Least Squares Approximate Feedback Linearization

Andrzej Banaszuk, Georgia Tech

We present the least squares approximate feedback linearization problem: given a single input nonlinear system, find a linearizable nonlinear system that is close to the given system in a least squares sense over a given (possibly large) region of state space. A generalization of this approach will allow approximation of nonlinear systems by linearizable ones in higher order Sobolev spaces, and thus (via Sobolev embeddings), in uniform sense. The approach uses least squares integrating factors that make a fixed characteristic one-form of the system close to being exact in an L2 sense and the Hodge decomposition to approximate the scaled characteristic by an exact form in L2.