## Tracking discrete almost-periodic signals under random perturbations.(English)Zbl 0642.93068

Let, for a $$k\in {\mathbb{Z}}$$, $$A_ k$$ and $$B_ k$$ be almost-periodic $$n\times n$$ matrices. Let us consider the system: $$x_{k+1}=A_ kx_ k+B_ ku_ k$$. Given the almost-periodic signal $$r_ k$$, one looks for a feedback control $$u_ k=L_ kx_ k+d_ k$$, such that the solution will be as close as possible to the signal $$r_ k.$$
The authors consider the deterministic situation and after that, supposing random perturbations, arrive at a result of the large numbers type for the cost of tracking a discrete almost-periodic signal. The result is a complete analogue to that given by the first and third author in Stochastics 21, 287-301 (1987; Zbl 0624.60073).
Reviewer: G.G.Vrânceanu

### MSC:

 93E20 Optimal stochastic control 93C05 Linear systems in control theory 93C55 Discrete-time control/observation systems 15A24 Matrix equations and identities 60G35 Signal detection and filtering (aspects of stochastic processes)

Zbl 0624.60073
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### References:

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