This thesis introduces two new extensions to L1 adaptive control theory. The first is an L1 adaptive state feedback controller with generalized proportional adaptation law for a class of linear systems with input–gain uncertainties and unmatched nonlinear disturbances. The proportional adaptation law provides an adaptive estimate that is directly proportional to the error between the output of the system and the state predictor. One advantage of the new adaptive law is the additional phase margin in the estimation loop, allowing for accommodation of first order sensor dynamics in the state predictor. An additional benefit is the reduction of the required computational resources, since the error bounds reduce at a rate directly proportional to the adaptation gain as compared to the square root of the adaptation gain achieved by the L1 adaptive controllers using gradient descent adaptation laws. In addition, an L1 adaptive funnel controller and variable dependent adaptation law are provided as particular cases for the generalized proportional framework. Also presented is the connection between the generalized proportional feedback law and previous L1 switching controller. The second extension is an L1 adaptive controller for a class of uncertain systems in the presence of time and output dependent unknown nonlinearities and uncertain input matrix with performance specifications defined via a time–varying reference system using output feedback. It is shown that both extensions exhibit the standard characteristics of the L1 adaptive control theory: scaling of transient responses, a guaranteed time–delay margin at high adaptation rates, and the trade off between robustness and performance is determined by the design of a low pass filter
