Neighbouring-extremal control for singular dynamic optimisation problems. Part I: Single-input systems

International Journal of Control

Volumn 82, Issue 6, 2009, Pages 1099-1112

  Gros, S ^a   Srinivasan, B ^b   Chachuat, B ^a   Bonvin, D ^a  

^a EPFL   (Switzerland)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

Dynamic optimisation; Neighbouring extremal control; Optimal control; Singular arcs; Singular control

Indexed keywords

ACTIVE CONSTRAINTS; BOUNDARY ARCS; CONTROL FORCE; EXTREMAL; EXTREMAL CONTROL; FEEDBACK LAWS; FIRST-ORDER; MULTIPLE INPUTS; NECESSARY CONDITIONS OF OPTIMALITY; NEIGHBOURING-EXTREMAL CONTROL; OPTIMAL CONTROL; OPTIMISATION; SEMI-BATCH; SINGLE-INPUT SYSTEMS; SINGULAR ARCS; SINGULAR CONTROL;

CHEMICAL REACTORS;

UNCERTAINTY ANALYSIS;

EID: 67749122106     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170802460024     Document Type: Article

References (36)

1. Abel, O., Helbig, A., Marquardt, W., Zwick, H., and Daszkowski, T. (2000), 'Productivity Optimization of an Industrial Semi-batch Polymerization Reactor Under Safety Constraints', Journal of Process Control, 10, 351-362.
2. Ascher, U.M., and Petzold, L.R. (1998), Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Philadelphia, PA: SIAM.
3. Bell, D.J., and Jacobson, D.H. (1975), Singular Optimal Control Problems, New York: Academic Press.
4. Biegler, L.T. (1984), 'Solution of Dynamic Optimization Problems by Successive Quadratic Programming and Orthogonal Collocation', Computers & Chemical Engineering, 8, 243-248.
5. Bonvin, D., and Srinivasan, B. (2003), 'Optimal Operation of Batch Processes via the Tracking of Active Constraints', ISA Transactions, 42, 123-134.
6. Breakwell, A.E., and Ho, Y.C. (1965), 'On the Conjugate Point Condition for the Control Problem', International Journal of Engineering Science, 2, 565-579.
7. Breakwell, A.E., Speyer, J.L., and Bryson, A.E. (1963), 'Optimization and Control of Nonlinear Systems Using the Second Variation', SIAM Journal on Control and Optimization, 1, 193-217.
8. Bryson, A.E., and Ho, Y.C. (1975), Applied Optimal Control, Washington, DC: Hemisphere.
9. Buskens, C., and Maurer, H. (2001), 'Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems using Nonlinear Programming Methods', in Online Optimization of Large Scale Systems, eds. M. Grötschel, S.O. Krumke, and J. Rambau, Berlin: Springer, pp. 57-68.
10. Büskens, C., Pesch, H.J., and Winderl, S. (2001), 'Real-Time Solutions of Bang-Bang and Singular Optimal Control Problems', in Online Optimization of Large Scale Systems, eds. M. Grötschel, S.O. Krumke, and J. Rambau, Berlin: Springer, pp. 129-142.
11. Eaton, J.W., and Rawlings, J.B. (1990), 'Feedback Control of Nonlinear Processes using Online Optimization Techniques', Computers & Chemical Engineering, 14, 469-479.
12. Fiacco, A.V. (1983), Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Volume 165 of Mathematics in Science and Engineering, New York: Academic Press.
13. François, G., Srinivasan, B., and Bonvin, D. (2005), 'Use of Measurements for Enforcing the Necessary Conditions of Optimality in the Presence of Constraints and Uncertainty', Journal of Process Control, 15, 701-712.
14. Gros, S., Buccieri, D., Mullhaupt, P., and Bonvin, D. (2007), 'A Two-time-scale Control Scheme for Fast Systems', Lecture Notes in Controls and Information, 358, 551-563.
15. Gros, S., Chachuat, B., and Bonvin, D. (2009), 'Neighbouring-Extremal Control for Singular Dynamic Optimization Problems. Part II: Multiple-Input Systems', International Journal of Control (DOI: 10.1080/ 00207170802460032).
16. Gros, S., Srinivasan, B., and Bonvin, D. (2008), 'Static Optimization Based on Output Feedback', Industrial & Engineering Chemistry Research. (Submitted).
17. Isidori, A. (1989), Nonlinear Control Systems (2nd ed.), Berlin: Springer-Verlag.
18. Kelley, H.J. (1962), 'Guidance Theory and Extremal Fields', IRE Transactions on Automatic Control, 7, 75-82.
19. Kelley, H.J. (1964), 'An Optimal Guidance Approximation Theory', IEEE Transactions on Automatic Control, 9, 129-145.
20. Kelley, H.J., Kopp, R.E., and Moyer, H.G. (1967), 'Singular Extremals', in Topics in Optimization, ed. G. Leitmann, New York: Academic Press, pp. 63-101.
21. Kugelmann, B., and Pesch, H.J. (1990), 'New General Guidance Method in Constrained Optimal Control. Part 1: Numerical Method', Journal of Optimization Theory and Applications, 67, 421-435.
22. Lee, A.Y. (1988), 'Neighbouring Extremals of Dynamic Optimization Problems with Path Equality Constraints', Journal of Optimization Theory and Applications, 57, 519-536.
23. Lee, E.B., and Markus, L. (1967), Foundations of Optimal Control Theory, New York: John Wiley and Sons.
24. Lewis, R.M. (1980), 'Definitions of Order and Junction Conditions in Singular Optimal Control Problems', SIAM Journal on Control and Optimization, 18, 21-32.
25. Maurer, H., and Pesch, H.J. (1995), 'Solution Differentiability for Parametric Nonlinear Control Problems with Control-State Constraints', Journal of Optimization Theory and Applications, 86, 285-309.
26. Pesch, H.J. (1989a), 'Real-Time Computation of Feedback Controls for Constrained Optimal Control Problems. Part I: Neighboring Extremals', Optimal Control Applications and Methods, 10, 129-145.
27. Pesch, H.J. (1989b), 'Real-Time Computation of Feedback Controls for Constrained Optimal Control Problems. Part II: A Correction Method Based on Multiple Shooting', Optimal Control Applications and Methods, 10, 147-171.
28. Pesch, H.J. (1990), 'The Accessory Minimum Problem and Its Importance for the Numerical Computation of Closed-loop Controls', in Proceedings of the 29th Conference on Decision and Control, Honolulu, HI, pp. 952-953.
29. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F. (1964), The Mathematical Theory of Optimal Processes, New York: Pergamon Press.
30. Robbins, H.M. (1967), 'A Generalized Legendre-Clebsch Condition for the Singular Cases of Optimal Control', IBM Journal of Research and Development, 11, 361-372.
31. Rugh, W.J. (1993), Linear System Theory, New Jersey: Prentice Hall.
32. Srinivasan, B., and Bonvin, D. (2007), 'Real-Time Optimization of Batch Processes via Tracking of Necessary Conditions of Optimality', Industrial & Engineering Chemistry Research, 46, 492-504.
33. Srinivasan, B., Bonvin, D., Visser, E., and Palanki, S. (2003a), 'Dynamic Optimization of Batch Processes-II: Role of Measurements in Handling Uncertainty', Computers & Chemical Engineering, 27, 27-44.
34. Srinivasan, B., Palanki, S., and Bonvin, D. (2003b), 'Dynamic Optimization of Batch Processes-I: Characterization of the Nominal Solution', Computers & Chemical Engineering, 27, 1-26.
35. Vossen, G. (2006), 'Numerische Lösungsmethoden, Hinreichende Optimalitatsbedingungen and
36. Sensitivitätsanalyse für Optimale Bang-bang Und Singuläre Steuerungen', PhD thesis, Universität Münster, Germany.