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The Robust Maximum Principle pp 269–283Cite as

Birkhäuser

Dynamic Programming for Robust Optimization

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Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

Abstract

In this chapter we extend the Dynamic Programming (DP) approach to multimodel Optimal Control Problems (OCPs). We deal with the robust optimization of multimodel control systems and are particularly interested in the Hamilton–Jacobi–Bellman (HJB) equation for the above class of problems. Here we study a variant of the HJB for multimodel OCPs and examine the natural relationship between the Bellman DP techniques and the Robust Maximum Principle (MP). Moreover, we describe how to carry out the practical calculations in the context of multimodel LQ problems and derive the associated Riccati-type equation. In this chapter we follow Azhmyakov et al. (Nonlinear Anal. 72:1110–1119, 2010).

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References

  • Azhmyakov, V., Boltyanski, V., & Poznyak, A. (2010), ‘The dynamic programming approach to multi-model robust optimization’, Nonlinear Anal. 72, 1110–1119.

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  • Fattorini, H.O. (1999), Infinite-Dimensional Optimization and Control Theory, Vol. 62 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge.

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  • Fleming, W.H., & Rishel, R.W. (1975), Optimal Deterministic and Stochastic Control, Applications of Mathematics, Springer, Berlin.

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  • Poznyak, A.S. (2008), Advanced Mathematical Tools for Automatic Control Engineers, Vol. 1: Deterministic Technique, Elsevier, Amsterdam.

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Author information

Authors and Affiliations

  1. CIMAT, Jalisco S/N, Col. Valenciana, 36240, Guanajuato, GTO, Mexico

    Vladimir G. Boltyanski

  2. Automatic Control Department, CINVESTAV-IPN, AP-14-740 Av. IPN-2508, Col. San Pedro Zacatenco, 07000, México, D.F., Mexico

    Alexander S. Poznyak

Authors
  1. Vladimir G. Boltyanski
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  2. Alexander S. Poznyak
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Corresponding author

Correspondence to Vladimir G. Boltyanski .

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© 2012 Springer Science+Business Media, LLC

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Boltyanski, V.G., Poznyak, A.S. (2012). Dynamic Programming for Robust Optimization. In: The Robust Maximum Principle. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8152-4_12

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