Local Controllability of Single-Input Nonlinear Systems Based on Deterministic Wiener Processes

This technical note proposes a new sufficient condition for local controllability of nonlinear control systems ensured by single inputs. The objective is achieved by allowing control inputs to have the limitation of the derivation of unbounded-variation functions as with white noises, provided that we just consider deterministic signals. The treatment of the signals is mathematically recognized via rough path analysis, and then the dynamics of the target systems are represented by rough differential equations as the extension of ordinary differential equations. Our sufficient condition is clarified by deterministic Wiener processes that produce an effect on the dynamics of the systems similar to Wiener processes despite the nonprobabilistic property. The novelty of our condition is confirmed by a single-input two-link underactuated robot arm moving on the horizontal plane.