A Time-Varying System Control Using Implicit Flatness: Case of an Inverted Pendulum

This paper focuses on a fundamental problem related to a characterization of differentially flat nonlinear system in implicit representation. The implicit differential flatness control is a central property for flat nonlinear systems, when the differential equations structure is complex. In this case the state variables and the input control cannot be explicitly expressed as functions of the components of the flat output and a finite number of their derivative. The purpose of this paper is investigated by the study of a tracking problem for a time-varying system which is obtained via the linearization of a nonlinear model around the desired trajectory. The performance study of the developed method is discussed on a non minimum phase model of an inverted pendulum.