Optimal evasion of a dynamic object from spherical obstacle (Q859364)

The authors consider the motion of a mass point in the \(n\)-dimensional Euclidean space, \(n \geq 1\), under the action of a limited value control force \(F\). \[ \begin{aligned} m\frac{d^2x}{dt^2} & = F,\\ | F| \leq F_0, x(0) &= 0,\\ \frac{dx}{dt}(0)& = v^0,\\ S_R^n &= {x : | x - x_0| \leq R}, x^0 \notin S_R^n. (| x^0 - x_0| >R).\end{aligned} \] The problem is to evade collision with a non-penetrable sphere of arbitrary center position \(x_0\) and radius \(R\), i.e. \(| x(t) - x_0| > R, t > 0.\)