Controllability

Let n and m be two positive integers. In this chapter we consider a control system in \(\mathbb {R}^n\) \(\displaystyle {} \dot {x}(t) = f(t,x(t),u(t)) \) where \(f:\mathbb {R}\times \mathbb {R}^n\times \mathbb {R}^m\rightarrow \mathbb {R}^n\) is of class \(C^1\) with respect to \((x,u)\) and locally integrable with respect to t, and the controls are measurable essentially bounded functions of time taking their values in some measurable subset \(\Omega \) of \(\mathbb {R}^m\) (set of control constraints).