Kristi Morgansen
Division of Engineering & Applied Sciences
Harvard University

Stabilization of Strongly Nonlinear Systems with Incomplete Model Information

We take the approach of representing a given unknown nonlinear system as the cascade of a linear time invariant system, a nonholonomic integrator of the appropriate dimension, and a second linear time invariant system. In the case where the linear systems are matrix transformations on the state and control spaces, we identify the system parameters by using a method of regression on the system inputs and the projected areas defined by the inputs. If either of the linear systems contain integrators, the resulting cascade will be second order. The placement of integrators relative to the nonholonomic integrator strongly affects the qualitative properties of the resulting system and consequently the structure of the control methods used. In either of these situations, our main interest is to extend the idea of an approximate inverse to this setting. It has previously been shown that the approximate inverse provides a conceptually clear way to approach tracking and stabilization problems associated with the nonholonomic integrator. The work presented shows that the approximate inverse retains its usefulness in the more complex situations encountered here. As a concrete demonstration of the ideas discussed, we present stabilization and tracking results for the well known``ball-plate'' system when we do not have complete information for the system model parameters.