of data-based modeling, main modeling technologies and control strategies are discussed, and then fundamental concepts and various algorithms are presented for the design of a data-based controller. Finally, some remaining challenges are suggested.

Key words： offline and online data; intelligent modeling; data-based control; perspective

References

1 Brundle M, Naedele M. Security for process control systems: an overview. IEEE Security & Privacy, 2008, 6(6): 24-29

2 Katayama T, Mckelvey T, Sano A, Cassandras C G, Campi M C. Trends in systems and signals: status report prepred by the IFAC coordinating committee on systems and signals. Annual Reviews in Control, 2006, 30(1): 5-17

3 Chai T Y. Challenges of optimal control for plant-wide production processes in terms of control and optimization theories. Acta Automatica Sinica, 2009, 35(6): 641-648 (in Chinese)

4 Lee J H, Lee K S. Iterative learning control applied to batch processes: an overview. Control Engineering Practice, 2007, 15(10): 1306-1318

5 Hou Z S, Xu J X. On data-driven control theory: the state of the art and perspective. Acta Automatica Sinica, 2009, 35(6): 650-667 (in Chinese)

6 Hand D J, Mannila H, Smyth P. Principles of Data Mining. Cambridge: The MIT Press, 2000

7 Han J W, Kamber M. Data Mining: Concepts and Techniques. San Francisco: Morgan Kaufmann, 2006

8 Witten I H, Frank E. Data Mining: Practical Machine Learning Tools and Techniques. 2nd ed. San Francisco: Morgan Kaufmann, 2005

9 Sun C Y, Yu W. Neural network for control, robotics and diagnostics. Neural Computing & Applications, 2008, 17(4): 325-326

10 Hou Z G, Zeng Z G, Sun C Y. Computational intelligence for optimization, modeling and control. Neural Computing & Applications, 2009, 18(5): 407-408

11 Zhu D Q, Shi H. Artificial Neural Network Theory and Application. Beijing: Science Press, 2006 (in Chinese)

12 Deng N Y, Tian Y J. A New Method of Data Mining — Support Vector Machine. Beijing: Science Press, 2006 (in Chinese)

13 Sun C Y, Ju P, Li L F. Fuzzy modeling technique with PSO algorithm for short-term load forecasting. Lecture Notes in Computer Science, 2006, 4223: 933-936

14 Sun C Y, Song J Y, Li L F, Ju P. Implementation of hybrid short-term load forecasting system with analysis of temperature sensitivities. Soft Computing, 2008, 12(7): 633-638

15 Wu Z L, Li C H, Zhu J, Huang J. A semi-supervised SVM for manifold learning. In: Proceedings of the 18th International Conference on Pattern Recognition. 2006, 2: 490-493

16 Adankon M M, Cheriet M, Biem A. Semisupervised least squares support vector machine. IEEE Transactions on Neural Networks, 2009, 20(12): 1858-1870

17 Xu L L, White M, Schuurmans D. Optimal reverse prediction, a unified perspective on supervised, unsupervised and semi-supervised learning. In: Proceedings of the 26th International Conference on Machine Learning. 2009, 1137-1144

18 Xu J X, Hou Z S. Notes on data-driven system approaches. Acta Automatica Sinica, 2009, 35(6): 668-675

19 Crammer K, Dekel O, Keshet J, Shalev-Shwartz S, Singer Y. Online passive-aggressive algorithms. Journal of Machine Learning Research, 2006, 7(8): 551-585

20 Kivinen J, Smola A J, Williamson R C. Online learning with kernels. IEEE Transactions on Signal Processing, 2004, 52(8): 2165-2176

21 Cheng L, Vishwanathan S V N, Schuurmans D, Wang S, Caelli T. Implicit online learning with kernels. Advances in Neural Information Processing Systems, 2007, 19: 249-256

22 Dai X Z,Wang WC, Ding Y H, Sun Z Y. “Assumed inherent sensor” inversion based ANN dynamic soft-sensing method and its application in erythromycin fermentation process. Computers and Chemical Engineering, 2006, 30(8): 1203-1225

23 Wang H, Pi D Y, Sun Y X. Online SVM regression algorithmbased adaptive inverse control. Neurocomputing, 2007, 70(4-6): 952-959

24 Garcia C E, Morari M. Internal model control-1: a unifying review and some new results. Industrial Engineering Chemistry Process Design and Development, 1982, 21(2): 308-323

25 Garcia C E, Morari M. Internal model control-2: design procedure for multivariable systems. Industrial Engineering Chemistry Process Design and Development, 1985, 24(3): 472-484

26 Zhou Y, Chen Q W, Hu W L. New developments of research on internal model control. Control Theory & Applications, 2004, 21(3): 475-482

27 Nahas E P. Nonlinear internal model control strategy for neural network models. Computers Chemical Engineering, 1992, 16(12): 1039-1057

28 Wang D C, Fang T J. Internal model control approach based on support vector machines. Control Theory & Applications, 2004, 21(1): 85-88

29 Stephanopoulos G, Huang H P. The 2-port control system. Chemical Engineering Science, 1986, 41(6): 1611-1630

30 Hu Q, Saha P, Rangaiah G P. Internal model control with feedback compensation for uncertain non-linear systems. International Journal of Control, 2001, 74(14): 1456-1466

31 Song F H, Zheng E H. Nonlinear internal-model control based on support vector machine. Control Theory & Applications, 2008, 25(6): 1067-1071

32 Cueli J R, Bordons C. Iterative nonlinear model predictive control. Stability, robustness and applications. Control Engineering Practice, 2008, 16(9): 1023-1034

33 Tsaia P F, Chub J Z, Janga S S, Shiehc S S. Developing a robust model predictive control architecture through regional knowledge analysis of artificial neural networks. Journal of Process Control, 2002, 13(5): 423-435

34 Huang G S, Dexter L A. Realization of robust nonlinear model predictive control by offline optimisation. Journal of Process Control, 2008, 18(5): 431-438

35 Wang L P, Young P C. An improved structure for model predictive control using non-minimal state space realisation. Journal of Process Control, 2006, 16(4): 355-371

36 Xi X C, Poo A N, Chou S K. Support vector regression model predictive control on a HVAC plant. Control Engineering Practice, 2007, 15(8): 897-908

37 Al Seyab R K, Cao Y. Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation. Journal of Process Control, 2008, 18(6): 568-581

38 Mu C X, Zhang R M, Sun C Y. LS-SVM predictive control based on PSO for nonlinear systems. Control Theory & Applications, 2010, 27(2): 164-168

39 Spall J C. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 1992, 37(3): 332-341

40 Spall J C, Chin D C. Traffic-responsive signal timing for system-wide traffic control. Transportation Research, Part C: Emerging Technologies, 1997, 5(3-4): 153-163

41 Spall J C, Cristion J A. Model-free control of nonlinear stochastic systems with discrete-time measurements. IEEE Transactions on Automatic Control, 1998, 43(9): 1198-1210

42 Hou Z S. The parameter identication, adaptive control and model free learning adaptive control for nonlinear systems. Dissertation for the Doctoral Degree. Shenyang: Northeastern University, 1994 (in Chinese)

43 Hou Z S. Nonparametric Models and Its Adaptive Control Theory. Beijing: Science Press, 1999 (in Chinese)

44 Safonov M G, Tsao T C. The unfalsified control concept and learning. IEEE Transactions on Automatic Control, 1997, 42(6): 843-847

45 Yamamoto K, Takao G, Yamada T. Design of a data-driven PID control. IEEE Transactions on Control System Technology, 2009, 17(1): 29-39

46 Hjalmarsson H, Gunnarsson S, Gevers M. A convergent iterative restricted complexity control design scheme. In: proceedings of the 33rd IEEE Conference on Decision and Control. 1994, 1735-1740

47 Hjalmarsson H. Iterative feedback tuning: an overview. International Journal of Adaptive Control and Signal Processing, 2002, 16(5): 373-395

48 Hjalmarsson H. Control of nonlinear systems using iterative feedback tuning. In: Proceedings of the American Control Conference. 1998, 2083-2087

49 Lee J M, Lee J H. Approximate dynamic programming-based approaches for input-output data-driven control of nonlinear processes. Automatica, 2005, 41(7): 1281-1288

50 Bellman R E. Dynamic Programming. Princeton: Princeton University Press, 1957

51 Si J, Wang Y. Online learning control by association and reinforcement. IEEE Transactions on Neural Networks, 2001, 12(2): 264-276

52 Abu-Khalaf M, Lewis F L. Nearly optimal control laws for nonlinear systems with saturating actuators using a nerual network HJB approach. Automatica, 2005, 41(5): 779-791

53 Zhang H, Wei Q, Luo Y. A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear system based on greedy HDP iteration algorithm. IEEE Transactions on Systems, Man, and Cybernetics — Part B: Cybernetics, 2008, 38(4): 937-942

54 Zhang H, Luo Y, Liu D R. Neural-network-based nearoptimal control for a class of discrete-time affine nonlinear systems with control constraint. IEEE Transactions on Neural Networks, 2009, 20(9): 1490-1503

55 Arimoto S, Kawamura S, Miyazaki F. Bettering operation of dynamic systems by learning: a new control theory for servomechanism or mechatronic system. In: Proceedings of the 23rd Conference on Decision and Control. 1984, 1064-1069

56 Chen Y, Wen C, Sun M. A robust high-order P-type iterative learning controller using current-iteration tracking error. International Journal of Control, 1997, 68(2): 331-342

57 Chen Y Q, Wen C Y. Iterative Learning Control: Convergence, Robustness and Applications. Lecture Notes in Control and Information Sciences. Berlin: Springer-Verlag, 1999

58 Amann N, Owens D H, Rogers E. 2D systems theory applied to learning control systems. In: Proceedings of the 33rd Conference on Decision and Control. 1994, 985-986

59 Luca A, Paesano G, Ulivi G. A frequency-domain approach to learning control: implementation for a robot manipulator. IEEE Transations on Industrial Electronics, 1992, 39(1): 1-10

60 Deng H, Xu Z, Li H X. A novel neural internal model control for multi-input multi-output nonlinear discrete-time processes. Journal of Process Control, 2009, 19(8): 1392-1400