Date of Award
Summer 2012
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Electrical and Computer Engineering
First Advisor
Yaz, Edwin E.
Second Advisor
Schneider, Susan C.
Third Advisor
Merrill, Stephen J.
Abstract
This dissertation addresses the mixed criteria finite-time bounded controller and observer design of certain classes of nonlinear systems. Finite-time bounded controllers and observers are used to guarantee performance bounds on the transient response of the systems considered. A robust and resilient mixed criteria state-feedback controller design is developed for a class of nonlinear systems with conic-type nonlinearities lying within a hypersphere of uncertain center, additive disturbances, and controller gain perturbations in discrete and continuous-time. Furthermore, a robust and resilient mixed criteria state-dependent state-feedback controller design is developed for a class of nonlinear systems with state dependent system matrices and state-dependent additive bounded perturbations in the discrete- and continuous-time case. For both classes of systems, the controller satisfies the finite-time boundedness and H∞ properties, and thus maintains the state of the system within a prescribed bound over the finite-time interval while attenuating the energy of additive disturbances over the infinite horizon. In addition to the controller problem, a finite-time bounded Luenberger observer design is developed for a class of discrete-time nonlinear systems with nonlinear measurements. The observer is developed for the purpose of maintaining the estimation error within a prescribed bound over a fixed and finite interval of time. Moreover, the observer is robust for all additive vanishing nonlinear perturbations and disturbances in the system model and the measurement equation and resilient against perturbations in its gain. For both design problems, conditions guaranteeing the existence of a controller and an observer with the desired performances are derived based on quadratic Lyapunov energy functions. A solution for the observer and controller gains and the bounds on the corresponding maximum allowable gain perturbations is obtained using linear matrix inequality techniques. For the class of nonlinear systems with state-dependent system matrices, a set of state-dependent linear matrix inequalities, which are solved at each instant of time, are used for this purpose. Chua’s circuit and the system of a simple pendulum are used as numerical examples, and simulation results show the significance and applicability of the proposed design approaches.