Tracking control of an underactuated ship by modified dynamic inversion

The tracking control problem of an underactuated ship is investigated. We intend to use the underactuated ship as an example to extend the traditional dynamic inversion control method to underactuated systems. The difficulty lies in the fact that the system has no relative degree, which prevents the application of standard dynamic inversion. Three modified dynamic inversion methods are proposed that are applicable to this system. The first is the well-known dynamic extension-based dynamic inversion (DEDI), which treats an input as a state and takes dynamic extension to achieve a relative degree. The second is virtual input-based dynamic inversion (VIDI), which treats a state as a virtual input to achieve a relative degree. The third is output redefinition-based dynamic inversion (ORDI), which selects a particular variable as a new output to achieve a relative degree. The three methods are generalizations of dynamic inversion control and remove some of its inherent limitations, making it applicable to a wide variety of underactuated systems. The effectiveness of the proposed methods is verified by numerical simulations.