Adaptive Control based on Explicit Criterion Minimization

Sammanfattning: A common approach to regulator design is to define an objective function, which is minimized with respect to adjustable regulator parameters. Here we discuss how such objective functions can be minimized online, thus providingadaptive eon tro I. Such an approach has its roots in early contributions to learning systems and it is here further developed and discussed in the light of the recent development in the field.A general algorithm is given and it is then specialized to some concrete examples. One problem when to use this algorithm is that the convergence properties are tied to successful identification of the system dynamics. Therefore an Instrumental Variable identification method based on extra injected noise is analysed and convergence is proved under a boundedness assumption.Special attention is paid to the minimization of quadratic criteria. It is shown that if the regulator is flexible enough the minimum of such a criterion is unique. It is also shown that the self tuning regulator is obtained as a special case of the algorithm, corresponding toa particular quadratic criterion anda particular way of estimating the system dynamics.One specific feature of the algorithm is that it does not utilize specific knowledge about how to calculate the optimal regulator. The algorithm is thus the same for minimum phase as well as for non minimum phase systems.