Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.
References
[1]
Qin, S.J. and Badgwell, T.A. (2003) A Survey of Industrial Model Predictive Control Technology. Control Engineering Practice, 11, 733-764. https://doi.org/10.1016/S0967-0661(02)00186-7
[2]
Christofides, P.D., Scattolini, R., Muñoz de la Peña, D. and Liu, J. (2013) Distributed Model Predictive Control: A Tutorial Review and Future Research Directions. Computers & Chemical Engineering, 51, 21-41. https://doi.org/10.1016/j.compchemeng.2012.05.011
[3]
Xi, Y.G., Li, D.W. and Lin, S. (2013) Model Predictive Control—Status and Challenges. Acta Automatica Sinica, 39, 222-236. https://doi.org/10.1016/S1874-1029(13)60024-5
[4]
Riar, B.S. and Geyer, T. (2015) Model Predictive Direct Current Control of Modular Multilevel Converters: Modeling, Analysis and Experimental Evaluation. IEEE Transactions on Power Electronics, 30, 431-439. https://doi.org/10.1109/TPEL.2014.2301438
[5]
Ma, Y., Matusko, J. and Borrelli, F. (2015) Stochastic Model Predictive Control for Building HVAC Systems: Complexity and Conservatism. IEEE Transactions on Control Systems Technology, 23, 101-116. https://doi.org/10.1109/TCST.2014.2313736
[6]
Dochain, D. and Bastin, G. (1984) Adaptive Identification and Control Algorithms for Nonlinear Bacterial Growth Systems. Automatica, 20, 621-634. https://doi.org/10.1016/0005-1098(84)90012-8
[7]
Ding, F. (2014) Combined State and Least Squares Parameter Estimation Algorithms for Dynamic Systems. Applied Mathematical Modelling, 38, 403-412. https://doi.org/10.1016/j.apm.2013.06.007
[8]
Wang, D., Ding, F. and Liu, X. (2014) Least Squares Algorithm for an Input Nonlinear System with a Dynamic Subspace State Space Model. Nonlinear Dynamics, 75, 49-61. https://doi.org/10.1007/s11071-013-1048-8
[9]
Yin, S., Yang, X. and Karimi, H.R. (2012) Data-Driven Adaptive Observer for Fault Diagnosis. Mathematical Problems in Engineering, 2012, Article ID: 832836. https://doi.org/10.1155/2012/832836
[10]
Yin, S., Ding, S.X., Xie, X. and Luo, H. (2014) A Review on Basic Data-Driven Approaches for Industrial Process Monitoring. IEEE Transactions on Industrial Electronics, 61, 6418-6428. https://doi.org/10.1109/TIE.2014.2301773
[11]
Yin, S., Li, X., Gao, H. and Kaynak, O. (2015) Data-Based Techniques Focused on Modern Industry: An Overview. IEEE Transactions on Industrial Electronics, 62, 657-667. https://doi.org/10.1109/TIE.2014.2308133
[12]
Bryson, A.E. and Ho, Y.C. (1975) Applied Optimal Control. Hemisphere, Washington DC.
[13]
Teo, K.L., Goh, C.J. and Wong, K.H. (1991) A Unified Computational Approach to Optimal Control Problems. Longman Scientific and Technical, Harlow.
Lewis, F.L. and Syrmos, V.L. (1995) Optimal Control. 2nd Edition, John Wiley & Sons, New York.
[16]
Kirk, D.E. (2004) Optimal Control Theory: An Introduction. Dover Publications, Mineola.
[17]
Kek, S.L., Teo, K.L. and Aziz, M.I.A. (2010) An Integrated Optimal Control Algorithm for Discrete-Time Nonlinear Stochastic System. International Journal of Control, 83, 2536-2545. https://doi.org/10.1080/00207179.2010.531766
[18]
Kek, S.L., Teo, K.L. and Aziz, M.I.A. (2012) Filtering Solution of Nonlinear Stochastic Optimal Control Problem in Discrete-Time with Model-Reality Differences. Numerical Algebra, Control and Optimization, 2, 207-222. https://doi.org/10.3934/naco.2012.2.207
[19]
Kek, S.L., Aziz, M.I.A., Teo, K.L. and Rohanin, A. (2013) An Iterative Algorithm Based on Model-Reality Differences for Discrete-Time Nonlinear Stochastic Optimal Control Problems. Numerical Algebra, Control and Optimization, 3, 109-125. https://doi.org/10.3934/naco.2013.3.109
[20]
Kek, S.L., Teo, K.L. and Aziz, M.I.A. (2015) Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences. Mathematical Problems in Engineering, 2015, Article ID: 659506. https://doi.org/10.1155/2015/659506
[21]
Roberts, P.D. and Williams, T.W.C. (1981) On an Algorithm for Combined System Optimization and Parameter Esti-mation. Automatica, 17, 199-209. https://doi.org/10.1016/0005-1098(81)90095-9
[22]
Roberts, P.D. (1992) Optimal Control of Nonlinear Systems with Model-Reality Differences. Proceedings of the 31st IEEE Conference on Decision and Control, 1, 257-258. https://doi.org/10.1109/CDC.1992.371744
[23]
Becerra, V.M. and Roberts, P.D. (1996) Dynamic Integrated System Optimization and Parameter Estimation for Discrete-Time Optimal Control of Nonlinear Systems. International Journal of Control, 63, 257-281. https://doi.org/10.1080/00207179608921843
[24]
Kek, S.L., Li, J. and Teo, K.L. (2017) Least Square Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences. Applied Mathematics, 8, 1-14. https://doi.org/10.4236/am.2017.81001
[25]
Verhaegen, M. and Verdult, V. (2007) Filtering and System Identification: A Least Squares Approach. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511618888
[26]
Minoux, M. (1986) Mathematical Programming Theory and Algorithms. John Wiley & Sons, New York.
[27]
Chong, E.K.P. and Zak, S.H. (2013) An Introduction to Optimization. 4th Edition, John Wiley & Sons, New York.
[28]
Poursafar, N., Taghirad, H.D. and Haeri, M. (2010) Model Predictive Control of Nonlinear Discrete-Time Systems: A Linear Matrix Inequality Approach. IET Control Theory and Applications, 4, 1922-1932. https://doi.org/10.1049/iet-cta.2009.0650
[29]
Haeri, M. (2004) Improved EDMC for the Processes with High Variations and/or Sign Changes in Steady-State Gain. COMPEL: International Journal of Computations & Mathematics in Electrical, 23, 361-380. https://doi.org/10.1108/03321640410510541
[30]
Shridhar, R. and Cooper, D.J. (1997) A Tuning Strategy for Unconstrained SISO Model Predictive Control. Industrial & Engineering Chemistry Research, 36, 729-746. https://doi.org/10.1021/ie9604280
[31]
Kravaris, C. and Daoutidis, P. (1990) Nonlinear State-Feedback Control of Second Order Non-Minimum Phase Systems. Computers & Chemical Engineering, 14, 439-449. https://doi.org/10.1016/0098-1354(90)87019-L
