Adaptive Systems: History, Techniques, Problems, and Perspectives

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

ES-MRAC: A new paradigm for adaptive control, theory and applications

In this dissertation, we develop a method for the model reference adaptive control (MRAC) of systems via Extremum Seeking (ES), where extremum seeking is used as a means of estimating parameters in adaptive control. This provides a new approach to adaptive control that unifies real time optimization with adaptive control, thereby giving the designer far greater freedom in the choice of both cost functions and controller structure. Furthermore, conditions for persistency of excitation (PE) are explicit in our adaptive system. This renders the possibility of providing explicit and predictable rates for convergence of parameters, when the PE conditions are satisfied. Finally, our method provides a unified approach to adaptation that can be applied to many linear and nonlinear system structures, without having to modify the adaptation scheme. We show that our control/adaptation framework is extendable to a large class of nonlinear systems including adaptive backstepping and feedback linearization. As applications of our method, we apply it to the control of a two input, two output nonlinear model of a hypersonic vehicle in longitudinal plane, and the control of a rotary hydraulic crane with an underactuated mode. This dissertation opens up many interesting theoretical and practical problems to be addressed. A study on the noise rejection properties, the use of damped sinusoidal perturbations and stochastic perturbations in ES loops are just a few to name