Local controllability of control systems with feedback
We prove sufficient conditions for the instantaneous local controllability of nonlinear (nonsmooth) control systems with feedback. We introduce for that purpose the high-order variation of the reachable map, which is related strongly to its shape. It is a direction in which the reachable map evolves. The cone of variations is convex. This allows one to prove the following theorem: if there exist variations \(v_ 1\),..., \(v_ p\) such that \(\theta\) \(\in int co\{v_ 1,...,v_ p\}\), then the system is small-time locally controllable at the point of equilibrium. We provide a short proof of the main result due to \textit{H. Sussmann} [see, e.g., SIAM J. Control Optimization 16, 790-802 (1978; Zbl 0391.93004)] and extend it to differential inclusions.
differential calculus of set-valued maps
scientific article; zbMATH DE number 4031491
scientific article