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- W4387680905 abstract "We consider a controlled system for the differential equation x ̇(t)=f(t,x(t),u(t),ξ),t∈[a,b],x(a)=x, where the parameter ξ is an element of some given metric space, the control u satisfies the constraint u(t)∈U(t,x(t),ξ),t∈[a,b]. It is assumed that at each given moment of time t_k∈(a,b) a solution x:[a; b]→R^n (a phase trajectory) suffers discontinuity, the magnitude of which belongs to a non-empty compact set I_k (x(t_k ) )⊂R^n, and is an absolutely continuous function on intervals (t_(k-1),t_k]. The control function is assumed to be measurable. A theorem on estimating the distance from a given piecewise absolutely continuous function y:[a,b]→R^n to the set of phase trajectories for all initial values from a neighborhood of a vector x_0 and for all parameters from a neighborhood of a point ξ_0 is proven. It is assumed that for the given initial value x=x_0 of the solution and for the value ξ=ξ_0 of the parameter, the set of phase trajectories is a priori limited. The proven theorem allows, by selecting the function y, to obtain an approximate solution of the controlled system, as well as an estimate of the error of such solution." @default.
- W4387680905 created "2023-10-17" @default.
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- W4387680905 date "2023-01-01" @default.
- W4387680905 modified "2023-10-17" @default.
- W4387680905 title "Estimates of the phase trajectories of controlled systems with multi-valued impulses" @default.
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- W4387680905 doi "https://doi.org/10.20310/2686-9667-2023-28-143-326-334" @default.
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