Time varying parameters in adaptive control: a review and a preview

The author notes that there seem to be four basic issues in adaptive control in the presence of VPs (time-varying parameters): how to choose a control law; what the stability or boundedness properties of the resulting closed-loop system are; what robustness properties it has; and what the system performance is. He briefly reviews the literature with an eye on these issues and then looks at future prospects by giving some new performance calculations in a simple setting. A procedure is outlined for answering the question of how to calculate the performance of PCE (pseudo certainty equivalent) adaptive controllers in the presence of VPs. Until these calculations are made it will not be clear whether so-called dual controllers obtained by a perturbation computation will be able to outperform PCE adaptive controllers. The construction of perturbed Lyapunov functions, needed for showing stochastic boundedness, draws on Lyapunov computations made in a deterministic setting. Even in a noise-free setting, DACs (deterministic adaptive controls) will have invariant measures that can be computed by the methods indicated