Second order sufficient conditions and sensitivity analysis for the optimal control of a container crane under state constraints

Optimization

Volumn 49, Issue 4, 2001, Pages 351-368

  Augustin, Dirk ^a   Maurer, Helmut ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

Computational sensitivity analysis; Crane control; Differentiability of solutions; Parametric nonlinear optimal control; State constraints

Indexed keywords

EID: 8644287265     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Augustin, D. and Maurer, H., Computational Sensitivity Analysis of State Constrained Optimal Control Problems, to appear in Annals of Operations Research, 2000.
2. Dontchev, A. L. and Hager, W. W. (1993). Lipschitz Stability in Nonlinear Control and Optimization, SIAM J. Control and Optimization, 31, 569-603.
3. Dontchev, A. L., Hager, W. W., Poore, A. B. and Yang, B. (1995). Optimality, Stability and Convergence in Nonlinear Control, Applied Mathematics and Optimization, 31, 297-326.
4. Dontchev, A. L. and Hager, W. W. (1998). Lipschitzian Stability for State Constrained Nonlinear Optimal Control, SIAM J. Control and Optimization, 36, 698-718.
5. Hartl, R. F., Sethi, S. P. and Vickson, R. G. (1995). A Survey of the Maximum Principles for Optimal Control Problems with State Constraints, SIAM Review, 37, 181-218.
6. Malanowski, K. (1995). Stability and Sensitivity of Solutions to Nonlinear Optimal Control Problems, Applied Mathematics and Optimization, 32, 111-141.
7. Malanowski, K. (1997). Sufficient Optimality Conditions for Optimal Control Subject to State Constraints, SIAM J. on Control and Optimization, 35, 205-227.
8. Malanowski, K. and Maurer, H. (1996). Sensitivity Analysis for Parametric Control Problems with Control-State Constraints, Computational Optimization and Applications, 5, 253-283.
9. Malanowski, K. and Maurer, H. (1998). Sensitivity Analysis for State Constrained Optimal Control Problems, Discrete and Continuous Dynamical Systems, 4, 241-272.
10. Malanowski, K. and Maurer, H., Sensitivity Analysis of Optimal Control Problems Subject to Higher Order State Constraints, to appear in Annals of Operations Research, 2000.
11. Maurer, H. and Pesch, H. J. (1994). Solution Differentiability for Parametric Nonlinear Control Problems with Control-State Constraints, Control and Cybernetics, 23, 201-227.
12. Maurer, H. and Pickenhain, S. (1995). Second Order Sufficient Conditions for Optimal Control Problems with Mixed Control-State Constraints, Journal of Optimization Theory and Applications, 86, 649-667.
13. Oberle, H. J. and Grimm, W., BNDSCO - A Program for the Numerical Solution of Optimal Control Problems, Institute for Flight Systems Dynamics, DLR, Oberpfaffenhofen, Germany, Internal Report No. 515-89/22, 1989.
14. Pesch. H. J. (1989). Real-Time Computation of Feedback Controls for Constrained Optimal Control Problems, Part 1: Neighbouring Extremals, Optimal Control Applications & Methods, 10, 129-145.
15. Pesch, H. J. (1989). Real-Time Computation of Feedback Controls for Constrained Optimal Control Problems, Part 2: A Correction Method Based on Multiple Shooting, Optimal Control Applications & Methods, 10, 147-171.
16. Pytlak, R. and Vinter, R. B. (1999). Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation, Journal of Optimization Theory and Applications, 101, 623-649.
17. Sakawa, Y. and Shindo, Y. (1982). Optimal Control of Container Cranes, Automatica, 18, 257-266.
18. Teo, K. L. and Jennings, L. S. (1989). Nonlinear Optimal Control Problems with Continuous State Inequality Constraints, Journal of Optimization Theory and Applications, 63, 1-22.