Input constraints handling in an MPC/feedback linearization scheme

Deng, J. ; Becerra, V. M. ; Stobart, R.

International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 2, pp. 219-232.

Résumé

The combination of model predictive control based on linear models (MPC) with feedback linearization (FL) has attracted interest for a number of years, giving rise to MPC+FL control schemes. An important advantage of such schemes is that feedback linearizable plants can be controlled with a linear predictive controller with a fixed model. Handling input constraints within such schemes is difficult since simple bound contraints on the input become state dependent because of the nonlinear transformation introduced by feedback linearization. This paper introduces a technique for handling input constraints within a real timeMPC/FL scheme, where the plant model employed is a class of dynamic neural networks. The technique is based on a simple affine transformation of the feasible area. A simulated case study is presented to illustrate the use and benefits of the technique.

Détail

Keywords: predictive control, feedback linearization, neural network, nonlinear system, constraints
Mots-clés : sterowanie predykcyjne, sterowanie odwrotne, sieć neuronowa, system nieliniowy

Bibliographie

[1] Ayala-Botto, M., Boom, T. V. D., Krijgsman, A. and da Costa, J. S. (1999). Predictive control based on neural network models with I/O feedback linearization, International Journal of Control 72(17): 1538-1554.

[2] Ayala-Botto, M., Braake, H. T., da Costa, J. S. and Verbruggen, H. (1996). Constrained nonlinear predictive control based on input-output linearization using a neural network, Proceedings of the 13-th IFACWorld Congress, San Francisco, CA, USA, pp. 175-180.

[3] Becerra, V. M., Roberts, P. D. and Griffiths, G. W. (2001). Applying the extended Kalman filter to systems desribed by nonlinear differential-algebraic equations, Control Engineering Practice 9(3): 267-281.

[4] Casavola, A. and Mosca, E. (1996). Reference governor for constrained uncertain linear systems subject to bounded input disturbances, Preceedings of the 35-th Conference on Decision and Control, Kobe, Japan, pp. 3531-3536.

[5] Del-Re, L., Chapuis, J. and Nevistic, V. (1993). Stability of neural net based model predivtive control, Proceedings of the 32-nd Conference on Decision and Control, San Antonio, TX, USA, pp. 2984-2989.

[6] Deng, J. and Becerra, V. M. (2004). Real-time constrained predictive control of a 3d crane system, Proceedings of the 2004 IEEE Conference on Robotics, Automation and Mechatronics, Singapore, pp. 583-587.

[7] Garces, F. (2000). Dynamic Neural Networks for Approximate Input-Output Linearisation-Decoupling of Dynamic Systems, Ph.D. thesis, University of Reading.

[8] Garces, F., Becerra, V., Kambhampati, C. and Warwick, K. (2003). Strategies for Feedback Linearisation: A Dynamic Neural Network Approach, Springer, London.

[9] Guemghar, K., Srinivasan, B., Mullhaupt, P. and Bonvin, D. (2005). Analysis of cascade structure with predictive control and feedback linearisation, IEE Proceedings: Control Theory and Applications 152(3): 317-324.

[10] Henson, M. A. and Kurtz, M. J. (1994). Input-output linearisation of constrained nonlinear processes, Nonlinear Control, AICHE Annual Meeting, San Franciso, CA, USA, pp. 1-20.

[11] Henson, M. A. and Seborg, D. E. (1993). Theoretical analysis of unconstrained nonlinear model predictive control, International Journal of Control 58(5): 1053-1080.

[12] Isidori, A. (1995). Nonlinear Control Systems, 2nd Edition, Springer, Berlin/New York, NY.

[13] Kurtz, M. and Henson, M. (1997). Input-output linearizing control of constrained nonlinear processes, Journal of Process Control 7(1): 3-17.

[14] Maciejowski, J. M. (2002). Predictive Control with Constraints, Prentice Hall, London.

[15] Maybeck, P. S. (1982). Stochastic Models, Estimation and Control, Academic Press, New York, NY.

[16] Nevistic, V. (1994). Feasible Suboptimal Model Predictive Control for Linear Plants with State Dependent Constraints, Postdiploma thesis, Swiss Federal Institute of Technology, Automatica Control Laboratory, ETH, Zurich.

[17] Nevistic, V. and Morari, M. (1995). Constrained control of feedback-linearizable systems, Proceedings of the European Control Conference, Rome, Italy, pp. 1726-1731.

[18] Nevistic, V. and Primbs, J. A. (1996). Model predictive control: Breaking through constraints, Proceedings of the 35-th Conference on Decision and Control, Kobe, Japan, pp. 3932-3937.

[19] Oliveiria, S. D., Nevistic, V. and Morari, M. (1995). Control of nonlinear systems subject to input constraints, Preprints of the IFAC Symposium on Nonlinear Control Systems, NOLCOS'95, Tahoe City, CA, USA, Vol. 1, pp. 15-20.

[20] Perttunen, C. D., Jones, D. R. and Stuckman, B. E. (1993). Lipschitzian optimization without the Lipschitz constant, Journal of Optimization Theory and Application 79(1): 157-181.

[21] Poznyak, A. S., Sanchez, E. N. and Yu, W. (2001). Differential Neural Networks for Robust Nonlinear Control, World Scientific, Singapore.

[22] Rossiter, J. A. (2003). Model Based Predictive Control: A Practical Approach, CRC Press, Boca Raton, FL, USA.

[23] Scattolini, R. and Colaneri, P. (2007). Hierarchical model predictive control, Proceedings of the 46-th IEEE Conference on Decision and Control, New Orleans, LA, USA, pp. 4803-4808.

[24] van den Boom, T. (1997). Robust nonlinear predictive control using feedback linearization and linear matrix inequalities, Proceedings of the American Control Conference, Albuquerque, NM, USA, pp. 3068-3072.