Abstract
The theory of implicit models, introduced in previous papers, is used here in order to define a new adaptive control algorithm based on either m-step-ahead or infinite horizon LQ optimization and on recursive least squares identification techniques in the presence of systems having an ARMAX structure. The adaptive algorithm is based on the identification of a single ARX implicit model, which is defined as a model capable of representing the system input-output behaviour correctly only in certain closed-loop conditions. It is shown that, by properly structuring the algorithm, a single whitening (i.e. yielding a white residual sequence) possible convergence point exists coinciding with the optimal control law. Simple conditions assuring that a generic convergence point coincides with the above one are also provided, as well as preliminary simulation experience.
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