Self-organizing approximation for controllable nonaffine systems

Adaptive nonlinear control methods for controllable nonaffine systems typically use approximators with predefined basis functions, which require significant on-line computation and memory for applications with high state dimensions. In order to address this issue, self-organizing approximators have been introduced that define the basis set during system operation. All existing self-organizing results in the literature are trajectory-based in the sense that new locally supported basis elements were defined along the trajectory when existing basis elements were insufficiently excited. Recently, performance dependent self-organizing approximators were introduced that only define new basis elements when necessary to achieve a prespecified performance objective. In this article, the self-organizing approach uses a state estimator, which monitors the state estimation performance and adds basis elements only as needed to achieve a prespecified state estimation error specification. The dynamic inversion control approach applied to the approximation-based state estimator is shown to achieve bounded tracking errors determined by the designer´s specification.