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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)

Citations:

Zbl 0624.60073
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References:

[1] ARTSTEIN , Z. , 1984 , On criteria for infinite horizon optimization . Preprint . Weizman Institute of Science , Rehovot .
[2] DOI: 10.1073/pnas.48.12.2039 · Zbl 0112.31401
[3] FINK A. M., Almost Periodic Differential Equations (1974) · Zbl 0325.34039
[4] HALANAY A., Stochastics 21 pp 287– (1987) · Zbl 0624.60073
[5] HALANAY A., Teoria Calitativ[acaron] a Sistemelor cu Impulsuri. (1968)
[6] KWAKERNAAK H., Linear Optimal Control Systems (1972) · Zbl 0276.93001
[7] SHIRYAEV A. M., Probability (1984)
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