Approximate I/O-Linearization of Nonlinear Systems

Nonlinear controller design by exact input-output linearization (I/O-linearization) has become a popular approach for controlling nonlinear systems during the past decade. In contrast to the common Jacobi-linearization approach, where higher order terms in the Taylor series are just neglected, these nonlinear terms of higher order are exactly compensated in the I/O-linearization approach and no approximation error is made. Hence, I/O-linearized dynamical systems exhibit exactly linear I/O behavior. Subsequently to the I/O-linearization step a linear controller can be designed for this exactly linear system to achieve the desired performance using the well-developed methods of linear control theory. Only the first step, namely the I/O-linearization, requires a large design effort. However, this step has to be performed only once for a given plant. Necessary design iterations for achieving satisfactory performance and a satisfying compromise between conflicting design specifications can then be dealt with exclusively in the second, linear step, where these iterations can be performed efficiently and without significant cost. For a summary on a one-step design using I/O-linearization see the papers of Kravaris in this volume.