Zaika, Yu. V.; Kruchek, M. M. Suboptimal integral observation operators in dynamical systems with delay. (Russian. English summary) Zbl 0919.93013 Tr. Petrozavodsk. Gos. Univ., Ser. Mat. 4, 62-75 (1997). Dynamical time-delay systems with uncertain initial data are considered: \[ \dot x(t)= \sum_j A_jx(t- h_j)+ \int^0_{-h} A(s)x(t+ s)ds+ R(t) u(t), \] \(x(0)= x_0\) with unknown \(x_0\) and \(L_2\)-control \(u\).Information of the systems is obtained by the observation \(y(t)= Gx(t)\), \(t\geq 0\). To minimize, there is a functional of type \[ J= p^0 x(rh)+ \int^0_{-h} p(\tau)x(rh+ \tau)d\tau. \] An algorithm of estimation of the functional \(J\) on solutions of the system by the measurement’s results is derived. Optimal weight functions \(p^0\), \(p\) in the integral observation operator that minimize guaranteed estimation are constructed approximately by means of dynamic programming. Reviewer: W.H.Schmidt (Greifswald) MSC: 93B07 Observability 90C90 Applications of mathematical programming 93C41 Control/observation systems with incomplete information 34K35 Control problems for functional-differential equations 49N70 Differential games and control 49N75 Pursuit and evasion games Keywords:approximation algorithm; optimal observation; optimal weight functions; time-delay systems; uncertain initial data; dynamic programming PDFBibTeX XMLCite \textit{Yu. V. Zaika} and \textit{M. M. Kruchek}, Tr. Petrozavodsk. Gos. Univ., Ser. Mat. 4, 62--75 (1997; Zbl 0919.93013)