Computational methods for the exact linearization and observer linearization problems for nonlinear systems

We have a multidimensional dynamic system described by a nonlinear function with a control input, a measured output, and added measurement noise. We want to control the measurement to a constant, called stabilization control, or to a reference signal, called tracking control, such that the error asymptotically approaches zero while keeping all the closed-loop signals bounded. The concentration is on single-input, single-output nonlinear systems. The solutions to the problem use the techniques of exact linearization and observer linearization. The exact linearization technique uses feedback linearization to algebraically transform the nonlinear system's dynamics into linear dynamics via an exact state transformation. The solution to the observer linearization problem is to use a nonlinear state transformation and design an observer with prescribed eigenvalues such that the observation error is linear and spectrally assignable. The solutions to the problem are expanded to include situations where there are some uncertainties about the functional description of the nonlinear system because of unknown system parameters. The problems arising out of these uncertainties are addressed by an algorithm that adapts system parameters to effect the best control solution.; The dissertation provides a systematic and detailed presentation of exact linearization and observer linearization as well as algorithmic implementations for exact linearization and observer linearization. Also included is the algorithmic development for adaptive parameters in the case where system parameters are unknown, and the development of Matlab and MapleV applications that provide the symbolic and numerical computational support for the algorithmic solutions. All algorithms are executed on four example systems with both types of control, stabilization and tracking. The dissertation includes results that indicate how all developed algorithms will behave in the presence of limited measurement noise.