L1 adaptive control with proportional adaptation law

This paper presents an L₁ adaptive state feedback controller with 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 of the advantages of this new adaptation law is the additional phase margin in the estimation loop, which allows for modification of the state predictor towards accommodating first order sensor dynamics. 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. Simulations verify the theoretical findings.