Nominal stability of real-time iteration scheme for nonlinear model predictive control

IEE Proceedings: Control Theory and Applications

Volumn 152, Issue 3, 2005, Pages 296-308

  Diehl, M ^a   Findeisen, R ^b   Allgower F ^b   Bock, H G ^a   Schloder J P ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; ITERATIVE METHODS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; REAL TIME SYSTEMS; THEOREM PROVING;

FEEDBACK DELAY; NEWTON-TYPE ITERATION; NONLINEAR MODEL PREDICTIVE CONTROL (NMPC); OPTIMIZER DYNAMICS;

NONLINEAR CONTROL SYSTEMS;

EID: 18844462210     PISSN: 13502379     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1049/ip-cta:20040008     Document Type: Article

References (46)

1. Qin, S.J., and Badgwell, T.A.: 'Review of nonlinear model predictive control applications', in Kouvaritakis, B., and Cannon, M. (Eds.): 'Nonlinear model predictive control: theory and application' (IEE, London, 2001), pp. 3-32
2. Henson, M.A.: 'Nonlinear model predictive control: Current status and future directions', Comput. Chem. Eng., 1998, 23, pp. 187-202
3. Mayne, D.Q., Rawlings, J.B., Rao, C.V., and Scokaert, P.O.M.: 'Constrained model predictive control: stability and optimality', Automatics, 2000, 26, (6), pp. 789-814
4. Allgöwer, F., and Zheng, A. (Eds.): 'Nonlinear predictive control' (Birkhäuser, Basel, 2000)
5. Wright, S.J.: 'Applying new optimization algorithms to model predictive control', in Kantor, J.C., Garcia, C.E., and Carnahan, B. (Eds.): Proc. 9th AIChE Conf. on Chemical Process Control (CPC), 1996, pp. 147-155
6. Bartlett, R.A., Wächter, A., and Biegler, L.T.: 'Active set vs. interior point strategies for model predictive control'. Proc. American Control Conf. Chicago, II, 2000, pp. 4229-4233
7. Tenny, M.J., and Rawlings, J.B.: 'Feasible real-time nonlinear model predictive control'. 6th AIChE Int. Conf. on Chemical Process Control - (CPC), 2001
8. Biegler, L.T.: 'Efficient solution of dynamic optimization and NMPC problems', in Allgöwer, F., and Zheng, A. (Eds.): 'Nonlinear predictive control' (Birkhäuser, Basel, 2000), pp. 219-244
9. Li, W.C., and Biegler, L.T.: 'Multistep, Newton-type control strategies for constrained nonlinear processes.', Chem, Eng. Res. Des., 1989, 67, pp. 562-577
10. de Oliveira, N.M.C., and Biegler, L.T.: 'An extension of Newton-type algorithms for nonlinear process control', Automatica, 1995, 31, (2)
11. Tenny, M.J., Wright, S.J., and Rawlings, J.B.: 'Nonlinear model predictive control via feasibility-perturbed sequential quadratic programming'. Technical report TWMCC-2002-02, Texas-Wisconsin Modeling and Control Consortium, 2002
12. Martinsen, F., Biegler, L.T., and Foss, B.A.: 'Application of optimization algorithms to nonlinear MPC'. Proc. 15th IFAC World Congress, 2002
13. Leineweber, D.B., Schäfer, A., Bock, H.G., and Schlöder, J.P.: 'An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimisation. Part II: Software aspects and applications', Comput. Chem. Eng., 2003, 27, pp. 167-174
14. Scokaert, P.O.M., Mayne, D.Q., and Rawlings, J.B.: 'Suboptimal model predictive control (feasibility implies stability)', IEEE Trans. Autom. Control, 1999, 44, (3), pp. 648-654
15. Mayne, D.Q., and Michalska, H.: 'Receding horizon control of nonlinear systems', IEEE Trans. Autom. Control, 1990, 35, (7), pp. 814-824
16. Allgöwer, F., Badgwell, T.A., Qin, J.S., Rawlings, J.B., and Wright, S.J.: 'Nonlinear predictive control and moving horizon estimation - An introductory overview', in Frank, P.M. (Ed.): 'Advances in control, Highlights of ECC'99' (Springer, 1999), pp. 391-449
17. De Nicplao, G., Magni, L., and Scattolini, R.: 'Stability and robustness of nonlinear receding horizon control', in Allgöwer, F., and Zheng, A. (Eds.): 'Nonlinear predictive Control' (Birkhäuser, Basel, 2000), pp. 3-23
18. Findeisen, R., and Allgöwer, F.: 'Computational delay in nonlinear model predictive control'. Proc. Int. Symp. on Advances in Control of Chemical Processes (ADCHEM), 2003 (to be published)
19. Chen, W., Balance, D.J., and O'Reilly, J.: 'Model predictive control of nonlinear systems: Computational delay and stability', IEE Proc., Control Theory Appl., 2000, 147, (4), pp. 387-394
20. Bock, H.G., Diehl, M., Leineweber, D.B., and Schlöder, J.P.: 'A direct multiple shooting method for real-time optimization of nonlinear DAE processes', in Allgöwer, F., and Zheng, A. (Eds.): 'Nonlinear predictive control' (Birkhäuser, Basel, 2000), pp. 246-267
21. Diehl, M., Bock, H.G., Schl̈der, J.P., Findeisen, R., Nagy, Z., and Allgöwer, F.: 'Real-time optimisation and nonlinear model predictive control of processes governed by differential-algebraic equations', J. Process Control, 2002, 12, (4), pp. 577-585
22. Diehl, M.: 'Real-time optimisation for large-scale nonlinear processes', 'vol. 920 of Fortschr.-Ber. VDI Reihe 8, Meß-, Steuerungs- und Regelungstechnik' (VDI Verlag, Düsseldorf, 2002), Download also at: http://www.ub.uni-heidelberg.de/archiv/1659/
23. Diehl, M., Findeisen, R., Schwarzkopf, S., Uslu, I., Allgöwer, F., Bock, H.G., Gilles, E.D., and Schlöder, J.P.: 'An efficient algorithm for nonlinear model predictive control of large-scale systems. Part I: Description of the method', Automatisierungstechnik, 2002, 50, (12), pp. 557-567
24. Findeisen, R., Diehl, M., Uslu, I., Schwarzkopf, S., Allgöwer, F., Bock, H.G., Schlöder, J.P., and Gilles, E.D.: 'Computation and performance assessment of nonlinear model predictive control'. Proc. 42th IEEE Conf. on Decision and Control, Las Vegas, USA, 2002, pp. 4613-4618
25. Diehl, M., Bock, H.G., and Schlöder, J.P.: 'Newton-type methods for the approximate solution of nonlinear programming problems in real-time', in Di Pillo, G., and Murli, A. (Eds.): 'High-performance algorithms and software for nonlinear optimisation' (Kluwer, 2002)
26. Bock, H.G., and Plitt, K.J.: 'A multiple shooting algorithm for direct solution of optimal control problems'. Proc. 9th IFAC World Congress, Budapest, 1984
27. Leineweber, D.B.: 'Efficient reduced SQP methods for the optimisation of chemical processes described by large sparse DAE models', 'vol. 613 of Fortschr.-Ber. VDI Reihe 3, Verfahrenstechnik' (VDI Verlag, Düsseldorf, 1999)
28. Diehl, M., Uslu, I., Findeisen, R., Schwarzkopf, S., Allgöwer, F., Bock, H.G., Burner, T., Gilles, E.D., Kienle, A., Schöder, J.P., and Stein, E.: 'Real-time optimisation for large-scale processes: Nonlinear model predictive control of a high-purity distillation column', in Grötschel, M., Krumke, S.O., and Rambau, J., (Eds.): 'Online Optimisation of large-scale systems: State of the art' (Springer, 2001), pp. 363-384, Download at: http://www.zib.de/dfgechtzeit/Publikationen/Preprints/Preprint-01-16.html
29. Diehl, M., Findeisen, R., Schwarzkopf, S., Uslu, I., Allgöwer, F., Bock, H.G., Gilles, E.D., and Schlöder, J.P.: 'An efficient algorithm for nonlinear model predictive control of large-scale systems. Part II: Application to a distillation column', Automastisierungstechnik, 2003, 51, (1), pp. 22-29
30. Binder, T., Blank, L., Bock, H.G., Bulirsch, R., Dahmen, W., Diehl, M., Kronseder, T., Marquardt, W., Schlöder, J.P., and Stryk, O.v.: 'Introduction to model-based optimisation of chemical processes on moving horizons', in Grötschel, M., Krumke, S.O., and Rambau, J., (Eds.), Online optimisation of large-scale systems: State of the art (Springer, 2001), pp. 295-340, Download at: http://www.zib.de/dfg-echtzeit/Publikationen/Preprints/ Preprint-01-15.html
31. Biegler, L.T., and Rawlings, J.B.: 'Optimisation approaches to nonlinear model predictive control'. Proc. 4th Int. Conf. on Chemical Process Control-(CPC), 1991, pp. 543-571
32. Pytlak, R.: 'Numerical methods for optimal control problems with state constraints', Lect. Notes Math., 1999
33. Baake, E., Baake, M., Bock, H.G., and Briggs, K.: 'Fitting ordinary differential equations to chaotic data', Phys. Rev. A, 1992, 45, pp. 5524-5529
34. Bock, H.G.: 'Randwertproblemmethoden zur Parameteridentifizierung in System nichtlinearer Differentialgleichungen', 'vol. 183 of Bonner Mathematische Schriften' (University of Bonn, Bonn, 1987)
35. Liebman, M.J., Edgar, T.F., and Lasdon, L.S.: 'Efficient data reconciliation and estimation for dynamic processes using nonlinear programming techniques', Comput. Chem. Eng., 1992, 16, (10/11), pp. 963-986
36. de Oliveira, N.M.C., and Biegler, L.T.: 'Newton-type algorithms for nonlinear process control algorithm and stability results', Automation, 1995, 31, (2), pp. 281-286
37. Deuflhard, P., and Heindl, G.: 'Affine invariant convergence theorems for Newton's method and extensions to related methods', SIAM J. Numer, Anal., 1979, pp. 1-10
38. Khalil, H.K.: 'Nonlinear Systems' (Prentice Hall, Upper Saddle River, NJ, 1996, 2nd edn.)
39. Scokaert, P.O.M., Rawlings, J.B., and Meadows, E.S.: 'Discrete-time stability with perturbations: Application to model predictive control', Automatica, 1997, 33, (3), pp. 463-470
40. Kellett, C.M., and Teel, A.R.: 'On robustness of stability and Lyapunov functions for discontinuous difference equations'. Proc. 42th IEEE Conf. on Decision Control, Las Vegas, USA, 2002, pp. 4282-4287
41. Findeisen, R., Imsland, L., Allgöwer, F., and Foss, B.A.: 'State and output feedback nonlinear model predictive control: An overview', Eur. J. Control, 2003, 9, (2-3), pp. 190-207
42. Findeisen, R., Imsland, L., Allgöwer, F., and Foss, B.A.: 'Towards a sampled-data theory for nonlinear model predictive control', Lect. Notes Comput. Sci., 2003, 295, pp. 295-313
43. Meadows, E.S., Henson, M.A., Eaton, J.W., and Rawlings, J.B.: 'Receding horizon control and discontinuous state feedback stabilisation', Int. J. Control, 1995, 62, (5), pp. 1217-1229
44. Fontes, F.A.: 'A general framework to design stabilizing nonlinear model predictive controllers', Syst. Control Lett., 2000, 42, (2), pp. 127-143
45. Grimm, G., Messina, M.J., Teel, A.R., and Tuna, S.: 'Examples when model predictive control is nonrobust'. Proc. American Control Conf., 2003
46. Grimm, G., Messina, M.J., Teel, A.R., and Tuna, S.: 'Model predictive control: for want of a local control Lyapunov function, all is not lost', 2003 (to be published)