Self-organizing approximation-based control for higher order systems

Adaptive approximation-based control typically uses approximators with a predefined set of basis functions. Recently, spatially dependent methods have defined self-organizing approximators where new locally supported basis elements were incorporated when existing basis elements were insufficiently excited. In this paper, performance-dependent self-organizing approximators will be defined. The designer specifies a positive tracking error criteria. The self-organizing approximation-based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification. The method of this paper is applicable to general nth-order input-state feedback linearizable systems. This paper includes a complete stability analysis and a detailed simulation example.