Complete Parametric Solutions to the Fundamental Problem in High-order Fully Actuated System Approach

The high-order fully actuated system (HOFAS) approach has recently been proposed, aiming at establishing a unified architecture for control of general nonlinear systems. Its core idea is to firstly obtain a HOFAS model for a dynamical system, and then to cancel the nonlinearity using the full-actuation property. Based on this, the control problem of both linear and many types of nonlinear systems is finally turned into a specific eigenstructure assignment problem of a particular matrix pair. Because of this, the specific eigenstructure assignment problem is considered as the fundamental problem of the HOFAS approach, and is investigated in detail in this paper. A general parametric solution is established in an iterative form with all the degrees of freedom provided, and special solutions for some commonly used cases are also given. These form a database for various design problems and provide some ready-to-use results. Finally, illustrative examples demonstrate the usage of the database.