Sufficient conditions for robust performance of adaptive controllers with general uncertainty structure

Abstract

Sufficient conditions are given under which an adaptive control system is robustly stable and achieves a guaranteed robust asymptotic performance level equal to that of the robust controller given perfect parameter information. The conditions are general in several respects. For example, structured non-parametric uncertainty (e.g. block diagonal) is allowed, as well as exogenous noise inputs. In addition, the structure of the parametric uncertainty is very general, and even allows for parameters which scale the uncertainty magnitudes. This allows one to identify the size of the non-parametric uncertainty and to schedule the controller based on this size. Finally, the robust gain scheduled controller is largely unrestricted. Identification mechanisms which are proven to satisfy the sufficient conditions are not given here and, for the general problem, have not yet been developed. However, an example of such a mechanism for a subclass of systems does exist and is referenced. For the general problem, this paper provides properties to be sought in the development of robust identification laws for robust adaptive control.