Performance Oriented Adaptive Architectures with Guaranteed Bounds

While adaptive control has been used in numerous applications to achieve given system stabilization or command following criteria, the ability to obtain a predictable transient performance is a challenging problem when there is no a priori knowledge about system uncertainties (e.g., their upper bounds and/or domains). In order to address this problem, a new method is presented in [1, 2] utilizing artificial basis functions in the update law of an adaptive control design. This approach is predicated on a gradient minimization procedure and achieves a predictable transient performance without inducing oscillations in the system response as the constant gain due to the nature of this minimization approach is judiciously increased. However, selection of this gain is problem dependent and may need to be adjusted for each different design. To address this problem, we present a new approach which has an ability to auto-tune an adaptive control design with artificial basis functions employed when the controlled system is about to violate a given design constraint on error dynamics (i.e., only when it is necessary). In particular, our approach is based on a controller architecture that allows the assignment of a priori known (user-defined) transient performance bounds. These bounds are constructed through a restricted potential function approach [3] that yields to an error dependent gain to adjust system performance for time instants when it is required to meet given design criteria. In addition to the theoretical results based on Lyapunov stability arguments highlighting transient performance of an uncertain system that stays within a priori given performance bounds, an illustrative example is provided to demonstrate the efficacy of the proposed framework.