The approximation of reachable domains of control systems (Q2714652)

The authors study the controlled system NEWLINE\[NEWLINE \frac{dx}{dt} = f(t,x,u),\quad u\in P,\quad t\in I,\quad I=[t_0,\vartheta], \quad t_0<\vartheta<\infty,\tag{1} NEWLINE\]NEWLINE \(x\in \mathbb{R}^m\), \(P\) is a compact set in \(\mathbb{R}^n\).NEWLINENEWLINENEWLINEIt is proposed to generate an approximate construction of the reachable sets of system (1) by dividing the phase space of the system into an \(\varepsilon\)-lattice. The preciseness estimates are presented for the approximate calculations of the reachable sets and an example of a second order system is considered.