Performance-based Self-organizing Approximation for Scalar State Estimation and Control

Adaptive approximation based control typically uses approximators with predefined basis functions. Recently, self-organizing approximators have been introduced that define the basis set during system operation. In exploration dependent self-organization methods, new locally supported basis elements were defined when existing basis elements were insufficiently excited. More recently, performance dependent self-organizing approximators were introduced that only define new basis elements when necessary to achieve a prespecified performance objective. Herein, a new performance dependent self-organizing approach is developed. A positive tracking error criteria and controller bandwidth are specified, the state estimator monitors the state estimation performance and adds basis elements only as needed to achieve a derived state estimation error specification. The controller designed based on the state estimator model is shown to achieve the tracking specifications.