Damping of a system of linear oscillators using the generalized dry friction (Q338031)

The authors consider a control system consisting of \(N\) linear oscillators under the common control: \[ \begin{aligned} \dot x_i & = y_i, \\ \dot y_i & = \omega^2_i x_i + u, \, |u| \leq 1, \, i=1,\dots,N. \end{aligned} \] Here, \(\omega_i\) stands for intrinsic frequency of the oscillator \(i\) and \(u\) is scalar control (common for all oscillators). The problem discussed in the paper is damping the oscillators in minimal time. The authors investigate controls in the form of dry friction, leading to a system of differential equations with discontinuous right hand sides.