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


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
Full Text: DOI


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