On the extremum seeking of model reference adaptive control in higher-dimensional systems

We develop a method for the model reference adaptive control (MRAC) of first order systems via extremum seeking. We show, in special cases in which there exists a partial knowledge of parameter values, proofs of global and exponential convergence of both the tracking and parameter tracking errors. We then extend the proposed method from first order systems to linear systems of any higher dimensions. We prove that our method has similar properties as MRAC. Results are partially illustrated through simulations of a simplified roll rate model of a fixed wing aircraft.