Adaptive stabilization and disturbance rejection for continuous-time systems

In this dissertation we present adaptive control algorithms for stabilization of nonlinear systems, linear time-varying systems, linear systems in the presence of disturbances, and linear non-minimum-phase systems. We present a state-feedback adaptive controller that renders a class of second-order nonlinear systems Lyapunov stable and guarantees convergence of the output and gains. We then apply the same controller to a class of second-order linear time-varying systems and prove uniform Lyapunov stability of the closed-loop systems as well as convergence of the output and gains. We demonstrate the effectiveness of the algorithm on several example systems.; Next we consider adaptive stabilization of a linear system in the presence of disturbances. Using a discontinuous feedback algorithm we prove uniform stability of the closed-loop system and convergence of the output. We show existence and uniqueness of solutions of the closed-loop system in the sense of Filippov. We use a numerical example to demonstrate the controller, including an example in which we stabilize the longitudinal elevator to angle of attack transfer function of an aircraft.; Finally, we consider adaptive stabilization of non-minimum-phase systems. The plant parameters are required to be bounded with known bounds and the bounds are required to satisfy an inequality constraint. We demonstrate the controller on two example systems.