On dynamical reconstruction of control in a system with time delay. Finite-dimensional models (Q2755711)

The authors consider a linear control system described by the functional-differential equation NEWLINE\[NEWLINEdx(t)/dt = Lx_t+Bu(t)+F(t), \quad x_t=x(t+s),NEWLINE\]NEWLINE where \(L\) is the time-delay map NEWLINE\[NEWLINELx_t=\sum_s A_sx(t+\theta_s) +\int_{-r}^0A(\theta)x(t+\theta) d\theta, \quad-r<\theta_l<\dots <\theta_0=0.NEWLINE\]NEWLINE The authors study the inverse problem of the reconstruction of an unknown control \(u(t)\), given the discrete-time measurements of the system's trajectory \(x(t)\). They propose an approach based on the approximation to the functional-differential equation by a system of ordinary differential equations and show that the solving algorithm is stable with respect to noise and computational errors.