Jay A. Farrell, University of California, Riverside

Abstract: Nonlinear dynamics and model uncertainty exist in all physical plants and must be addressed directly by the control system when a high level of performance is desired. This workshop will discuss self-organizing adaptive approximation based control algorithms designed to achieve stability and accurate reference input tracking for nonlinear systems with modeling uncertainty. Within this context the workshop will distinguish between adaptation, learning, and self-organization. It will also discuss how the objective of learning can be achieved by implementing approximations to unknown functions within the model or controller during on-line operation.

Typical adaptive approximation based controllers use approximators with a predefined set of basis functions. The designer must therefore over design the approximator structure to guarantee that desired approximation accuracy is achievable for the unknown nonlinearities. Self-organizing approximation based control defines and adapts both the approximator structure and its parameters during on-line operation. This offers the potential for increased performance with fewer computational resources. This workshop will review previously existing trajectory exploration dependent self-organizing approximators where new locally supported basis elements were incorporated when existing basis elements are insufficiently excited. These methods are open-loop in the sense that augmentation of the approximation structure is not dependent on the performance of the closed-loop control system.

The workshop will also present a novel performance-dependent self-organizing approximator approach that has been recently developed. The designer specifies a positive performance criterion. In the self-organizing approach, the structure of the function approximator is defined by the control system during operation. New approximator resources are allocated as necessary to achieve the performance specification. For high dimensional systems, the decrease in the approximator resources allocated via performance-dependent self-organization, relative to prior allocation over the entire operation region, may be significant enough to enable more applications.