Adaptive stabilization and disturbance rejection for linear systems and Hammerstein systems

In this dissertation we present control algorithms for stabilization and asymptotic disturbance rejection for Linear Systems and Hammerstein systems with positive-real linear dynamics. We present the novel idea of Lyapunov wells, which are scalar positive-valued continuously differentiable functions defined on open intervals on the real line. We introduce this concept with applications to plants that have a control input, a state or a parameter constrained to operate within an interval. Next, we consider the problem of adaptive stabilization of second-order minimum phase systems subjected to exogenous plant and measurement disturbances. This case is of particular interest as it has been shown that, in presence of exogenous disturbances several direct adaptive control schemes for minimum phase plants with relative degree 1 exhibit parameter divergence eventually leading to instability. The proof of convergence is based on a variation of Lyapunov's method in which the Lyapunov derivative is shown to be asymptotically nonpositive. Next, The technique of Lyapunov wells and the nonlinear controllers developed for Hammerstein systems are used to design control systems for electromagnetic oscillators which guarantee that the oscillator mass and the electromagnetic plates never make contact. We provide extensive numerical results for each theoretical result presented. The second part of the thesis develops an indirect extension of the ARMARKOV adaptive control algorithm with simultaneous identification. This algorithm requires a model of only the secondary path (control input to performance variable) transfer function which is identified on-line using the time-domain ARMARKOV/Toeplitz identification technique. For a 5-mode acoustic duct model, we present numerical as well as experimental results for single-tone, dual-tone, and broadband disturbance rejection.