Investigating Noise Rejection with Gradient-Based Update Laws in Discrete-Time Adaptive Control

This paper investigates discrete-time adaptive control of time-invariant feedback-linearizable plants whose states are accessible in the presence of noise. A state-space representation is adopted rather than a standard input-output one. It is shown that boundedness can be guaranteed using an error model approach that was proposed in [1]. An augmented error is utilized to derive useful properties of the state error, and boundedness of all states is established using first principles of real analysis. Simulation results show that the steady-state value of the augmented error is reduced in a high-order tuner compared to a first-order adaptive law, and that the reverse is surprisingly true for the steady-state value of the state error, motivating future work on the convergence properties of discrete-time high-order tuners.