Pré-Publication, Document De Travail Année : 2020

Long term average cost control problems without ergodicity

Résumé

We consider a stochastic control problem with time-inhomogeneous linear dynamics and a long-term average quadratic cost functional. We provide sufficient conditions for the problem to be well-posed. We describe an explicit optimal control in terms of a bounded and non-negative solution of a Riccati equation on $[0, \infty)$, without an initial and terminal condition. We show that, in contrast to the time-homogeneous case, in the inhomogeneous case the optimally controlled state dynamics are not necessarily ergodic.

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hal-02990007 , version 1 (05-11-2020)

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  • HAL Id : hal-02990007 , version 1

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Stefan Ankirchner, Stefan Engelhardt. Long term average cost control problems without ergodicity. 2020. ⟨hal-02990007⟩

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