Sampled-data nonlinear model predictive control for constrained continuous time systems

Lecture Notes in Control and Information Sciences

Volumn 346, Issue , 2007, Pages 207-235

  Findeisen, Rolf ^a   Raff, Tobias ^a   Allgöwer, Frank ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; DYNAMIC PROGRAMMING; DYNAMICAL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; OPTIMAL CONTROL SYSTEMS;

CLOSED SOLUTIONS; CONTINOUS TIME SYSTEMS; CONTINUOUS-TIME SYSTEM; CONTROL STRATEGIES; HAMILTON JACOBI BELLMAN EQUATION; MODEL-PREDICTIVE CONTROL; NONLINEAR MODEL PREDICTIVE CONTROL; OPEN LOOP OPTIMAL CONTROL; OPTIMAL CONTROLS; SAMPLED DATA;

MODEL PREDICTIVE CONTROL;

EID: 34547229593     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-37010-9_7     Document Type: Article

References (84)

1. 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, London, 1999.
2. R.A. Bartlett, A. Wächter, and L.T. Biegler. Active set vs. interior point strategies for model predictive control. In Proc. Amer. Contr. Conf., pages 4229-4233, Chicago, Il, 2000.
3. R. Bellman. Dynamic Programming. Princeton University Press, Princeton, New Jersey, 1957.
4. L.D. Berkovitz. Optimal Control Theory. Springer-Verlag, New York, 1974.
5. L. Biegler. Efficient solution of dynamic optimization and NMPC problems. In R Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 219-244. Birkhäuser, Basel, 2000.
6. L.T. Biegler and J.B Rawlings. Optimization approaches to nonlinear model predictive control. In W.H. Ray and Y Arkun, editors, Proc. 4th International Conference on Chemical Process Control - CPC IV, pages 543-571. AIChE, CACHE, 1991.
7. T. Binder, L. Blank, H.G. Bock, R. Burlisch, W Dahmen, M. Diehl, T. Kronseder, W. Marquardt, J.P. Schlöder, and O. von Stryk. Introduction to model based optimization of chemical processes on moving horizons. In M. Groetschel, S.O. Krumke, and J. Rambau, editors, Online Optimization of Large Scale Systems: State of the Art, pages 295-339. Springer, Berlin, 2001.
8. R. Blauwkamp and T. Basar. A receding-horizon approach to robust output feedback control for nonlinear systems. In Proc. 38th IEEE Conf. Decision Contr., pages 4879-4884, San Diego, 1999.
9. C.C. Chen and L. Shaw. On receding horizon feedback control. Automatica, 18(3):349-352, 1982.
10. H. Chen. Stability and Robustness Considerations in Nonlinear Model Predictive Control. Fortschr.-Ber. VDI Reihe 8 Nr. 674. VDI Verlag, Düsseldorf, 1997.
11. H. Chen and R 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.
12. H. Chen and R Allgöwer. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 34(10):1205-1218, 1998.
13. H. Chen, C.W. Scherer, and R Allgöwer. A game theoretic approach to nonlinear robust receding horizon control of constrained systems. In Proc. Amer. Contr. Confi, pages 3073-3077, Albuquerque, 1997.
14. W Chen, D.J. Ballance, and J. O'Reilly. Model predictive control of nonlinear systems: Computational burden and stability. IEE Proceedings, Part D, 147(4):387-392, 2000.
15. W Chen, D.J. Ballance, and J. O'Reilly. Optimisation of attraction domains of nonlinear mpc via lmi methods. In Proc. Amer. Contr. Confi, pages 3067-3072, Arlington, 2002.
16. R.H. Clark, Y.S. Leydaev, R.J. Stern, and P.R. Wolenski. Nonsmooth Analysis and Control Theory. Number 178 in Graduate Texts in Mathematics. Springer Verlag, New York, 1998.
17. G. De Nicolao, L. Magni, and R. Scattolini. Stability and robustness of nonlinear receding horizon control. In R Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 3-23. Birkhäuser, Basel, 2000.
18. N.M.C, de Oliveira and L.T. Biegler. An extension of Newton-type algorithms for nonlinear process control. Automatica, 31(2):281-286,1995.
19. S. de Oliveira Kothare and M. Morari. Contractive model predictive control for constrained nonlinear systems. IEEE Trans. Aut. Control, 45(6):1053-1071, 2000.
20. M. Diehl, R. Findeisen, R Allgöwer, J.P. Schlöder, and H.G. Bock. Stability of nonlinear model predictive control in the presence of errors due to numerical online optimization. In Proc. 43th IEEE Confi Decision Contr., pages 1419-1424, Maui, 2003.
21. M. Diehl, R. Findeisen, H.G. Bock, J.P. Schlöder, and R Allgöwer. Nominal stability of the real-time iteration scheme for nonlinear model predictive control. IEE Control Theory Appl., 152(3):296-308, 2005.
22. M. Diehl, R. Findeisen, Z. Nagy, H.G. Bock, J.P. Schlöder, and R Allgöwer. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. J. Proc. Contr., 4(12):577-585, 2002.
23. M. Diehl, R. Findeisen, S. Schwarzkopf, I. Uslu, R Allgöwer, H.G. Bock, and J.P. Schlöder. An efficient approach for nonlinear model predictive control of large-scale systems. Part I: Description of the methodology. Automatisierungstechnik, 12:557-567, 2002.
24. M. Diehl, R. Findeisen, S. Schwarzkopf, I. Uslu, R Allgöwer, H.G. Bock, and J.P. Schlöder. An efficient approach for nonlinear model predictive control of large-scale systems. Part II: Experimental evaluation considering the control of a distillation column. Automatisierungstechnik, 1:22-29, 2003.
25. A.M. Elaiw and Gyurkovics É. Multirate sampling and delays in receding horizon stabilization of nonlinear systems. In Proc. 16th IFAC World Congress, Prague, Czech Republic, 2005.
26. R. Findeisen. Nonlinear Model Predictive Control: A Sampled-Data Feedback Perspective. Fortschr.-Ber. VDI Reihe 8 Nr. 1087, VDI Verlag, Düsseldorf, 2005.
27. R. Findeisen and R Allgöwer. Stabilization using sampled-data open-loop feedback - a nonlinear model predictive control perspective. In Proc. Symposium on Nonlinear Control Systems, NOLCOS'2004, Stuttgart, Germany, 2004.
28. R. Findeisen, H. Chen, and R Allgöwer. Nonlinear predictive control for setpoint families. In Proc. Amer. Contr. Confi, pages 260-265, Chicago, 2000.
29. R. Findeisen, M. Diehl, I. Uslu, S. Schwarzkopf, R Allgöwer, H.G. Bock, J.P. Schlöder, and E.D. Gilles. Computation and performance assessment of nonlinear model predictive control. In Proc. 42th IEEE Confi Decision Contr., pages 4613-4618, Las Vegas, 2002.
30. R. Findeisen, L. Imsland, R Allgöwer, and B.A. Foss. Output feedback nonlinear predictive control - a separation principle approach. In Proc. of 15th IFAC World Congress, Barcelona, Spain, 2002. Paper ID 2204 on CD-ROM.
31. R. Findeisen, L. Imsland, R Allgöwer, and B.A. Foss. Output feedback stabilization for constrained systems with nonlinear model predictive control. Int. J. of Robust and Nonlinear Control, 13(3-4):211-227, 2003.
32. R. Findeisen, L. Imsland, R Allgöwer, and B.A. Foss. State and output feedback nonlinear model predictive control: An overview. Europ. J. Contr., 9(2-3):190-207, 2003.
33. R. Findeisen, L. Imsland, R Allgöwer, and B.A. Foss. Towards a sampled-data theory for nonlinear model predictive control. In W. Kang, C Borges, and M. Xiao, editors, New Trends in Nonlinear Dynamics and Control, volume 295 of Lecture Notes in Control and Information Sciences, pages 295-313, New York, 2003. Springer-Verlag.
34. R. Findeisen, Z. Nagy, M. Diehl, R Allgöwer, H.G. Bock, and J.P. Schlöder. Computational feasibility and performance of nonlinear model predicitve control. In Proc. 6th European Control Conference ECC'01, pages 957-961, Porto, Portugal, 2001.
35. W H. Fleming and R. W. Rishel. Deterministic and stochastic optimal control. Springer, Berlin, 1982.
36. F.A. Fontes. A general framework to design stabilizing nonlinear model predictive controllers. Syst. Contr. Lett., 42(2):127-143, 2000.
37. F.A. Fontes. Discontinuous feedbacks, discontinuous optimal controls, and continuous-time model predictive control. Int. J. of Robust and Nonlinear Control, 13(3-4):191-209, 2003.
38. F.A. Fontes and L. Magni. Min-max predictive control of nonlinear systems using discontinuous feedback. IEEE Trans. Aut. Control, 48(10):1750-1755, 2003.
39. R. Freeman and J. Primbs. Control Lyapunov functions: New ideas from an old source. In Proc. 35th IEEE Conf. Decision Contr., pages 3926-3931, Kobe, Japan, December 1996.
40. J. B. Froisy. Model predictive control: Past, present and future. ISA Transactions, 33:235-243, 1994.
41. C.E. García, D.M. Prett, and M. Morari. Model Predictive Control: Theory and practice -A survey. Automatica, 25(3):335-347, 1989.
42. G. Grimm, M.J. Messina, S. Tuna, and A.R. Teel. Model predictive control: for want of a local control lyapunov function, all is not lost. IEEE Trans. Aut. Control, 50(5):546-558, 2005.
43. R. Grossman, A. Nerode, A. Ravn, and H. Rischel, editors. Hybrid Dynamical Systems. Springer-Verlag, New York, 1993.
44. L. Grüne and D. Nešić. Optimization based stabilization of sampled-data nonlinear systems via their approximate discrete-time models. SIAM J. Contr. Optim., 42:98-122, 2003.
45. L. Grüne, D. Nešić, and J. Pannek. Model predictive control for nonlinear sampleddata systems. In R. Findeisen, L.B. Biegler, and R Allgöwer, editors, Assessment and Future Directions of Nonlinear Model Predictive Control, Lecture Notes in Control and Information Sciences, Berlin, 2006. Springer-Verlag, to appear.
46. L. Hou, A.N. Michel, and H. Ye. Some qualitative properties of sampled-data control systems. IEEE Trans. Aut. Control, 42(42):1721-1725,1997.
47. L. Imsland, R. Findeisen, E. Bullinger, R Allgöwer, and B.A. Foss. A note on stability, robustness and performance of output feedback nonlinear model predictive control. J. Proc. Contr., 13(7):633-644, 2003.
48. K. Ito and K. Kunisch. Asymptotic properties of receding horizon optimal control problems. SIAM J. Contr. Optim., 40(5):1585-1610, 2002.
49. A. Jadbabaie and J. Hauser. On the stability of receding horizon control with a general cost. IEEE Trans. Aut. Control, 50(5):674-678, 2005.
50. A. Jadbabaie, J. Yu, and J. Hauser. Unconstrained receding horizon control of nonlinear systems. IEEE Trans. Aut. Control, 46(5):776 -783, 2001.
51. S.S. Keerthi and E.G. Gilbert. An existence theorem for discrete-time infinite-horizon optimal control problems. IEEE Trans. Aut. Control, 30(9):907-909, 1985.
52. 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.
53. M.V. Kothare, V. Balakrishnan, and M. Morari. Robust constrained model predictive control using linear matrix inequalities. Automatica, 32(10):1361-1379, 1996.
54. S. Lall and K. Glover. A game theoretic approach to moving horizon control. In D. Clarke, editor, Advances in Model-Based Predictive Control. Oxford University Press, 1994.
55. 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.
56. W.C. Li and L.T. Biegler. Multistep, Newton-type control strategies for constrained nonlinear processes. Chem. Eng. Res. Des., 67:562-577, 1989.
57. L. Magni, G. De Nicolao, R. Scatollini, and R Allgöwer. Robust model predictive control for nonlinear discrete-time systems. Int. J. of Robust and Nonlinear Control, 13(3-4):229-246, 2003.
58. L. Magni, G. De Nicolao, and R. Scattolini. Output feedback and tracking of nonlinear systems with model predictive control. Automatica, 37(10):1601-1607, 2001.
59. L. Magni, G. De Nicolao, R. Scattolini, and R Allgöwer. Robust receding horizon control for nonlinear discrete-time systems. In Proc. of 15th IFAC World Congress, Barcelona, Spain, 2001. Paper ID 759 on CD-ROM.
60. ∞ control problem. Automatica, 37(5):429-435, 2001.
61. L. Magni and R. Scattolini. State-feedback MPC with piecewise constant control for continuous-time systems. In Proc. 42th IEEE Conf. Decision Contr., pages 4625 - 4630, Las Vegas, 2002.
62. L. Magni and R. Scattolini. Model predictive control of continuous-time nonlinear systems with piecewise constant control. IEEE Trans. Aut. Control, 49(5):900-906, 2004.
63. L. Magni and R. Sepulchre. Stability margins of nonlinear receding-horizon control via inverse optimality. Syst. Contr. Lett., 32(4):241-245, 1997.
64. R. Mahadevan and F.J. Doyle III. Efficient optimization approaches to nonlinear model predictive control. Int. J. of Robust and Nonlinear Control, 13(3-4):309-329, 2003.
65. R Martinsen, L.T. Biegler, and B.A Foss. Application of optimization algorithms to nonlinear MPC In Proc. of 15th IFAC World Congress, Barcelona, Spain, 2002. Paper ID 1245 on CD-ROM.
66. D.Q. Mayne. Optimization in model based control. In Proc. IFAC Symposium Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes, pages 229-242, Helsingor, 1995.
67. D.Q. Mayne and H. Michalska. Receding horizon control of nonlinear systems. IEEE Trans. Aut. Control, 35(7):814-824, 1990.
68. D.Q. Mayne, J.B. Rawlings, CV Rao, and P.O.M. Scokaert. Constrained model predictive control: stability and optimality. Automatica, 26(6):789-814, 2000.
69. E.S. Meadows, M.A. Henson, J.W. Eaton, and J.B. Rawlings. Receding horizon control and discontinuous state feedback stabilization. Int. J. Contr., 62(5):1217-1229, 1995.
70. H. Michalska. Trajectory tracking control using the receding horizon stratrgy. In Symposium on Control, Optimization and Supervision, CESA'96 IMACS Multiconference, pages 298-303, Lille, 1996.
71. H. Michalska and D.Q. Mayne. Robust receding horizon control of constrained nonlinear systems. IEEE Trans. Aut. Control, 38(11):1623-1633, 1993.
72. H. Michalska and D.Q. Mayne. Moving horizon observers and observer-based control. IEEE Trans. Aut. Control, 40(6):995-1006, 1995.
73. H. Michalska and R.B. Vinter. Nonlinear stabilization using discontinuous movinghorizon control. IMA Journal of Mathematical Control & Information, 11:321-340,1994.
74. A.N. Michel. Recent trends in the stability analysis of hybride dynamical systems. IEEE Trans. on Circuits and System, 45(1):120-133, 1999.
75. M. Morari and J.H. Lee. Model predicitve control: Past, present and future. Comp. & Chem. Eng., 23(4/5):667-682, 1999.
76. R. Pytlak. Numerical Methods for Optimal Control Problems with State Constraints. Lecture Notes in Mathematics. Springer, Berlin, 1999.
77. S.J. Qin and T.A. Badgwell. An overview of nonlinear model predictive control applications. In R Allgöwer and A. Zheng, editors, Nonlinear Predictive Control, pages 369-393. Birkhäuser, 2000.
78. S.J. Qin and T.A. Badgwell. A survey of industrial model predictive control technology. Control Engineering Practice, 11(7):733-764, July 2003.
79. P.O.M. Scokaert, D.Q. Mayne, and J.B. Rawlings. Suboptimal model predictive control (feasibility implies stability). IEEE Trans. Aut. Control, 44(3):648-654, 1999.
80. 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.
81. M.J. Tenny and J.B. Rawlings. Feasible real-time nonlinear model predictive control. In 6th International Conference on Chemical Process Control - CPC VI, AIChE Symposium Series, 98(326), pages 187-193, 2001.
82. R. Vinter. Optimal Control. Systems & Control: Foundations & Applications. Birkhäuser Verlag, Boston, 2000.
83. S. J. Wright. Applying new optimization algorithms to model predictive control. In J.C. Kantor, C.E. Garcia, and B. Carnahan, editors, Fifth International Conference on Chemical Process Control - CPC V, pages 147-155. AIChE Symposium Series, 93(316), 1996.
84. H. Ye, A.N. Michel, and L. Hou. Stability theory for hybrid dynamical systems. IEEE Trans. Aut. Control, 43(4):461-474, 1998.