Optimal control based tracking error estimation for model reference adaptive control

The present paper is concerned with the approximation of the maximum tracking errors for Model Reference Adaptive Controllers (MRAC). Especially for the use in safety critical contexts such as aerospace applications the quantification of this error is of utmost importance. As MRAC is particularly suited for highly uncertain plants, these uncertainties and, additionally, worst case command inputs are the main driving factors for tracking errors. We propose a novel approach based on the Distance Field on Grids (DFOG) method to estimate those tracking errors by approximating the outer boundary of the reachable set in the error state subspace. This approach extends upon the idea of the DFOG method and solves optimal control problems for the boundary of an appropriate grid in the state space of interest. Thus it is possible to obtain an approximation of the outer boundary of the reachable set and provide for an estimate of the maximum tracking errors with respect to parametric uncertainties and worst case continuous inputs. Its application is illustrated using a short period approximation of the F16 fighter aircraft which is controlled by an adaptive controller. Concluding, the numerical results are compared to a conservative analytical solution derived from Lyapunov stability theory.