Singular stratified manifolds of involutive controlled systems (Q1874755)

Using the rather abstract setting of differential 1-forms, the authors obtain in Theorem 6 some characterizations of the optimal feedback control (``synthesis'', in their terminology) of the minimal-time problem for systems of the form: \[ \dot x=\sum_1^nu^i(t)\varphi_i(x), \;x(0)=a\in \mathbb R^n, \;x(T)=b\in W_{1\dots n}, \] \[ u(t)\in U:=\left\{u\in \mathbb R^n; \;\sum_1^n u^i=1, \;u^i\geq 0\right\}, \;t\in [0,T], \] in the case the set of smooth vector fields \(\{\varphi_1(\cdot),\dots ,\varphi_n(\cdot) \}\) is such that ``the distribution induced by any of its subsets'' is integrable. The authors are using, rather loosely, a large number of their previous concepts and results on this topic.