Carleman Linearization for Control and for State and Disturbance Estimation of Nonlinear Dynamical Processes

In this paper, techniques based on Carleman linearization are presented which are applicable to the design of controllers and state estimators for nonlinear dynamical systems. Originally, Carleman linearization has been developed to transform sets of polynomial ordinary differential equations into infinite dimensional linear system representations. After choosing suitable finite orders for truncation of Carleman linearization, finite dimensional linear and bilinear system representations are obtained for which the design of controllers and state estimators can be performed in a straightforward way. To visualize the practical applicability of the presented procedures, state as well as disturbance estimation for a linear axis driven by pneumatic muscle actuators is studied.