Long term average cost control problems without ergodicity

Stefan Ankirchner, Stefan Engelhardt

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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, ∞), 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.
Original languageEnglish
Article number42
JournalApplied Mathematics and Optimization
Issue number3
Early online date14 Sept 2022
Publication statusPublished - 31 Dec 2022
Externally publishedYes


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