New Concepts in Adaptive Control Using Multiple Models

The concept of using multiple models to cope with transients which arise in adaptive systems with large parametric uncertainties was introduced in the 1990s. Both switching between multiple fixed models, and switching and tuning between fixed and adaptive models was proposed, and the stability of the resulting schemes was established. In all cases, the number of models needed is generally large (c
ⁿ
where
n
is the dimension of the parameter vector and
c
an integer), and the models do not “cooperate” in any real sense. In this paper, a new approach is proposed which represents a significant departure from past methods. First, it requires (
n
+1) models (in contrast to
c
ⁿ
) which is significantly smaller, when “
n
” is large. Second, while each of the (
n
+1) models chosen generates an estimate of the plant parameter vector, the new approach provides an estimate which depends on the collective outputs of all the models, and can be viewed as a time-varying convex combination of the estimates. It is then shown that control based on such an estimate results in a stable overall system. Further, arguments are given as to why such a procedure should result in faster convergence of the estimate to the true value of the plant parameter as compared to conventional adaptive controllers, resulting in better performance. Simulation studies are included to practically verify the arguments presented, and demonstrate the improvement in performance.