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Friday, March 26, 1999, 3:00 p.m.
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.

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