Identification and Control of a Nonlinear Dynamical System Based on its Linearization: Part II

In Part II of this paper, the identification and control problems of a nonlinear dynamical system are considered in a simplified framework. First it is shown that when the linearized system is observable, the state vector of the nonlinear system can be reconstructed from the input and the output together with their past values. This establishes the existence of solutions to regulation problems using only the input and the output. If the linearized system has a relative degree and asymptotically stable zero dynamics, under certain conditions, the nonlinear system also has a well-defined relative degree and asymptotically stable zero dynamics. In such a case, an input-output representation (the NARMA model) can be obtained in which the output is affected by the input through linear terms no later than through nonlinear terms, and by using the Implicit Function Theorem, the existence of a control law can be established such that the output follows any given reference trajectory in a neighborhood of the origin.