Abstract
A method for designing a nonlinear state regulator is presented. The method consists of the following steps: (1) finding a fictitious linear system which is homeomorphic to a given nonlinear plant, (2) designing an optimal state regulator for the above linear system, and (3) constructing the nonlinear state regulator having the same topological structure as the above designed optimal state regulator. Control laws are derived in terms of the homeomorphism.
To describe the homeomorphism, a Riemannian geometric model, based on the idea that in the state space a nonlinear system referred to appropriate curvilinear coordinates will behave as a linear system, is developed. Equations which determine the curvilinear coordinate system are also derived.
Numerical examples are given to demonstrate the usefulness of the method.
