Reducing Overparametrization in MRAC for Hyperbolic PDEs

We construct a method of dealing with the problem of overparameterization in model reference adaptive control (MRAC) of $2 \times 2$ linear hyperbolic partial differential equations (PDEs). The method is based on linear interpolation of the uncertain parameters. The proposed method is demonstrated in simulations of the fluid mechanics of a drilling system, and compared to a previously derived, overparameterized MRAC scheme, showing improved tracking and convergence properties.