| With the emergence of various systematic design tools for nonlinear and adaptive control systems, notably the integrator backstepping, nonlinear damping, and tuning functions and modular design techniques, new classes of adaptive controllers are proposed for linear and nonlinear systems. These controllers deviate from the traditional polynomial and certainty equivalence based ones and are usually highly nonlinear regardless of the linearity of the plant. For linear time invariant systems without modeling errors, these new controllers not only retain the desired asymptotic properties, but also achieve significantly improved transient performance superior to that of the traditional ones. However, the high nonlinearity of the controllers poses other issues, the most outstanding one being their robustness with respect to modeling uncertainties. This dissertation takes global boundedness as the goal for robustness of the controllers, and attempts to analyze and solve the robustness problem. It is shown that the new controllers may exhibit instability even if the modeling uncertainties are relatively small, and modification methods for the controller design are suggested to overcome these difficulties. New robustification tools, including smooth {dollar}sigma{dollar}-modification and several normalization schemes, as well as new tools for analysis are developed in achieving these goals. The role of persistent excitation in performance is also analyzed in the dissertation. Finally, a robustness analysis of a general nonlinear control system is presented in the form of a first order example, showing the necessary and sufficient conditions on the plant or control law nonlinearities for achieving robustness with respect to high frequency unmodeled dynamics in the global sense. |
