Computational Sensitivity Analysis for State Constrained Optimal Control Problems

作者: Dirk Augustin , Helmut Maurer

DOI: 10.1023/A:1010960221295

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摘要: A theoretical sensitivity analysis for parametric optimal control problems subject to pure state constraints has recently been elaborated in [7,8]. The articles consider both first and higher order develop conditions solution differentiability of solutions with respect parameters. In this paper, we treat the numerical aspects computing differentials via appropriate boundary value problems. particular, methods are proposed that allow verify all assumptions underlying differentiability. Three examples one, two four discussed detail.

参考文章(13)
Kazimierz Malanowski, Helmut Maurer, Sensitivity Analysis for Optimal Control Problems Subject to Higher Order State Constraints Annals of Operations Research. ,vol. 101, pp. 43- 73 ,(2001) , 10.1023/A:1010956104457
B. Kugelmann, H. J. Pesch, New general guidance method in constrained optimal control, part 2: application to space shuttle guidance Journal of Optimization Theory and Applications. ,vol. 67, pp. 437- 446 ,(1990) , 10.1007/BF00939643
Richard F. Hartl, Suresh P. Sethi, Raymond G. Vickson, A Survey of the Maximum Principles for Optimal Control Problems with State Constraints SIAM Review. ,vol. 37, pp. 181- 218 ,(1995) , 10.1137/1037043
Christof Büskens, Helmut Maurer, SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control Journal of Computational and Applied Mathematics. ,vol. 120, pp. 85- 108 ,(2000) , 10.1016/S0377-0427(00)00305-8
Kazimierz Malanowski, , Helmut Maurer, , Sensitivity analysis for state constrained optimal control problems Discrete and Continuous Dynamical Systems. ,vol. 4, pp. 241- 272 ,(1998) , 10.3934/DCDS.1998.4.241
B. Kugelmann, H. J. Pesch, New general guidance method in constrained optimal control, part 1: numerical method Journal of Optimization Theory and Applications. ,vol. 67, pp. 421- 435 ,(1990) , 10.1007/BF00939642
Roland Bulirsch, Josef Stoer, Introduction To Numerical Analysis ,(1956)
H. Maurer, H. J. Pesch, Solution differentiability for parametric nonlinear control problems with control-state constraints Journal of Optimization Theory and Applications. ,vol. 86, pp. 285- 309 ,(1995) , 10.1007/BF02192081