Coupling MPC and DP Methods for an Efficient Solution of Optimal Control Problems

  • A. Alla
  • G. FabriniEmail author
  • M. Falcone
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 494)


We study the approximation of optimal control problems via the solution of a Hamilton-Jacobi equation in a tube around a reference trajectory which is first obtained solving a Model Predictive Control problem. The coupling between the two methods is introduced to improve the initial local solution and to reduce the computational complexity of the Dynamic Programming algorithm. We present some features of the method and show some results obtained via this technique showing that it can produce an improvement with respect to the two uncoupled methods.


Optimal control Dynamic Programming Model Predictive Control Semi-Lagrangian schemes 


  1. 1.
    Alla, A., Falcone, M., Kalise, D.: An efficient policy iteration algorithm for dynamic programming equations. SIAM J. Sci. Comput. 37(1), 181–200 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bardi, M., Capuzzo Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Basel (1997)CrossRefzbMATHGoogle Scholar
  3. 3.
    Falcone, M.: Numerical solution of dynamic programming equations. Appendix A in the volume. In: Bardi, M., Capuzzo Dolcetta, I. (eds.) Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, pp. 471–504. Birkhäuser, Boston (1997)Google Scholar
  4. 4.
    Falcone, M., Ferretti, R.: Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations. SIAM (2014)Google Scholar
  5. 5.
    Grüne, L., Pannek, J.: Nonlinear Model Predictive Control. Springer, London (2011)CrossRefzbMATHGoogle Scholar
  6. 6.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Operation Research and Financial Engineering, 2nd edn. Springer, New York (2006)zbMATHGoogle Scholar
  7. 7.
    Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Publishing, LLC, Madison (2009)Google Scholar
  8. 8.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  9. 9.
    Zhao, H.: A fast sweeping method for Eikonal equations. Math. Comput. 74, 603–627 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2016

Authors and Affiliations

  1. 1.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA
  2. 2.DIMEUniversità di GenovaGenovaItaly
  3. 3.Laboratoire Jacques-Louis Lions, Sorbonne Universités UPMC Univ Paris 06ParisFrance
  4. 4.Dipartimento di MatematicaLa Sapienza Università di RomaRomaItaly

Personalised recommendations