An adaptive control design for 3D curve tracking based on robust forward invariance

We study a class of adaptive controllers for three dimensional (3D) curve tracking under control uncertainty and unknown control gains. Using robust forward invariance and a Lyapunov-Krasovskii functional, we prove input-to-state stable tracking and parameter identification under input delays and a class of polygonal state constraints. This yields predictable tolerance and safety bounds, and compensation of arbitrarily long input delays in the important case where the delays only occur in the speed measurements in the controls.