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Suboptimal integral observation operators in dynamical systems with delay. (Russian. English summary) Zbl 0919.93013

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.

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
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