We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control.

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.

We present a novel approach to adaptation of nonlinear multi-input multi-output (MIMO) systems, in the existence of parametric uncertainties. We use feedback linearization to provide a stabilizing Model Reference Control (MRC). Next, we estimate the unknown parameters of the system, by optimizing a cost function based on the tracking error from MRC. We use extremum seeking (ES) to optimize the cost function.

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