Abstract
In the past decade nonlinear model predictive control (NMPC) has witnessed steadily increasing attention from control theoretists as well as control practitioners. The practical interest is driven by the fact that today’s processes need to be operated under tighter performance specifications. At the same time more and more constraints, stemming for example from environmental and safety considerations, need to be satisfied. Often these demands can only be met when process nonlinearities and constraints are explicitly considered in the controller. This paper reviews one NMPC technique, often referred to as quasi-infinite horizon NMPC (QIH-NMPC). An appealing feature of QIH-NMPC is the fact that a short control horizon can be realized, implying reduced computational load. At the same time the controller achieves favorable properties such as stability and performance. After introducing the basic concept of model predictive control, the key ideas behind QIH-NMPC are discussed and the resulting properties for the state feedback case are presented. Additionally some new results on output feedback NMPC using high-gain observers are given. With the use of a realistic process control example, it is demonstrated, that even fairly large problems can be considered using NMPC techniques if state-of-the-art optimization techniques are combined with efficient NMPC schemes.
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References
F. Allgöwer, T.A. Badgwell, J.S. Qin, J.B. Rawlings, and S.J. Wright. Nonlinear predictive control and moving horizon estimation — An introductory overview. In P. M. Frank, editor, Advances in Control, Highlights of ECC’99, pages 391–449. Springer, 1999.
F. Allgöwer, R. Findeisen, Z. Nagy, M. Diehl, H.G. Bock, and J.P. Schlöder. Efficient nonlinear model predictive control for large scale constrained processes. In Proceedings of the Sixth International Conference on Methods and Models in Automation and Robotics, pages 43–54. Miedzyzdroje, Poland, 2000.
A.N. Atassi and H. Khalil. A separation principle for the stabilization of a class of nonlinear systems. IEEE Trans. Automat. Contr., 44(9):1672–1687, 1999.
L. Biegler. Efficient solution of dynamic optimization and NMPC problems. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 219–244. Birkhäuser, 2000.
H.G. Bock, M. Diehl, D. Leineweber, and J. Schlöder. A direct multiple shooting method for real-time optimization of nonlinear DAE processes. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 245–268. Birkhäuser, 2000.
H.G. Bock and K.J. Plitt. A multiple shooting algorithm for direct solution of optimal control problems. In Proc. 9th IFAC World Congress, Budapest, 1984.
H. Chen. Stability and Robustness Considerations in Nonlinear Model Predictive Control. Fortschr.-Ber. VDI Reihe 8 Nr. 674. VDI Verlag, Düsseldorf, 1997.
H. Chen and F. Allgöwer. A quasi-infinite horizon predictive control scheme for constrained nonlinear systems. In Proc. 16th Chinese Control Conference, pages 309–316, Qindao, 1996.
H. Chen and F. Allgöwer. Nonlinear model predictive control schemes with guaranteed stability. In R. Berber and C. Kravaris, editors, Nonlinear Model Based Process Control, pages 465–494. Kluwer Academic Publishers, Dodrecht, 1998.
H. Chen and F. Allgöwer. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 34(10):1205–1218, 1998.
H. Chen, C.W. Scherer, and F. Allgöwer. A game theoretic approach to nonlinear robust receding horizon control of constrained systems. In Proc. Amer. Contr. Conf., pages 3073–3077, Albuquerque, 1997.
H. Chen, C.W. Scherer, and F. Allgöwer. A robust model predictive control scheme for constrained linear systems. In 5th IFAC Symposium on Dynamics and Control of Process Systems, DYCOPS-5, pages 60–65, Korfu, 1998.
G. De Nicolao, L. Magni, and R. Scattolini. Stabilizing nonlinear receding horizon control via a nonquadratic terminal state penalty. In Symposium on Control, Optimization and Supervision, CESA’96 IMACS Multiconference, pages 185–187, Lille, 1996.
G. De Nicolao, L. Magni, and R. Scattolini. Stabilizing receding-horizon control of nonlinear time-varying systems. In Proc. 4rd European Control Conference ECC’97, Brussels, 1997.
G. De Nicolao, L. Magni, and R. Scattolini. Stability and robustness of nonlinear receding horizon control. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 3–23. Birkhäuser, 2000.
M. Diehl. Real-Time Optimization for Large Scale Processes. PhD thesis, University of Heidelberg, 2001.
M. Diehl, R. Findeisen, Z. Nagy, H.G. Bock, J.P. Schlöder, and F. Allgöwer. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. To appear in J. Proc. Contr., 2001.
M. Diehl, I. Uslu, R. Findeisen, S. Schwarzkopf, F. Allgöwer, H.G. Bock, T. Bürner, E.D. Gilles, A. Kienle, J.P. Schlöder, and E. Stein. Real-time optimization of large scale process models: Nonlinear model predictive control of a high purity distillation column. In M. Groetschel, S.O. Krumke, and J. Rambau, editors, Online Optimization of Large Scale Systems: State of the Art, pages 363–384. Springer, 2001.
F. Esfandiari and H. Khalil. Output feedback stabilization of fully linearizable systems. Int. J. Contr., 56(5):1007–1037, 1992.
R. Findeisen and F. Allgöwer. Nonlinear model predictive control for index-one DAE systems. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 145–162. Birkhäuser, 2000.
R. Findeisen and F. Allgöwer. A nonlinear model predictive control scheme for the stabilization of setpoint families. Journal A, Benelux Quarterly Journal on Automatic Control, 41(1):37–45, 2000.
R. Findeisen, F. Allgöwer, M. Diehl, H.G. Bock, J.P. Schlöder, and Z. Nagy. Efficient nonlinear model predictive control. In 6th International Conference on Chemical Process Control — CPC VI, pages 454–460, 2000. 6th International Conference on Chemical Process Control — CPC VI.
R. Findeisen, H. Chen, and F. Allgöwer. Nonlinear predictive control for setpoint families. In Proc. Amer. Contr. Conf., pages 260–4, Chicago, 2000. ACC.
R. Findeisen, M. Diehl, Z. Nagy, F. Allgöwer, H.G. Bock, and J.P. Schlöder. Computational feasibility and performance of nonlinear model predicitve control. In Proc. 6st European Control Conference ECC’01, pages 957–961, 2001.
R. Findeisen, L. Imsland, F. Allgöwer, and B.A. Foss. Output feedback nonlinear Predictive control-a separation principle approach. Submitted to 15th IFAC World Congress, 2001.
R. Findeisen and J.B. Rawlings. Suboptimal infinite horizon nonlinear model predictive control for discrete time systems. Technical Report # 97.13, Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland, 1997. Presented at the NATO Advanced Study Institute on Nonlinear Model Based Process Control.
F.A. Fontes. A general framework to design stabilizing nonlinear model predictive controllers. Syst. Contr. Lett., 42(2):127–143, 2000.
L. Imsland, R. Findeisen, F. Allgöwer, and B.A. Foss. A note on stability, robustness and performance of output feedback nonlinear model predictive control. Submitted to Journal of Process Control, 2001.
L. Imsland, R. Findeisen, E. Bullinger, F. Allgöwer, and B.A. Foss. On output feedback nonlinear model predictive control using high gain observers for a class of systems. In 6th IFAC Symposium on Dynamics and Control of Process Systems, DYCOPS-6, pages 91–96, Jejudo, Korea, 2001.
A. Jadbabaie, J. Yu, and J. Hauser. Unconstrained receding horizon control of nonlinear systems. IEEE Trans. Automat. Contr., 46(5):776–783, 2001.
S.S. Keerthi and E.G. Gilbert. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations. J. Opt. Theory and Appl., 57(2):265–293, 1988.
J.H. Lee and B. Cooley. Recent advances in model predictive control and other related areas. In J.C. Kantor, C.E. Garcia, and B. Carnahan, editors, Fifth International Conference on Chemical Process Control — CPC V, pages 201–216. American Institute of Chemical Engineers, 1996.
L. Magni, D. De Nicolao, and R. Scattolini. Output feedback receding-horizon control of discrete-time nonlinear systems. In Preprints of the 4th Nonlinear Control Systems Design Symposium 1998-NOLCOS’98, pages 422–427. IFAC, July 1998.
L. Magni, G. De Nicolao, R. Scattolini, and F. Allgöwer. Robust receding horizon control for nonlinear discrete-time systems. Submitted to 15th IFAC World Congress, 2002, 2001.
D.Q. Mayne. Nonlinear model predictive control: An assessment. In J.C. Kantor, C.E. Garcia, and B. Carnahan, editors, Fifth International Conference on Chemical Process Control — CPC V, pages 217–231. American Institute of Chemical Engineers, 1996.
D.Q. Mayne. Nonlinear model predictive control: Challenges and opportunities. In F. Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 23–44. Birkhäuser, 2000.
D.Q. Mayne and H. Michalska. Receding horizon control of nonlinear systems. IEEE Trans. Automat. Contr., 35(7):814–824, 1990.
D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert. Constrained model predictive control: stability and optimality. Automatica, 26(6):789–814, 2000.
E.S. Meadows and J.B. Rawlings. Receding horizon control with an infinite horizon. In Proc. Amer. Contr. Conf., pages 2926–2930, San Francisco, 1993.
H. Michalska and D.Q. Mayne. Robust receding horizon control of constrained nonlinear systems. IEEE Trans. Automat. Contr., AC-38(11):1623–1633, 1993.
H. Michalska and D.Q. Mayne. Moving horizon observers and observer-based control. IEEE Trans. Automat. Contr., 40(6):995–1006, 1995.
M. Morari and J.H. Lee. Model predictive control: Past, present and future. Comp. & Chem. Eng., 23(4):667–682, 1999.
Z. Nagy, R. Findeisen, M. Diehl, F. Allgöwer, H.G. Bock, S. Agachi, J.P. Schlöder, and D. Leineweber. Real-time feasibility of nonlinear predictive control for large scale processes — a case study. In Proc. Amer. Contr. Conf., pages 4249–4254, Chicago, 2000. ACC.
T. Parisini and R. Zoppoli. A receding horizon regulatro for nonlinear systems and a neural approximation. Automatica, 31(11):1443–1451, 1995.
J. Primbs, V Nevisitc, and J. Doyle. Nonlinear optimal control: A control lyapunov function and receding horizon perspective. Asian Journal of Control, 1(1):14–24, 1999.
S.J. Qin and T.A. Badgwell. An overview of industrial model predictive control technology. In J.C. Kantor, C.E. Garcia, and B. Carnahan, editors, Fifth International Conference on Chemical Process Control — CPC V, pages 232–256. American Institute of Chemical Engineers, 1996.
J.B. Rawlings. Tutorial overview of model predictive control. IEEE Contr. Syst. Magazine, 20(3):38–52, 2000.
P.O.M. Scokaert, D.Q. Mayne, and J.B. Rawlings. Suboptimal model predictive control (feasibility implies stability). IEEE Trans. Automat. Contr., 44(3):648–654, 1999.
P.O.M. Scokaert, J.B. Rawlings, and E.S. Meadows. Discrete-time stability with perturbations: Application to model predictive control. Automatica, 33(3):463–470, 1997.
A. Teel and L. Praly. Tools for semiglobal stabilization by partial state and output feedback. SIAM J. Contr. Optim., 33(5):1443–1488, 1995.
A. Tornambè. High-gain observers for non-linear systems. Int. J. Sys. Sci., 23(9):1475–1489, 1992.
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Findeisen, R., Allgöwer, F. (2003). The quasi-infinite horizon approach to nonlinear model predictive control. In: Zinober, A., Owens, D. (eds) Nonlinear and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45802-6_8
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DOI: https://doi.org/10.1007/3-540-45802-6_8
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