Robustness of Discrete-time Adaptive Controllers: An Input-Output Approach

This paper presents a general input-output approach that can be used for the design and analysis of robust discrete-time adaptive control schemes. The design approach involves the use of the Certainty Equivalence Principle to combine a robust control structutre with a robust adaptive law. Using exponentially weighted l2 norms and exploiting the properties of the adaptive law and the control structure, robust stability is established for the closed loop adaptive control scheme. For clarity of presentation, only the model reference adaptive control scheme is considered, although the results can be easily extended to other adaptive schemes such as pole placement or linear quadratic. Robustness of discrete-time adaptive controllers has been established in several earlier papers using "conventional" adaptive control techniques. However, the simplicity and elegance of the methodology presented here makes this approach particularly appealing.