• Previous Article
    Existence results for general systems of differential equations on one-dimensional networks and prewavelets approximation
  • DCDS Home
  • This Issue
  • Next Article
    Exponential attractors for nonautonomous first-order evolution equations
April  1998, 4(2): 241-272. doi: 10.3934/dcds.1998.4.241

Sensitivity analysis for state constrained optimal control problems

1. 

Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland

2. 

Westfälische Wilhelms-Universität Münster, Institut für Numerische und instrumentelle Mathematik, Einsteinstrasse 62, 48149 Münster, Germany

Received  September 1996 Revised  January 1997 Published  February 1998

A family of parameter dependent optimal control poblems for nonlinear ODEs is considered. The problems are subject to pointwise control and state inequality type constraints. It is assumed that, at the reference value of the parameter the reference optimal solution exists and is regular. Regularity conditions are formulated under which the original problems are locally equivalent to some problems subject to equality type constraints only. The classical implicit function theorem is applied to these new problems to investigate Fréchet differentiability of the solutions with respect to the parameter. A numerical example is provided.
Citation: Kazimierz Malanowski, Helmut Maurer. Sensitivity analysis for state constrained optimal control problems. Discrete & Continuous Dynamical Systems, 1998, 4 (2) : 241-272. doi: 10.3934/dcds.1998.4.241
[1]

Nguyen Huy Chieu, Jen-Chih Yao. Subgradients of the optimal value function in a parametric discrete optimal control problem. Journal of Industrial & Management Optimization, 2010, 6 (2) : 401-410. doi: 10.3934/jimo.2010.6.401

[2]

Nguyen Hai Son. Solution stability to parametric distributed optimal control problems with finite unilateral constraints. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021047

[3]

Eduardo Casas, Fredi Tröltzsch. Sparse optimal control for the heat equation with mixed control-state constraints. Mathematical Control & Related Fields, 2020, 10 (3) : 471-491. doi: 10.3934/mcrf.2020007

[4]

Huaiqiang Yu, Bin Liu. Pontryagin's principle for local solutions of optimal control governed by the 2D Navier-Stokes equations with mixed control-state constraints. Mathematical Control & Related Fields, 2012, 2 (1) : 61-80. doi: 10.3934/mcrf.2012.2.61

[5]

Vincenzo Basco, Piermarco Cannarsa, Hélène Frankowska. Necessary conditions for infinite horizon optimal control problems with state constraints. Mathematical Control & Related Fields, 2018, 8 (3&4) : 535-555. doi: 10.3934/mcrf.2018022

[6]

Luís Tiago Paiva, Fernando A. C. C. Fontes. Adaptive time--mesh refinement in optimal control problems with state constraints. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 4553-4572. doi: 10.3934/dcds.2015.35.4553

[7]

Theodore Tachim-Medjo. Optimal control of a two-phase flow model with state constraints. Mathematical Control & Related Fields, 2016, 6 (2) : 335-362. doi: 10.3934/mcrf.2016006

[8]

Dariusz Idczak. A global implicit function theorem and its applications to functional equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2549-2556. doi: 10.3934/dcdsb.2014.19.2549

[9]

Matthias Gerdts, Martin Kunkel. A nonsmooth Newton's method for discretized optimal control problems with state and control constraints. Journal of Industrial & Management Optimization, 2008, 4 (2) : 247-270. doi: 10.3934/jimo.2008.4.247

[10]

Maria do Rosário de Pinho, Ilya Shvartsman. Lipschitz continuity of optimal control and Lagrange multipliers in a problem with mixed and pure state constraints. Discrete & Continuous Dynamical Systems, 2011, 29 (2) : 505-522. doi: 10.3934/dcds.2011.29.505

[11]

Elimhan N. Mahmudov. Optimal control of second order delay-discrete and delay-differential inclusions with state constraints. Evolution Equations & Control Theory, 2018, 7 (3) : 501-529. doi: 10.3934/eect.2018024

[12]

Md. Haider Ali Biswas, Maria do Rosário de Pinho. A nonsmooth maximum principle for optimal control problems with state and mixed constraints - convex case. Conference Publications, 2011, 2011 (Special) : 174-183. doi: 10.3934/proc.2011.2011.174

[13]

Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems. Journal of Industrial & Management Optimization, 2018, 14 (3) : 913-930. doi: 10.3934/jimo.2017082

[14]

Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020110

[15]

Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations & Control Theory, 2017, 6 (3) : 319-344. doi: 10.3934/eect.2017017

[16]

Piermarco Cannarsa, Hélène Frankowska, Elsa M. Marchini. On Bolza optimal control problems with constraints. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 629-653. doi: 10.3934/dcdsb.2009.11.629

[17]

Mikhail Gusev. On reachability analysis for nonlinear control systems with state constraints. Conference Publications, 2015, 2015 (special) : 579-587. doi: 10.3934/proc.2015.0579

[18]

M. Arisawa, P.-L. Lions. Continuity of admissible trajectories for state constraints control problems. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 297-305. doi: 10.3934/dcds.1996.2.297

[19]

Canghua Jiang, Zhiqiang Guo, Xin Li, Hai Wang, Ming Yu. An efficient adjoint computational method based on lifted IRK integrator and exact penalty function for optimal control problems involving continuous inequality constraints. Discrete & Continuous Dynamical Systems - S, 2020, 13 (6) : 1845-1865. doi: 10.3934/dcdss.2020109

[20]

Changjun Yu, Shuxuan Su, Yanqin Bai. On the optimal control problems with characteristic time control constraints. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021021

2020 Impact Factor: 1.392

Metrics

  • PDF downloads (177)
  • HTML views (0)
  • Cited by (40)

Other articles
by authors

[Back to Top]