On the Regularity of Linear-Quadratic Optimal Control Problems with Bang-Bang Solutions

  • J. Preininger
  • T. Scarinci
  • V. M. VeliovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)


The paper investigates the stability of the solutions of linear-quadratic optimal control problems with bang-bang controls in terms of metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems.


Optimal control Regularity Linear-quadratic problems Bang-bang controls 


  1. 1.
    Alt, W., Schneider, C., Seydenschwanz, M.: Regularization and implicit Euler discretization of linear-quadratic optimal control problems with bang-bang solutions. Appl. Math. Comput. 287–288, 104–105 (2016)MathSciNetGoogle Scholar
  2. 2.
    Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings: A View from Variational Analysis. SSORFE. Springer, New York (2014). CrossRefzbMATHGoogle Scholar
  3. 3.
    Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47, 324–353 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Felgenhauer, U.: On stability of bang-bang type controls. SIAM J. Control Optim. 41(6), 1843–1867 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Pietrus, A., Scarinci, T., Veliov, V.M.: High order discrete approximations to Mayer’s problems for linear systems. Research report 2016–04, ORCOS, TU Wien (2016, to appear)Google Scholar
  6. 6.
    Quincampoix, M., Veliov, V.: Metric regularity and stability of optimal control problems for linear systems. SIAM J. Control Optim. 51(5), 4118–4137 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Seydenschwanz, M.: Convergence results for the discrete regularization of linear-quadratic control problems with bang-bang solutions. Comput. Optim. Appl. 61(3), 731–760 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Veliov, V.M.: On the convexity of integrals of multivalued mappings: applications in control theory. J. Optim. Theory Appl. 54(3), 541–563 (1987)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of Statistics and Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  2. 2.Department of Statistics and Operations ResearchUniversity of ViennaViennaAustria

Personalised recommendations