JournalsaihpcVol. 36, No. 5pp. 1361–1399

Taylor expansions of the value function associated with a bilinear optimal control problem

  • Tobias Breiten

    Institute of Mathematics, University of Graz, Austria
  • Karl Kunisch

    Institute of Mathematics, University of Graz, Austria, RICAM Institute, Austrian Academy of Sciences, Linz, Austria
  • Laurent Pfeiffer

    Institute of Mathematics, University of Graz, Austria
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Abstract

A general bilinear optimal control problem subject to an infinite-dimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated formal differentiation of the Hamilton–Jacobi–Bellman equation. The terms of the approximations are described by multilinear forms, which can be obtained as solutions to generalized Lyapunov equations with recursively defined right-hand sides. They form the basis for defining a suboptimal feedback law. The approximation properties of this feedback law are investigated. An application to the optimal control of a Fokker–Planck equation is also provided.

Cite this article

Tobias Breiten, Karl Kunisch, Laurent Pfeiffer, Taylor expansions of the value function associated with a bilinear optimal control problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 5, pp. 1361–1399

DOI 10.1016/J.ANIHPC.2019.01.001