Lyapunov-based robust and adaptive control of nonlinear systems using a novel feedback structure

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy LYAPUNOV-BASED ROBUST AND ADAPTIVE CONTROL OF NONLINEAR SYSTEMS USING A NOVEL FEEDBACK STRUCTURE By Parag Patre August 2009 Chair: Warren E. Dixon Major: Mechanical Engineering The focus of this research is an examination of the interplay between different intelligent feedforward mechanisms with a recently developed continuous robust feedback mechanism, coined Robust Integral of the Sign of the Error (RISE), to yield asymptotic tracking in the presence of generic disturbances. This result solves a decades long open problem of how to obtain asymptotic stability of nonlinear systems with general sufficiently smooth disturbances with a continuous control method. Further, it is shown that the developed technique can be fused with other feedforward methods such as function approximation and adaptive control methods. The addition of feedforward elements adds system knowledge in the control structure, which heuristically, yields better performance and reduces control effort. This heuristic notion is supported by experimental results in this research. One key element in the development of the novel feedforward mechanisms presented in this dissertation is the modularity between the controller and update law. This modularity provides flexibility in the selection of different update laws that could be easier to implement or help to achieve faster parameter convergence and better tracking performance. The efficacy of the feedforward mechanisms is further enhanced by including a prediction error in the learning process. The prediction error, which directly relates to