Time-varying parameter model reference adaptive control and its application to aircraft

A new Second Order (SO) adaptive control approach, that accounts for both matched and unmatched unknown time-varying uncertainties, is proposed in this paper. It is developed based on the Predictor based Model Reference Adaptive Control (PMRAC) structure. In this approach, the estimated parameter dynamics is composed of a σ-modified PMRAC update law and a predicted parameter dynamics, with projection operator. The predicted parameter dynamics consists of a stable known eigendynamics, a feedback of an approximate parameter error, and the remaining part linearly parameterized by a set of known regressor functions combined with an adaptive estimate of unknown second-order parameters, which are updated by a Lyapunov design. Due to the estimation of time derivatives of the parameters, the proposed predictor based SO-MRAC is hence capable of capturing the rapid parameter variations in system dynamics. Furthermore, a generalized ultimate boundedness formulation based on the Lyapunov theory is presented for its stability analysis. This formulation provides separate bounds for each of the state vector partitions, mainly tracking and parameter estimation errors. Finally, this proposed approach is applied to control of lateral dynamics of an unmanned aircraft to illustrate the usefulness of the proposed approach. The simulation results are found to be quite satisfactory both in terms of tracking and adaptation performance.