Dynamic optimization with state variable path constraints

Computers and Chemical Engineering

Volumn 22, Issue 9, 1998, Pages 1241-1256

  Feehery, William F ^a   Barton, Paul I ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

OPTIMIZATION;

OPTIMIZATION;

EID: 0032552259     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0098-1354(98)00012-X     Document Type: Article

References (39)

1. Bartholomew-Biggs M.C. A penalty method for point and path state constraints in trajectory optimization. Opt. Control Appl. Meth. 16:1995;291-297.
2. Barton P.I., Pantelides C.C. Modeling of combined discrete/continuous processes. AIChE J. 40:1994;966-979.
3. Bellman R. Dynamic programming. 1957;Princeton University Press, Princeton NJ.
4. Brenan K.E., Campbell S.L., Petzold L.R. Numerical solution of initial value problems in differential-algebraic equations. 1996;SIAM, Philadelphia, PA.
5. Brüll L., Pallaske R. On consistent initialization of differential-algebraic equations with discontinuities. Proc. 4th European Conference on Mathematics in Industry. 1992;213-217 Shuttgart, Teubner.
6. Brusch R.G., Schapelle R.H. Solution of highly constrained optimal control problems using nonlinear programming. AIAA J. 11:1973;135-136.
7. Bryson A.E., Ho Y. Applied optimal control. 1975;Hemisphere, New York.
8. Denham W.F., Bryson A.E. Optimal programming problems with inequality constraints II. solution by steepest ascent AIAA J. 2(1):1964;25-34.
9. Dixon L.C.W., Bartholomew-Biggs M.C. Adjoint-control transformations for solving practical optimal control problems. Opt. Control. Appl Meth. 2:1981;365-381.
10. Dreyfus S.E. Variational problems with state variable inequality constraints. J. Math. Anal. Appl. 4:1962;297-308.
11. Feehery, W.F., Banga, J.R. Barton, P.I. A novel approach to dynamic optimization of ODE and DAE systems as high-index problems. AIChE Annual Meeting, Miami (1995).
12. Feehery W.F., Barton P.I. A differentiation-based approach to dynamic simulation and optimization with high-index differential-algebraic equations. Berz M., Bischof Ch., Corliss G., Griewank A. Computational differentiation. techniques, applications, and tools:1996;239-252 SIAM, Philadelphia, PA.
13. Feehery W.F., Tolsma J.E., Barton P.I. Efficient sensitivity analysis of large-scale differential-algebraic equations. Appl. Numer. Math. 25:1997;41-54.
14. Galán, S., Feehery, W.F. and Barton, P.I. (1998) Parametric sensitivity functions for hybrid discrete/continuous systems. Appl. Numer. Math., submitted (1997).
15. Gill, P.E., Murray, W., Saunders, M.A. Large-scale SQP methods and their application in trajectory optimization. In R. Bulirsch & D. Kraft, (Eds), Computational optimal control (Chapter 1, pp. 29-42). Birkhäuser Verlag. Basel, (1994).
16. Gopal, V. and Biegler, L.T. A successive linear programming approach for initialization and reinitialization after discontinuities of differential algebraic equations. SIAM J. Scientific Comput., to appear.
17. Jacobson D.H., Lele M.M. A transformation technique for optimal control problems with a state variable inequality constraint. IEEE Trans. Automat. Control. 5:1969;457-464.
18. Jacobson D.H., Lele M.M., Speyer J.L. New necessary conditions of optimality for control problems with state variable inequality constraints. J. Math. Anal. Appl. 35:1971;255-284.
19. Kelley H.J. A trajectory optimization technique based upon the theory of the second variation. Prog. Astronaut. Aeronaut. 14:1964;559-582.
20. Kraft D. Algorithm 733. TOMP - Fortran modules for optimal control calculations ACM Trans. Math. Software. 20(3):1994;263-281.
21. Logsdon J.S., Biegler L.T. Accurate solution of differential-algebraic optimization problems. Ind. Engng Chem. Res. 28:1989;1628-1639.
22. Luus R. Piecewise linear continuous optimal control by iterative dynamic programming. Ind. Engng Chem. Res. 32(5):1993;859-865.
23. Majer C., Marquardt W., Gilles E.D. Reinitialization of DAEs after discontinuities. Comput. Chem. Engng. 19:1995;S507-S512.
24. Maly T., Petzold L.R. Numerical methods and software for sensitivity analysis of differential-algebraic systems. Appl. Numer. Math. 20:1996;57-79.
25. Mattsson S.E., Söderlind G. Index reduction in differential-algebraic equations using dummy derivatives. SIAM J. Sci. Statist. Comput. 14:1993;677-692.
26. Miele A., Mohanty B.P., Venkataraman P., Kuo Y.M. Numerical solution of minimax problems of optimal control, Part 2. JOTA. 38(1):1982;111-135.
27. Pantelides C.C. The consistent initialization of differential-algebraic systems. SIAM J. Sci. Statist. Comput. 9:1988;213-231.
28. Park T., Barton P.I. State event location in differential-algebraic models. ACM Trans. Modeling Comput. Simulation. 6:1996;137-165.
29. Park T., Barton P.I. Analysis and control of combined discrete/continuous systems. Progress and challenges in the chemical processing industries AIChE Symp. Ser. 93(316):1997;102-114.
30. Pesch H.J. Real-time computation of feedback controls for constrained optimal control problems. part 2. a correction method based on multiple shooting Opt. Control. Appl. Meth. 10:1989;147-171.
31. Petzold, L., Rosen, J.B., Gill, P.E., Jay, L.O. and Park, K.Numerical optimal control of parabolic PDEs using DASOPT. Proc. IMA Workshop on Large-Scale Optimization (1996).
32. Rosen O., Luus R. Evaluation of gradients for piecewise optimal control. Comput. Chem. Engng. 15(4):1991;273-281.
33. Sargent R.W.H., Sullivan G.R. The development of an efficient optimal control package. Proc. 8th IFIP Conf. Optimization Tech Pt. 2:1977.
34. Tanartkit P., Biegler L.T. Stable decomposition for dynamic optimization. Ind. Engng Chem. Res. 34:1995;1253-1266.
35. Valentine F.A. The problem of Lagrange with differential inequalities as added side conditions. Contributions to the Calculus of Variations. 1937;407-448 Chicago University Press, Chicago.
36. Vassiliadis V.S. Computational solution of dynamic optimization problems with general differential-algebraic constraints. Ph. D. thesis, University of London, London, UK (1993).
37. Vassiliadis V.S., Sargent R.W.H., Pantelides C.C. Solution of a class of multistage dynamic optimization problems. 2. Problems with path constraints. Ind. Engng Chem. Res. 33:1994;2123-2133.
38. Xing, A. and Wang, C. Applications of the exterior penalty method in constrained optimal control problems. Opt. Control Appl. Meth. 10, 333-345, 1989 (1989).
39. Yen V., Nagurka M. Optimal control of linearly constrained linear systems via state parameterization. Opt. Control Appl. Meth. 13:1992;155-167.