Discrete-time Robust Adaptive Control using the Lyapunov-SPR Approach

This paper presents a discrete-time robust model reference adaptive control scheme where the robust adaptive law is designed using the Lyapunov-SPR synthesis approach. A crucial ingredient of the SPR design is the definition of a normalized estimation error, which permits the standard robustness analysis of gradient and least squares algorithms to carry over to this design also. However, unlike adaptive schemes derived using least squares or gradient methods, the normalization of the estimation error here is not carried out pointwise in time. Instead, the signal being normalized is the quasi steady-state value of the estimation error. The result bridges the gap, as it were, between the early ideal case discrete-time results obtained using the Lyapunov-SPR Synthesis Approach and the later discrete-time robustness results obtained using the Gradient and Least Squares methods.