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Partial Observer Canonical Form Design Method for Single-output Affine Nonlinear System with Simple Validation Conditions

Haotian Xu and Jingcheng Wang*
International Journal of Control, Automation, and Systems, vol. 20, no. 7, pp.2211-2221, 2022

Abstract : The problem concerning observer error linearization is to find a new state coordinate transformation (diffeomorphism) to transform the underlying nonlinear system into a Partial Observer Canonical Form (POCF). Since the complexity of the existing verification conditions associated with the existence of POCF, this paper develops a two-steps method for calculating POCF to simplify the verification conditions. This method also shows that POCF is equivalent to a compound diffeomorphism that consists of two coordinate transformations. One of them is a diffeomorphism which transforms the system into an observable canonical form based on maximum invariant distribution, and the other one is a diffeomorphism of transforming the observable subsystem into an observer linearization form. With the help of this method, a part of the original conditions are replaced by a group of new conditions that are easier to be verified, and another part of the original conditions are proved to be redundant and could not be verified anymore. At last, three examples are used to demonstrate the validity of this paper.

Keyword : "Diffeomorphism, nonlinear observer, observer error linearization, partial observable canonical form. "

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