Advantages of nonlinear-programming-based methodologies for inequality path-constrained optimal control problems - A numerical study

SIAM Journal on Scientific Computing

Volumn 30, Issue 2, 2007, Pages 957-981

  Kameswaran, Shivakumar ^a   Biegler, Lorenz T ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Constraint qualifications; Direct transcription; Nonlinear programming; Optimal control; Path constraints

Indexed keywords

CONSTRAINED OPTIMIZATION; DIFFERENTIAL EQUATIONS; HEAT CONDUCTION; NUMERICAL METHODS; QUADRATIC PROGRAMMING;

CHICAGO; CONSTRAINED OPTIMAL CONTROL PROBLEMS; CONSTRAINED OPTIMI-ZATION PROBLEMS; CONSTRAINT QUALIFICATION; DIFFERENTIAL/ALGEBRAIC EQUATIONS; DIRECT TRANSCRIPTION; ONE-DIMENSIONAL; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; PATH CONSTRAINT;

TRANSCRIPTION;

EID: 55549098567     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/050644938     Document Type: Article

References (22)

1. U.M. ASCHER AND L.R. PETZOLD, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, PA, 1998.
2. J.T. BETTS, Practical Methods for Optimal Control Using Nonlinear Programming, Adv. Des. Control, SIAM, Philadelphia, PA, 2001.
3. J.T. BETTS AND S.L. CAMPBELL, Discretize Then Optimize, Mathematics in Industry: Challenges and Frontiers A Process View: Practice and Theory (PR121) by Ferguson and Peters, SIAM, Philadelphia, 2005.
4. J.T. BETTS, S.L. CAMPBELL, AND A. ENGELSONE, Direct transcription of inequality constrained optimal control problems, in Proceedings of the American Control Conference, Boston, IEEE Press, Piscataway, NJ, 2004, pp. 1622-1626.
5. J.T. BETTS, S.L. CAMPBELL, AND A. ENGELSONE, Direct transcription of optimal control problems with high order state constraints: Theory vs. practice, Optim. Eng., 8 (2007), pp. 1-19.
6. J.T. BETTS AND W.P. HUFFMAN, Estimating Adjoint Variables from a Direct Transcription Solution, M&CT-TECH-04-001, Technical document Series, Phantom Works, Mathematics and Computing Technology, Seattle, WA, 2004.
7. J.T. BETTS, N. BIEHN, S.L. CAMPBELL, AND W.P. HUFFMAN, Convergence of nonconvergent IRK discretizations of optimal control problems, in Proceedings of IMACS, Lausanne, 2000.
8. L.T. BIEGLER, A.M. CERVANTES, AND A. WÁCHTER, Advances in simultaneous strategies for dynamic process optimization, Chem. Eng. Sci., 57 (2002), pp. 575-593.
9. K.E. BRENAN, S.L. CAMPBELL, AND L.R. PETZOLD, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
10. A.E. BRYSON AND Y.C. HO, Applied Optimal Control, Hemisphere, Washington D.C., 1975.
11. W.F. FEEHERY AND P.I. BARTON, Dynamic simulation and optimization with inequality path constraints, Comput. Chem. Eng., 20 Suppl. (1996), pp. S707-S712.
12. W.F. FEEHERY AND P.I. BARTON, Dynamic optimization with state variable path constraints, Comput. Chem. Eng., 22 (1998), pp. 1241-1256.
13. A. FORSGREN, P.E. GILL, AND M.H. WRIGHT, Interior methods for nonlinear optimization, SIAM Rev., 44 (2002), pp. 525-597.
14. R. FOURER, D. GAY, AND B. KERNIGHAN, AMPL, The Scientific Press, San Francisco, CA, 1993.
15. R.F. HARTL, S.P. SETHI, AND R.G. VICKSON, A survey of the maximum principles for optimal control problems with state constraints, SIAM Rev., 37 (1995), pp. 181-218.
16. D.H. JACOBSON, M.M. LELE, AND J.L. SPEYER, New necessary conditions of optimality for control problems with state-variable inequality constraints, J. Math. Anal. Appl., 35 (1971), pp. 255-284.
17. S. KAMESWARAN AND L.T. BIEGLER, Convergence rates for direct transcription of optimal control problems using collocation at Radau points, Control. Optim. Appl., available online DOI 10.1007/sl0589-007-9098- 9.
18. I. NEITZEL AND F. TRÖLTZSCH, On Regularization Methods for the Numerical Solution of Parabolic Control Problems with Pointwise State Constraints, Technical report, Technical University of Berlin, 2007; also available online from http://www.math.tuberlin.de/troeltz/arbeiten/neitro. pdf.
19. G.W. REDDIEN, Collocation at Gauss points as a discretization in optimal control, SIAM J. Control Optim., 17 (1979), pp. 298-306.
20. V.S. VASSILIADIS, R.W.H. SARGENT, AND C.C. PANTELIDES, Solution of a class of multistage dynamic optimization problems. Part II - Problems with path constraints, Ind. Eng. Chem. Res., 33 (1994), pp. 2123-2133.
21. O. VON STRYK AND R. BULIRSCH, Direct and indirect methods for trajectory optimization, Ann. Oper. Res., 37 (1992), pp. 357-373.
22. A. WÄCHTER, AND L.T. BLEGLER, On the implementation of a primal-dual interior point filter line search, algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), pp. 25-57.