Trajectory stabilization for nonlinear systems using time varying observer-based controller

For trajectory tracking control of general nonlinear systems, the most basic strategy might be applying linear control technique to a linear approximate model around the trajectory. However, it seems that this basic method has not been commonly used. This is because this approximate model becomes a time-varying system, and hence, controller design procedure is not simple. The author proposed the simple design procedure of pole placement controller for linear time-varying systems. Furthermore, we also proposed the observer design method for linear time-varying multi-output systems by applying the pole placement design technique to adjoint systems. In this paper, these design methods will be applied to the trajectory tracking controller design problem for nonlinear systems by stabilizing some desired trajectory around it.