Controllability and reachability sets of nonlinear control systems (Q760362)

Reachability and controllability problems for control systems of the form \((*)\quad y^{(n)}+f(y,...,y^{(n-1)})=g(y,...,y^{(n-1)})u\) are considered. The evolution curve \((y(t),...,y^{(n-1)}(t))\) is assumed to lie in a given constraint set. It is shown that if \(g\neq 0\), then reachability along solutions of (*) is equivalent to reachability along curves with piecewise-continuous n-th derivative. The possibility of reducing a general system to the form (*) is discussed.