LDV approach to circular trajectory tracking of the underactuated hovercraft model

This paper shows that circular trajectory tracking of an underactuated hovercraft vehicle can be achieved by linear dynamically varying (LDV) techniques. LDV control is a technique for directing a controlled trajectory to be asymptotically synchronized with a preselected trajectory. A linearized tracking error model is obtained as a linear system parameterized by the nominal nonlinear dynamics. The nontrivial part of the LDV theory is to prove existence of a sufficiently well behaved solution to the partial differential Riccati equation. This in turn provides an exact solution to a Lyapunov inequality, showing that the underactuated hovercraft can be stabilized around the circular trajectory