Full Text:   <3335>

CLC number: TP273

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2011-09-28

Cited: 1

Clicked: 8656

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE C 2011 Vol.12 No.11 P.919-931

http://doi.org/10.1631/jzus.C10a0512


Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm


Author(s):  Jiao-na Wan, Zhi-jiang Shao, Ke-xin Wang, Xue-yi Fang, Zhi-qiang Wang, Ji-xin Qian

Affiliation(s):  State Key Lab of Industrial Control Technology, Institute of Industrial Control, Department of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   joyce523@126.com, zjshao@iipc.zju.edu.cn

Key Words:  Nonlinear model predictive control (NMPC), Computational delay, Termination criteria, Continuously stirred tank reactor (CSTR)


Jiao-na Wan, Zhi-jiang Shao, Ke-xin Wang, Xue-yi Fang, Zhi-qiang Wang, Ji-xin Qian. Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm[J]. Journal of Zhejiang University Science C, 2011, 12(11): 919-931.

@article{title="Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm",
author="Jiao-na Wan, Zhi-jiang Shao, Ke-xin Wang, Xue-yi Fang, Zhi-qiang Wang, Ji-xin Qian",
journal="Journal of Zhejiang University Science C",
volume="12",
number="11",
pages="919-931",
year="2011",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.C10a0512"
}

%0 Journal Article
%T Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm
%A Jiao-na Wan
%A Zhi-jiang Shao
%A Ke-xin Wang
%A Xue-yi Fang
%A Zhi-qiang Wang
%A Ji-xin Qian
%J Journal of Zhejiang University SCIENCE C
%V 12
%N 11
%P 919-931
%@ 1869-1951
%D 2011
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C10a0512

TY - JOUR
T1 - Reduced precision solution criteria for nonlinear model predictive control with the feasibility-perturbed sequential quadratic programming algorithm
A1 - Jiao-na Wan
A1 - Zhi-jiang Shao
A1 - Ke-xin Wang
A1 - Xue-yi Fang
A1 - Zhi-qiang Wang
A1 - Ji-xin Qian
J0 - Journal of Zhejiang University Science C
VL - 12
IS - 11
SP - 919
EP - 931
%@ 1869-1951
Y1 - 2011
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C10a0512


Abstract: 
We propose a novel kind of termination criteria, reduced precision solution (RPS) criteria, for solving optimal control problems (OCPs) in nonlinear model predictive control (NMPC), which should be solved quickly for new inputs to be applied in time. computational delay, which may destroy the closed-loop stability, usually arises while non-convex and nonlinear OCPs are solved with differential equations as the constraints. Traditional termination criteria of optimization algorithms usually involve slow convergence in the solution procedure and waste computing resources. Considering the practical demand of solution precision, RPS criteria are developed to obtain good approximate solutions with less computational cost. These include some indices to judge the degree of convergence during the optimization procedure and can stop iterating in a timely way when there is no apparent improvement of the solution. To guarantee the feasibility of iterate for the solution procedure to be terminated early, the feasibility-perturbed sequential quadratic programming (FP-SQP) algorithm is used. Simulations on the reference tracking performance of a continuously stirred tank reactor (CSTR) show that the RPS criteria efficiently reduce computation time and the adverse effect of computational delay on closed-loop stability.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Aguilar-Lopez, R., Martinez-Guerra, R., 2005. State estimation for nonlinear systems under model unobservable uncertainties: application to continuous reactor. Chem. Eng. J., 108(1-2):139-144.

[2]Barkhordari Yazdi, M., Jahed-Motlagh, M.R., 2009. Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization. Chem. Eng. J., 155(3):838-843.

[3]Bequette, B.W., 2002. Behavior of CSTR with a Recirculating Jacket Heat Transfer System. American Control Conf., p.3275-3280.

[4]Bock, H.G., Diehl, M., Kühl, P., Kostina, E., Schlöder, J.P., Wirsching, L., 2007. Numerical methods for efficient and fast nonlinear model predictive control. Lect. Notes Control Inform. Sci., 358:163-179.

[5]Chen, H., Allgöwer, F., 1998. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 34(10):1205-1217.

[6]Chen, W., Shao, Z., Wang, K., Chen, X., Biegler, L.T., 2010. Convergence depth control for interior point methods. AIChE J., 56(12):3146-3161.

[7]Chen, W.H., Ballance, D.J., O′Reilly, J., 2000. Model predictive control of nonlinear systems: computational burden and stability. IEE Proc.-Control Theory Appl., 147(4):387-394.

[8]Czeczot, J., 2006. Balance-based adaptive control methodology and its application to the non-isothermal CSTR. Chem. Eng. Process., 45(5):359-371.

[9]DeHaan, D., Guay, M., 2006. A new real-time perspective on non-linear model predictive control. J. Process Control, 16(6):615-624.

[10]Diehl, M., Bock, H.G., Schlöder, J.P., Findeisen, R., Nagy, Z., Allgöwer, F., 2002. Realtime optimization and non-linear model predictive control of processes governed by differential-algebraic equations. J. Process Control, 12(4):577-588.

[11]Diehl, M., Bock, H.G., Schlöder, J.P., 2005. A real-time iteration scheme for nonlinear optimization in optimal feedback control. SIAM J. Control Optim., 43(5):1714-1736.

[12]Diehl, M., Ferreau, H.J., Haverbeke, N., 2008. Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation. Workshhop on Assessment and Future Directions of NMPC.

[13]Findeisen, R., Allgöwer, F., 2002. An Introduction to Nonlinear Model Predictive Control. 21st Benelux Meeting on Systems and Control, p.119-141.

[14]Findeisen, R., Allgöwer, F., 2003. Computational Delay in Nonlinear Model Predictive Control. Proc. Int. Symp. on Advanced Control of Chemical Processes, p.427-452.

[15]Gill, P.E., Murray, W., Wright, M.H., 1981. Practical Optimization. Academic Press, London.

[16]Henson, M.A., 1998. Nonlinear model predictive control: current status and future directions. Comput. Chem. Eng., 23(2):187-202.

[17]Henson, M.A., Seborg, D.E., 1997. Nonlinear Process Control. Prentice Hall PTR, Upper Saddle River, New Jersey.

[18]Hindmarsh, A.C., Brown, P.N., Grant, K.E., Lee, S.L., Serban, R., Shumaker, D.E., Woodward, C.S., 2005. SUNDIALS, suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Software, 31(3):363-396.

[19]Jockenhövel, T., Biegler, L.T., Wächter, A., 2003. Dynamic optimization of the Tennessee Eastman process using the OptControlCentre. Comput. Chem. Eng., 27(11):1513-1531.

[20]Kameswaran, S., Biegler, L.T., 2006. Simultaneous dynamic optimization strategies: recent advances and challenges. Comput. Chem. Eng., 30(10-12):1560-1575.

[21]Lang, Y.D., Biegler, L.T., 2007. A software environment for simultaneous dynamic optimization. Comput. Chem. Eng., 31(8):931-942.

[22]Mansour, M., Ellis, J.E., 2008. Methodology of on-line optimization applied to a chemical reactor. Appl. Math. Model., 32(2):170-184.

[23]Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M., 2000. Constrained model predictive control: stability and optimality. Automatica, 36(6):789-814.

[24]Nocedal, J., Wright, S.J., 1999. Numerical Optimization. Springer, New York.

[25]Pan, T., Li, S., Cai, W., 2007. Lazy learning-based online identification and adaptive PID control: a case study for CSTR process. Ind. Eng. Chem. Res., 46(2):472-480.

[26]Qin, S.J., Badgwell, T.A., 2003. A survey of industrial model predictive control technology. Control Eng. Pract., 11(7):733-764.

[27]Santos, L.O., Afonso, P.A., Castro, J.A., Oliveira, N.M., Biegler, L.T., 2001. On-line implementation of nonlinear MPC: an experimental case study. Control Eng. Pract., 9(8):847-857.

[28]Schäfer, A., Kühl, P., Diehl, M., Schlöder, J., Bock, H.G., 2007. Fast reduced multiple shooting methods for nonlinear model predictive control. Chem. Eng. Process.: Process Intens., 46(11):1200-1214.

[29]Scokaert, P.O.M., Mayne, D.Q., Rawlings, J.B., 1999. Suboptimal model predictive control (feasibility implies stability). IEEE Trans. Autom. Control, 44(3):648-654.

[30]Tenny, M., 2002. Computational Strategies for Nonlinear Model Predictive Control. PhD Thesis, University of Wisconsin-Madison, Madison, Wisconsin, USA.

[31]Tenny, M., Wright, S.J., Rawlings, J.B., 2004. Nonlinear model predictive control via feasibility-perturbed sequential quadratic programming. Comput. Optim. Appl., 28(1):87-121.

[32]Vassiliadis, V.S., Sargent, R.W.H., Pantelides, C.C., 1994a. Solution of a class of multistage dynamic optimization problems. 1. Problems without path constrints. Ind. Eng. Chem. Res., 33(9):2111-2122.

[33]Vassiliadis, V.S., Sargent, R.W.H., Panteides, C.C., 1994b. Solution of a class of multistage dynamic optimization problems. 2. Problems with path constraints. Ind. Eng. Chem. Res., 33(9):2123-2133.

[34]Wang, K., Shao, Z., Zhang, Z., Chen, Z., Fang, X., Zhou, Z., 2007. Convergence depth control for process system optimization. Ind. Eng. Chem. Res., 46(23):7729-7738.

[35]Wright, S.J., Tenny, M., 2004. A feasible trust-region sequential quadratic programming algorithm. SIAM J. Optim., 14(4):1074-1105.

[36]Wu, W., 2000. Nonlinear bounded control of a nonisothermal CSTR. Ind. Eng. Chem. Res., 39(10):3789-3798.

[37]Zavala, V.M., Biegler, L.T., 2009. The advanced-step NMPC controller: optimality, stability and robustness. Automatica, 45(1):86-93.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE