A safe learning model reference adaptive controller for uncertain aircrafts models

In this paper, it is presented an approach for the design of a feedback Model Reference Adaptive Controller (MRAC) for uncertain linear systems with guaranteed evolution of the closed-loop error trajectories within a computable robust invariant set. The estimation of the UUB region has been derived exploiting robust quadratic stability arguments assuming bounded uncertainty on the state and input matrix as long as amplitude constrained adaptive control. In the scheme, a linear output feedback controller is augmented with an amplitude bounded adaptive control to improve the performance in the presence of significant modeling uncertainties. The robust invariant set design was performed solving a constrained convex optimization problem. The method allows the analysis of the joint effect of the modeling uncertainties and the adaptive control amplitude on the size of the UUB region, thus allowing the design of a safe MRAC scheme. An additional benefit is that no specific parameter adaptation algorithm is required, as long as the adaptive control output is confined within the predefined limits. For enforcing this confinement, the mechanism of adaptive control redistribution is introduced. A detailed simulation study was performed using the short period longitudinal dynamics of an F16 model to show the design steps and to highlight the benefits of the methodology.