Dynamic Observer of General Nonlinear Control Systems

Abstract

The d-restricted dynamic observer error linearization (RDOEL) problem of the general nonlinear control system is to find a restricted auxiliary dynamic system of dimension d such that the extended control system is state equivalent to a nonlinear observer canonical form. The autonomous version of the RDOEL problem can be found in the literature. In this paper, the vector fields are defined with parameter u and geometric necessary and sufficient conditions for RDOEL problem of the general (i.e. non-affine) nonlinear system are given. Our conditions with d = 0 also give the geometric necessary and sufficient conditions for the state equivalence of a general nonlinear control system to a nonlinear observer canonical form (NOCF) with output transformation (OT). Since our proofs are constructive, an extended state transformation can be found in the theorems. The conditions are simple and thus can be implemented by a MATLAB program.